├── Itspoint.m ├── Novel Coplanar Line-points Invariants for Robust Line Matching Across Views.pdf ├── README.md ├── TestLMDll ├── Debug │ ├── LineMatcher.dll │ ├── TestLMDll.exe │ ├── TestLMDll.ilk │ ├── TestLMDll.pdb │ ├── TestLMDll.suo │ ├── opencv_calib3d220.dll │ └── opencv_calib3d220d.dll ├── README ├── Release │ ├── LineMatcher.dll │ ├── TestLMDll.exe │ ├── TestLMDll.pdb │ ├── TestLMDll.suo │ ├── opencv_calib3d220.dll │ ├── opencv_core220.dll │ ├── opencv_features2d220.dll │ ├── opencv_flann220.dll │ ├── opencv_highgui220.dll │ ├── opencv_imgproc220.dll │ ├── test.exe │ └── test.pdb ├── TestLMDll.sdf ├── TestLMDll.sln ├── TestLMDll.suo └── TestLMDll │ ├── Debug │ ├── CL.read.1.tlog │ ├── CL.write.1.tlog │ ├── TestLMDll.exe.embed.manifest │ ├── TestLMDll.exe.embed.manifest.res │ ├── TestLMDll.exe.intermediate.manifest │ ├── TestLMDll.lastbuildstate │ ├── TestLMDll_manifest.rc │ ├── cl.command.1.tlog │ ├── link-cvtres.read.1.tlog │ ├── link-cvtres.write.1.tlog │ ├── link.2928-cvtres.read.1.tlog │ ├── link.2928-cvtres.write.1.tlog │ ├── link.2928.read.1.tlog │ ├── link.2928.write.1.tlog │ ├── link.command.1.tlog │ ├── link.read.1.tlog │ ├── link.write.1.tlog │ ├── lsd.obj │ ├── main.obj │ ├── mt.command.1.tlog │ ├── mt.read.1.tlog │ ├── mt.write.1.tlog │ ├── rc.command.1.tlog │ ├── rc.read.1.tlog │ ├── rc.write.1.tlog │ ├── vc100.idb │ └── vc100.pdb │ ├── LineMatcher.h │ ├── LineMatcher.lib │ ├── Release │ ├── CL.read.1.tlog │ ├── CL.write.1.tlog │ ├── TestLMDll.Build.CppClean.log │ ├── TestLMDll.exe.intermediate.manifest │ ├── TestLMDll.lastbuildstate │ ├── TestLMDll.log │ ├── TestLMDll.vcxprojResolveAssemblyReference.cache │ ├── TestLMDll.write.1.tlog │ ├── cl.command.1.tlog │ ├── link.command.1.tlog │ ├── link.read.1.tlog │ ├── link.write.1.tlog │ ├── lsd.obj │ ├── main.obj │ ├── mt.command.1.tlog │ ├── mt.read.1.tlog │ ├── mt.read.2.tlog │ ├── mt.write.1.tlog │ └── vc100.pdb │ ├── TestLMDll.vcxproj │ ├── TestLMDll.vcxproj.filters │ ├── TestLMDll.vcxproj.user │ ├── lsd.c │ ├── lsd.h │ └── main.cpp ├── addpointsnearby.m ├── charanums5.m ├── crossproduct.m ├── distline.p ├── getHpoints1L.m ├── getgoodpair.m ├── getpoints.m ├── imgs ├── 1_A.jpg └── 1_B.jpg ├── intspoints.m ├── linegradient.m ├── linematch.m ├── paras.m ├── projline.m ├── pts&lines ├── 1ABpoint.txt ├── 1Aline.txt └── 1Bline.txt └── sameside.m /Itspoint.m: -------------------------------------------------------------------------------- 1 | 2 | function [X, Y]=Itspoint(line1,line2) 3 | 4 | k1=line1.k; 5 | k2=line2.k; 6 | b1=line1.b; 7 | b2=line2.b; 8 | X=NaN; 9 | Y=NaN; 10 | if k1==k2 11 | %do nothing 12 | elseif k1~=Inf && k2~=Inf 13 | if abs(atan((k2 - k1)/(1+ k1*k2)))> 3.14/8 14 | X=(b2-b1)/(k1-k2); 15 | Y=k1*X+b1; 16 | end 17 | 18 | elseif k1==Inf 19 | if k2>2.4142 || k2<- 2.4142 20 | else 21 | X=line1.point1(1); 22 | Y=k2*X+b2; 23 | end 24 | elseif k2==Inf 25 | if k1>2.4142 || k1<- 2.4142 26 | else 27 | X=line2.point1(1); 28 | Y=k1*X+b1; 29 | end 30 | end 31 | 32 | end 33 | 34 | -------------------------------------------------------------------------------- /Novel Coplanar Line-points Invariants for Robust Line Matching Across Views.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/dlut-dimt/LineMatching/e05eb15c06303d724b9334f96ab2c6deb723deb2/Novel Coplanar Line-points Invariants for Robust Line Matching Across Views.pdf -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | This package includes the source codes for "Novel Coplanar Line-points Invariants for Robust Line Matching Across Views". 2 | 3 | To run the program, please: 4 | 5 | 1.Run 'TestLMDll' with Microsoft Visual Studio 2010 to get lines detected by LSD and points matched by SIFT. 6 | 7 | 2.Put the images into directory 'img' , and put the files of matched points and detected lines into directory 'pts&lines'. 8 | 9 | 3.Run linematch (linematch.m) in MATLAB. 10 | 11 | Some of the paths need to be changed. 12 | 13 | 14 | -------------------------------------------------------------------------------- /TestLMDll/Debug/LineMatcher.dll: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/dlut-dimt/LineMatching/e05eb15c06303d724b9334f96ab2c6deb723deb2/TestLMDll/Debug/LineMatcher.dll -------------------------------------------------------------------------------- /TestLMDll/Debug/TestLMDll.exe: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/dlut-dimt/LineMatching/e05eb15c06303d724b9334f96ab2c6deb723deb2/TestLMDll/Debug/TestLMDll.exe -------------------------------------------------------------------------------- /TestLMDll/Debug/TestLMDll.ilk: -------------------------------------------------------------------------------- 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5 | 6 | 7 | 8 | 9 | 10 | 11 | -------------------------------------------------------------------------------- /TestLMDll/TestLMDll/Release/TestLMDll.lastbuildstate: -------------------------------------------------------------------------------- 1 | #v4.0:v100 2 | Release|Win32|E:\图像处理\linematch\code\linematch\newcode - 副本\TestLMDll\| 3 | -------------------------------------------------------------------------------- /TestLMDll/TestLMDll/Release/TestLMDll.log: -------------------------------------------------------------------------------- 1 | 生成启动时间为 2016/7/7 11:05:29。 2 | 1>项目“E:\图像处理\linematch\code\linematch\newcode - 副本\TestLMDll\TestLMDll\TestLMDll.vcxproj”在节点 2 上(build 个目标)。 3 | 1>InitializeBuildStatus: 4 | 正在创建“Release\TestLMDll.unsuccessfulbuild”，因为已指定“AlwaysCreate”。 5 | ClCompile: 6 | D:\vs2010\VC\bin\CL.exe /c /Zi /nologo /W3 /WX- /O2 /Oi /Oy- /GL /D WIN32 /D NDEBUG /D _CONSOLE /D _UNICODE /D UNICODE /Gm- /EHsc /MD /GS /Gy /fp:precise /Zc:wchar_t /Zc:forScope /Fo"Release\\" /Fd"Release\vc100.pdb" /Gd /TC /analyze- /errorReport:prompt lsd.c 7 | lsd.c 8 | D:\vs2010\VC\bin\CL.exe /c /Zi /nologo /W3 /WX- /O2 /Oi /Oy- /GL /D WIN32 /D NDEBUG /D _CONSOLE /D _UNICODE /D UNICODE /Gm- /EHsc /MD /GS /Gy /fp:precise /Zc:wchar_t /Zc:forScope /Fo"Release\\" /Fd"Release\vc100.pdb" /Gd /TP /analyze- /errorReport:prompt main.cpp 9 | main.cpp 10 | 1>D:\Program Files\openCV2.2\include\opencv2/flann/logger.h(66): warning C4996: 'fopen': This function or variable may be unsafe. Consider using fopen_s instead. To disable deprecation, use _CRT_SECURE_NO_WARNINGS. See online help for details. 11 | D:\vs2010\VC\include\stdio.h(234) : 参见“fopen”的声明 12 | 1>main.cpp(107): warning C4244: “=”: 从“double”转换到“float”，可能丢失数据 13 | 1>main.cpp(108): warning C4244: “=”: 从“double”转换到“float”，可能丢失数据 14 | 1>main.cpp(116): warning C4244: “+=”: 从“double”转换到“float”，可能丢失数据 15 | 1>main.cpp(118): warning C4244: “=”: 从“double”转换到“float”，可能丢失数据 16 | 1>main.cpp(128): warning C4244: “+=”: 从“double”转换到“float”，可能丢失数据 17 | 1>main.cpp(130): warning C4244: “=”: 从“double”转换到“float”，可能丢失数据 18 | 1>main.cpp(164): warning C4244: “=”: 从“double”转换到“float”，可能丢失数据 19 | 1>main.cpp(165): warning C4244: “=”: 从“double”转换到“float”，可能丢失数据 20 | 1>main.cpp(166): warning C4244: “=”: 从“double”转换到“float”，可能丢失数据 21 | 1>main.cpp(167): warning C4244: “=”: 从“double”转换到“float”，可能丢失数据 22 | 1>main.cpp(168): warning C4244: “=”: 从“double”转换到“float”，可能丢失数据 23 | 1>main.cpp(169): warning C4244: “=”: 从“double”转换到“float”，可能丢失数据 24 | 1>main.cpp(317): warning C4996: 'sprintf': This function or variable may be unsafe. Consider using sprintf_s instead. To disable deprecation, use _CRT_SECURE_NO_WARNINGS. See online help for details. 25 | D:\vs2010\VC\include\stdio.h(371) : 参见“sprintf”的声明 26 | 1>main.cpp(335): warning C4996: 'sprintf': This function or variable may be unsafe. Consider using sprintf_s instead. To disable deprecation, use _CRT_SECURE_NO_WARNINGS. See online help for details. 27 | D:\vs2010\VC\include\stdio.h(371) : 参见“sprintf”的声明 28 | 1>main.cpp(355): warning C4018: “<”: 有符号/无符号不匹配 29 | Link: 30 | D:\vs2010\VC\bin\link.exe /ERRORREPORT:PROMPT /OUT:"E:\图像处理\linematch\code\linematch\newcode - 副本\TestLMDll\Release\TestLMDll.exe" /INCREMENTAL:NO /NOLOGO /LIBPATH:"D:\Program Files\openCV2.2\lib" /LIBPATH:"D:\Program Files\openCV2.2\bin" opencv_core220.lib opencv_highgui220.lib opencv_calib3d220.lib opencv_features2d220.lib kernel32.lib user32.lib gdi32.lib winspool.lib comdlg32.lib advapi32.lib shell32.lib ole32.lib oleaut32.lib uuid.lib odbc32.lib odbccp32.lib /MANIFEST /ManifestFile:"Release\TestLMDll.exe.intermediate.manifest" /MANIFESTUAC:"level='asInvoker' uiAccess='false'" /DEBUG /PDB:"E:\图像处理\linematch\code\linematch\newcode - 副本\TestLMDll\Release\TestLMDll.pdb" /SUBSYSTEM:CONSOLE /OPT:REF /OPT:ICF /LTCG /TLBID:1 /DYNAMICBASE /NXCOMPAT /IMPLIB:"E:\图像处理\linematch\code\linematch\newcode - 副本\TestLMDll\Release\TestLMDll.lib" /MACHINE:X86 Release\lsd.obj 31 | Release\main.obj 32 | 正在生成代码 33 | 已完成代码的生成 34 | TestLMDll.vcxproj -> E:\图像处理\linematch\code\linematch\newcode - 副本\TestLMDll\Release\TestLMDll.exe 35 | Manifest: 36 | C:\Program Files (x86)\Microsoft SDKs\Windows\v7.0A\bin\mt.exe /nologo /verbose /outputresource:"E:\图像处理\linematch\code\linematch\newcode - 副本\TestLMDll\Release\TestLMDll.exe;#1" /manifest Release\TestLMDll.exe.intermediate.manifest 37 | FinalizeBuildStatus: 38 | 正在删除文件“Release\TestLMDll.unsuccessfulbuild”。 39 | 正在对“Release\TestLMDll.lastbuildstate”执行 Touch 任务。 40 | 1>已完成生成项目“E:\图像处理\linematch\code\linematch\newcode - 副本\TestLMDll\TestLMDll\TestLMDll.vcxproj”(build 个目标)的操作。 41 | 42 | 生成成功。 43 | 44 | 已用时间 00:00:03.46 45 | -------------------------------------------------------------------------------- /TestLMDll/TestLMDll/Release/TestLMDll.vcxprojResolveAssemblyReference.cache: -------------------------------------------------------------------------------- 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Application 26 | false 27 | true 28 | Unicode 29 | 30 | 31 | 32 | 33 | 34 | 35 | 36 | 37 | 38 | 39 | 40 | 41 | true 42 | D:\Program Files\openCV2.2\include\opencv;D:\Program Files\openCV2.2\include;D:\Program Files\openCV2.2\include\opencv2;$(IncludePath) 43 | D:\Program Files\openCV2.2\lib;$(LibraryPath) 44 | 45 | 46 | false 47 | D:\Program Files\openCV2.2\include\opencv;D:\Program Files\openCV2.2\include;D:\Program Files\openCV2.2\include\opencv2;$(IncludePath) 48 | D:\Program Files\openCV2.2\lib;$(LibraryPath) 49 | 50 | 51 | 52 | 53 | 54 | Level3 55 | Disabled 56 | WIN32;_DEBUG;_CONSOLE;%(PreprocessorDefinitions) 57 | 58 | 59 | Console 60 | true 61 | opencv_core220d.lib;opencv_highgui220d.lib;opencv_calib3d220d.lib;opencv_features2d220d.lib;%(AdditionalDependencies) 62 | D:\Program Files\openCV2.2\lib;D:\Program Files\openCV2.2\bin;%(AdditionalLibraryDirectories) 63 | 64 | 65 | true 66 | 67 | 68 | 69 | 70 | Level3 71 | 72 | 73 | MaxSpeed 74 | true 75 | true 76 | WIN32;NDEBUG;_CONSOLE;%(PreprocessorDefinitions) 77 | 78 | 79 | Console 80 | true 81 | true 82 | true 83 | opencv_core220.lib;opencv_highgui220.lib;opencv_calib3d220.lib;opencv_features2d220.lib;%(AdditionalDependencies) 84 | D:\Program Files\openCV2.2\lib;D:\Program Files\openCV2.2\bin;%(AdditionalLibraryDirectories) 85 | 86 | 87 | 88 | 89 | 90 | 91 | 92 | 93 | 94 | 95 | 96 | 97 | 98 | -------------------------------------------------------------------------------- /TestLMDll/TestLMDll/TestLMDll.vcxproj.filters: -------------------------------------------------------------------------------- 1 |  2 | 3 | 4 | 5 | {4FC737F1-C7A5-4376-A066-2A32D752A2FF} 6 | cpp;c;cc;cxx;def;odl;idl;hpj;bat;asm;asmx 7 | 8 | 9 | {93995380-89BD-4b04-88EB-625FBE52EBFB} 10 | h;hpp;hxx;hm;inl;inc;xsd 11 | 12 | 13 | {67DA6AB6-F800-4c08-8B7A-83BB121AAD01} 14 | rc;ico;cur;bmp;dlg;rc2;rct;bin;rgs;gif;jpg;jpeg;jpe;resx;tiff;tif;png;wav;mfcribbon-ms 15 | 16 | 17 | 18 | 19 | Source Files 20 | 21 | 22 | Source Files 23 | 24 | 25 | 26 | 27 | Header Files 28 | 29 | 30 | Header Files 31 | 32 | 33 | -------------------------------------------------------------------------------- /TestLMDll/TestLMDll/TestLMDll.vcxproj.user: -------------------------------------------------------------------------------- 1 |  2 | 3 | 4 | L503_A.jpg L503_B.jpg 5 | 6 | 7 | ..\Debug 8 | WindowsLocalDebugger 9 | 10 | -------------------------------------------------------------------------------- /TestLMDll/TestLMDll/lsd.c: -------------------------------------------------------------------------------- 1 | /*---------------------------------------------------------------------------- 2 | 3 | LSD - Line Segment Detector on digital images 4 | 5 | Copyright 2007,2008,2009,2010 rafael grompone von gioi (grompone@gmail.com) 6 | 7 | This program is free software: you can redistribute it and/or modify 8 | it under the terms of the GNU Affero General Public License as 9 | published by the Free Software Foundation, either version 3 of the 10 | License, or (at your option) any later version. 11 | 12 | This program is distributed in the hope that it will be useful, 13 | but WITHOUT ANY WARRANTY; without even the implied warranty of 14 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 15 | GNU Affero General Public License for more details. 16 | 17 | You should have received a copy of the GNU Affero General Public License 18 | along with this program. If not, see . 19 | 20 | ----------------------------------------------------------------------------*/ 21 | 22 | /*---------------------------------------------------------------------------- 23 | 24 | This is an implementation of the Line Segment Detector described in the paper: 25 | 26 | "LSD: A Fast Line Segment Detector with a False Detection Control" 27 | by Rafael Grompone von Gioi, Jeremie Jakubowicz, Jean-Michel Morel, 28 | and Gregory Randall, IEEE Transactions on Pattern Analysis and 29 | Machine Intelligence, vol. 32, no. 4, pp. 722-732, April, 2010. 30 | 31 | and in more details in the CMLA Technical Report: 32 | 33 | "LSD: A Line Segment Detector, Technical Report", 34 | by Rafael Grompone von Gioi, Jeremie Jakubowicz, Jean-Michel Morel, 35 | Gregory Randall, CMLA, ENS Cachan, 2010. 36 | 37 | HISTORY: 38 | version 1.3 - feb 2010: Multiple bug correction and improved code. 39 | version 1.2 - dic 2009: First full Ansi C Language version. 40 | version 1.1 - sep 2009: Systematic subsampling to scale 0.8 41 | and correction to partially handle "angle problem". 42 | version 1.0 - jan 2009: First complete Megawave2 and Ansi C Language version. 43 | 44 | ----------------------------------------------------------------------------*/ 45 | 46 | #include 47 | #include 48 | #include 49 | #include 50 | //#include 51 | //#include 52 | #include "lsd.h" 53 | //using namespace std; 54 | 55 | #ifndef M_LN10 56 | #define M_LN10 2.30258509299404568402 57 | #endif /* !M_LN10 */ 58 | 59 | #ifndef M_PI 60 | #define M_PI 3.14159265358979323846 61 | #endif /* !M_PI */ 62 | 63 | #ifndef FALSE 64 | #define FALSE 0 65 | #endif /* !FALSE */ 66 | 67 | #ifndef TRUE 68 | #define TRUE 1 69 | #endif /* !TRUE */ 70 | 71 | #define NOTDEF -1024.0 72 | #define M_3_2_PI 4.71238898038 73 | #define M_2__PI 6.28318530718 74 | #define NOTUSED 0 75 | #define USED 1 76 | 77 | /*----------------------------------------------------------------------------*/ 78 | struct coorlist 79 | { 80 | int x,y; 81 | struct coorlist * next; 82 | }; 83 | 84 | /*----------------------------------------------------------------------------*/ 85 | struct point {int x,y;}; 86 | 87 | 88 | /*----------------------------------------------------------------------------*/ 89 | /*------------------------- Miscellaneous functions --------------------------*/ 90 | /*----------------------------------------------------------------------------*/ 91 | 92 | /*----------------------------------------------------------------------------*/ 93 | /* 94 | Fatal error, print a message to standard-error output and exit. 95 | */ 96 | static void error(char * msg) 97 | { 98 | fprintf(stderr,"LSD Error: %s\n",msg); 99 | exit(EXIT_FAILURE); 100 | } 101 | 102 | /*----------------------------------------------------------------------------*/ 103 | /* 104 | Compare doubles by relative error. 105 | 106 | The resulting rounding error after floating point computations 107 | depend on the specific operations done. The same number computed by 108 | different algorithms could present different rounding errors. For a 109 | useful comparison, an estimation of the relative rounding error 110 | should be considered and compared to a factor times EPS. The factor 111 | should be related to the cumulated rounding error in the chain of 112 | computation. Here, as a simplification, a fixed factor is used. 113 | */ 114 | #define RELATIVE_ERROR_FACTOR 100.0 115 | static int double_equal(double a, double b) 116 | { 117 | double abs_diff,aa,bb,abs_max; 118 | 119 | if( a == b ) return TRUE; 120 | 121 | abs_diff = fabs(a-b); 122 | aa = fabs(a); 123 | bb = fabs(b); 124 | abs_max = aa > bb ? aa : bb; 125 | 126 | /* DBL_MIN is the smallest normalized number, thus, the smallest 127 | number whose relative error is bounded by DBL_EPSILON. For 128 | smaller numbers, the same quantization steps as for DBL_MIN 129 | are used. Then, for smaller numbers, a meaningful "relative" 130 | error should be computed by dividing the difference by DBL_MIN. */ 131 | if( abs_max < DBL_MIN ) abs_max = DBL_MIN; 132 | 133 | /* equal if relative error <= factor x eps */ 134 | return (abs_diff / abs_max) <= (RELATIVE_ERROR_FACTOR * DBL_EPSILON); 135 | } 136 | 137 | /*----------------------------------------------------------------------------*/ 138 | /* 139 | Computes Euclidean distance between point (x1,y1) and point (x2,y2). 140 | */ 141 | static double dist(double x1, double y1, double x2, double y2) 142 | { 143 | return sqrt( (x2-x1)*(x2-x1) + (y2-y1)*(y2-y1) ); 144 | } 145 | 146 | 147 | /*----------------------------------------------------------------------------*/ 148 | /*----------------------- 'list of n-tuple' data type ------------------------*/ 149 | /*----------------------------------------------------------------------------*/ 150 | 151 | /*----------------------------------------------------------------------------*/ 152 | /* 153 | Free memory used in n-tuple 'in'. 154 | */ 155 | void free_ntuple_list(ntuple_list in) 156 | { 157 | if( in == NULL || in->values == NULL ) 158 | error("free_ntuple_list: invalid n-tuple input."); 159 | free( (void *) in->values ); 160 | free( (void *) in ); 161 | } 162 | 163 | /*----------------------------------------------------------------------------*/ 164 | /* 165 | Create an n-tuple list and allocate memory for one element. 166 | The parameter 'dim' is the dimension (n) of the n-tuple. 167 | */ 168 | ntuple_list new_ntuple_list(unsigned int dim) 169 | { 170 | ntuple_list n_tuple; 171 | 172 | if( dim <= 0 ) error("new_ntuple_list: 'dim' must be positive."); 173 | 174 | n_tuple = (ntuple_list) malloc( sizeof(struct ntuple_list_s) ); 175 | if( n_tuple == NULL ) error("not enough memory."); 176 | n_tuple->size = 0; 177 | n_tuple->max_size = 1; 178 | n_tuple->dim = dim; 179 | n_tuple->values = (double *) malloc( dim*n_tuple->max_size * sizeof(double) ); 180 | if( n_tuple->values == NULL ) error("not enough memory."); 181 | return n_tuple; 182 | } 183 | 184 | /*----------------------------------------------------------------------------*/ 185 | /* 186 | Enlarge the allocated memory of an n-tuple list. 187 | */ 188 | static void enlarge_ntuple_list(ntuple_list n_tuple) 189 | { 190 | if( n_tuple == NULL || n_tuple->values == NULL || n_tuple->max_size <= 0 ) 191 | error("enlarge_ntuple_list: invalid n-tuple."); 192 | n_tuple->max_size *= 2; 193 | n_tuple->values = 194 | (double *) realloc( (void *) n_tuple->values, 195 | n_tuple->dim * n_tuple->max_size * sizeof(double) ); 196 | if( n_tuple->values == NULL ) error("not enough memory."); 197 | } 198 | 199 | /*----------------------------------------------------------------------------*/ 200 | /* 201 | Add a 5-tuple to an n-tuple list. 202 | */ 203 | static void add_5tuple( ntuple_list out, double v1, double v2, 204 | double v3, double v4, double v5 ) 205 | { 206 | if( out == NULL ) error("add_5tuple: invalid n-tuple input."); 207 | if( out->dim != 5 ) error("add_5tuple: the n-tuple must be a 5-tuple."); 208 | if( out->size == out->max_size ) enlarge_ntuple_list(out); 209 | if( out->values == NULL ) error("add_5tuple: invalid n-tuple input."); 210 | out->values[ out->size * out->dim + 0 ] = v1; 211 | out->values[ out->size * out->dim + 1 ] = v2; 212 | out->values[ out->size * out->dim + 2 ] = v3; 213 | out->values[ out->size * out->dim + 3 ] = v4; 214 | out->values[ out->size * out->dim + 4 ] = v5; 215 | out->size++; 216 | } 217 | 218 | 219 | /*----------------------------------------------------------------------------*/ 220 | /*----------------------------- Image Data Types -----------------------------*/ 221 | /*----------------------------------------------------------------------------*/ 222 | 223 | /*----------------------------------------------------------------------------*/ 224 | /* 225 | Free memory used in image_char 'i'. 226 | */ 227 | void free_image_char(image_char i) 228 | { 229 | if( i == NULL || i->data == NULL ) 230 | error("free_image_char: invalid input image."); 231 | free( (void *) i->data ); 232 | free( (void *) i ); 233 | } 234 | 235 | /*----------------------------------------------------------------------------*/ 236 | /* 237 | Create a new image_char of size 'xsize' times 'ysize'. 238 | */ 239 | image_char new_image_char(unsigned int xsize, unsigned int ysize) 240 | { 241 | image_char image; 242 | 243 | if( xsize == 0 || ysize == 0 ) error("new_image_char: invalid image size."); 244 | 245 | image = (image_char) malloc( sizeof(struct image_char_s) ); 246 | if( image == NULL ) error("not enough memory."); 247 | image->data = (unsigned char *) calloc( xsize*ysize, sizeof(unsigned char) ); 248 | if( image->data == NULL ) error("not enough memory."); 249 | 250 | image->xsize = xsize; 251 | image->ysize = ysize; 252 | 253 | return image; 254 | } 255 | 256 | /*----------------------------------------------------------------------------*/ 257 | /* 258 | Create a new image_char of size 'xsize' times 'ysize', 259 | initialized to the value 'fill_value'. 260 | */ 261 | image_char new_image_char_ini( unsigned int xsize, unsigned int ysize, 262 | unsigned char fill_value ) 263 | { 264 | image_char image = new_image_char(xsize,ysize); 265 | unsigned int N = xsize*ysize; 266 | unsigned int i; 267 | 268 | if( image == NULL || image->data == NULL ) 269 | error("new_image_char_ini: invalid image."); 270 | 271 | for(i=0; idata[i] = fill_value; 272 | 273 | return image; 274 | } 275 | 276 | /*----------------------------------------------------------------------------*/ 277 | /* 278 | Free memory used in image_int 'i'. 279 | */ 280 | void free_image_int(image_int i) 281 | { 282 | if( i == NULL || i->data == NULL ) 283 | error("free_image_int: invalid input image."); 284 | free( (void *) i->data ); 285 | free( (void *) i ); 286 | } 287 | 288 | /*----------------------------------------------------------------------------*/ 289 | /* 290 | Create a new image_int of size 'xsize' times 'ysize'. 291 | */ 292 | image_int new_image_int(unsigned int xsize, unsigned int ysize) 293 | { 294 | image_int image; 295 | 296 | if( xsize == 0 || ysize == 0 ) error("new_image_int: invalid image size."); 297 | 298 | image = (image_int) malloc( sizeof(struct image_int_s) ); 299 | if( image == NULL ) error("not enough memory."); 300 | image->data = (int *) calloc( xsize*ysize, sizeof(int) ); 301 | if( image->data == NULL ) error("not enough memory."); 302 | 303 | image->xsize = xsize; 304 | image->ysize = ysize; 305 | 306 | return image; 307 | } 308 | 309 | /*----------------------------------------------------------------------------*/ 310 | /* 311 | Create a new image_int of size 'xsize' times 'ysize', 312 | initialized to the value 'fill_value'. 313 | */ 314 | image_int new_image_int_ini( unsigned int xsize, unsigned int ysize, 315 | int fill_value ) 316 | { 317 | image_int image = new_image_int(xsize,ysize); 318 | unsigned int N = xsize*ysize; 319 | unsigned int i; 320 | 321 | for(i=0; idata[i] = fill_value; 322 | 323 | return image; 324 | } 325 | 326 | /*----------------------------------------------------------------------------*/ 327 | /* 328 | Free memory used in image_double 'i'. 329 | */ 330 | void free_image_double(image_double i) 331 | { 332 | if( i == NULL || i->data == NULL ) 333 | error("free_image_double: invalid input image."); 334 | free( (void *) i->data ); 335 | free( (void *) i ); 336 | } 337 | 338 | /*----------------------------------------------------------------------------*/ 339 | /* 340 | Create a new image_double of size 'xsize' times 'ysize'. 341 | */ 342 | image_double new_image_double(unsigned int xsize, unsigned int ysize) 343 | { 344 | image_double image; 345 | 346 | if( xsize == 0 || ysize == 0 ) error("new_image_double: invalid image size."); 347 | 348 | image = (image_double) malloc( sizeof(struct image_double_s) ); 349 | if( image == NULL ) error("not enough memory."); 350 | image->data = (double *) calloc( xsize * ysize, sizeof(double) ); 351 | if( image->data == NULL ) error("not enough memory."); 352 | 353 | image->xsize = xsize; 354 | image->ysize = ysize; 355 | 356 | return image; 357 | } 358 | 359 | /*----------------------------------------------------------------------------*/ 360 | /* 361 | Create a new image_double of size 'xsize' times 'ysize', 362 | initialized to the value 'fill_value'. 363 | */ 364 | image_double new_image_double_ini( unsigned int xsize, unsigned int ysize, 365 | double fill_value ) 366 | { 367 | image_double image = new_image_double(xsize,ysize); 368 | unsigned int N = xsize*ysize; 369 | unsigned int i; 370 | 371 | for(i=0; idata[i] = fill_value; 372 | 373 | return image; 374 | } 375 | 376 | 377 | /*----------------------------------------------------------------------------*/ 378 | /*----------------------------- Gaussian filter ------------------------------*/ 379 | /*----------------------------------------------------------------------------*/ 380 | 381 | /*----------------------------------------------------------------------------*/ 382 | /* 383 | Compute a Gaussian kernel of length 'kernel->dim', 384 | standard deviation 'sigma', and centered at value 'mean'. 385 | For example, if mean=0.5, the Gaussian will be centered 386 | in the middle point between values 'kernel->values[0]' 387 | and 'kernel->values[1]'. 388 | */ 389 | static void gaussian_kernel(ntuple_list kernel, double sigma, double mean) 390 | { 391 | double sum = 0.0; 392 | double val; 393 | unsigned int i; 394 | 395 | if( kernel == NULL || kernel->values == NULL ) 396 | error("gaussian_kernel: invalid n-tuple 'kernel'."); 397 | if( sigma <= 0.0 ) error("gaussian_kernel: 'sigma' must be positive."); 398 | 399 | /* compute gaussian kernel */ 400 | if( kernel->max_size < 1 ) enlarge_ntuple_list(kernel); 401 | kernel->size = 1; 402 | for(i=0;idim;i++) 403 | { 404 | val = ( (double) i - mean ) / sigma; 405 | kernel->values[i] = exp( -0.5 * val * val ); 406 | sum += kernel->values[i]; 407 | } 408 | 409 | /* normalization */ 410 | if( sum >= 0.0 ) for(i=0;idim;i++) kernel->values[i] /= sum; 411 | } 412 | 413 | /*----------------------------------------------------------------------------*/ 414 | /* 415 | Subsample image 'in' with Gaussian filtering, to a scale 'scale' 416 | (for example, 0.8 will give a result at 80% of the original size), 417 | using a standard deviation sigma given by: 418 | 419 | sigma = sigma_scale / scale, if scale < 1.0 420 | sigma = sigma_scale, if scale >= 1.0 421 | */ 422 | static image_double gaussian_sampler( image_double in, double scale, 423 | double sigma_scale ) 424 | { 425 | image_double aux,out; 426 | ntuple_list kernel; 427 | unsigned int N,M,h,n,x,y,i; 428 | int xc,yc,j,double_x_size,double_y_size; 429 | double sigma,xx,yy,sum,prec; 430 | 431 | if( in == NULL || in->data == NULL || in->xsize <= 0 || in->ysize <= 0 ) 432 | error("gaussian_sampler: invalid image."); 433 | if( scale <= 0.0 ) error("gaussian_sampler: 'scale' must be positive."); 434 | if( sigma_scale <= 0.0 ) 435 | error("gaussian_sampler: 'sigma_scale' must be positive."); 436 | 437 | /* get memory for images */ 438 | N = (unsigned int) floor( in->xsize * scale ); 439 | M = (unsigned int) floor( in->ysize * scale ); 440 | aux = new_image_double(N,in->ysize); 441 | out = new_image_double(N,M); 442 | 443 | /* sigma, kernel size and memory for the kernel */ 444 | sigma = scale < 1.0 ? sigma_scale / scale : sigma_scale; 445 | /* 446 | The size of the kernel is selected to guarantee that the 447 | the first discarded term is at least 10^prec times smaller 448 | than the central value. For that, h should be larger than x, with 449 | e^(-x^2/2sigma^2) = 1/10^prec. 450 | Then, 451 | x = sigma * sqrt( 2 * prec * ln(10) ). 452 | */ 453 | prec = 3.0; 454 | h = (unsigned int) ceil( sigma * sqrt( 2.0 * prec * log(10.0) ) ); 455 | n = 1+2*h; /* kernel size */ 456 | kernel = new_ntuple_list(n); 457 | 458 | /* auxiliary double image size variables */ 459 | double_x_size = (int) (2 * in->xsize); 460 | double_y_size = (int) (2 * in->ysize); 461 | 462 | /* First subsampling: x axis */ 463 | for(x=0;xxsize;x++) 464 | { 465 | /* 466 | x is the coordinate in the new image. 467 | xx is the corresponding x-value in the original size image. 468 | xc is the integer value, the pixel coordinate of xx. 469 | */ 470 | xx = (double) x / scale; 471 | /* coordinate (0.0,0.0) is in the center of pixel (0,0), 472 | so the pixel with xc=0 get the values of xx from -0.5 to 0.5 */ 473 | xc = (int) floor( xx + 0.5 ); 474 | gaussian_kernel( kernel, sigma, (double) h + xx - (double) xc ); 475 | /* the kernel must be computed for each x because the fine 476 | offset xx-xc is different in each case */ 477 | 478 | for(y=0;yysize;y++) 479 | { 480 | sum = 0.0; 481 | for(i=0;idim;i++) 482 | { 483 | j = xc - h + i; 484 | 485 | /* symmetry boundary condition */ 486 | while( j < 0 ) j += double_x_size; 487 | while( j >= double_x_size ) j -= double_x_size; 488 | if( j >= (int) in->xsize ) j = double_x_size-1-j; 489 | 490 | sum += in->data[ j + y * in->xsize ] * kernel->values[i]; 491 | } 492 | aux->data[ x + y * aux->xsize ] = sum; 493 | } 494 | } 495 | 496 | /* Second subsampling: y axis */ 497 | for(y=0;yysize;y++) 498 | { 499 | /* 500 | y is the coordinate in the new image. 501 | yy is the corresponding x-value in the original size image. 502 | yc is the integer value, the pixel coordinate of xx. 503 | */ 504 | yy = (double) y / scale; 505 | /* coordinate (0.0,0.0) is in the center of pixel (0,0), 506 | so the pixel with yc=0 get the values of yy from -0.5 to 0.5 */ 507 | yc = (int) floor( yy + 0.5 ); 508 | gaussian_kernel( kernel, sigma, (double) h + yy - (double) yc ); 509 | /* the kernel must be computed for each y because the fine 510 | offset yy-yc is different in each case */ 511 | 512 | for(x=0;xxsize;x++) 513 | { 514 | sum = 0.0; 515 | for(i=0;idim;i++) 516 | { 517 | j = yc - h + i; 518 | 519 | /* symmetry boundary condition */ 520 | while( j < 0 ) j += double_y_size; 521 | while( j >= double_y_size ) j -= double_y_size; 522 | if( j >= (int) in->ysize ) j = double_y_size-1-j; 523 | 524 | sum += aux->data[ x + j * aux->xsize ] * kernel->values[i]; 525 | } 526 | out->data[ x + y * out->xsize ] = sum; 527 | } 528 | } 529 | 530 | /* free memory */ 531 | free_ntuple_list(kernel); 532 | free_image_double(aux); 533 | 534 | return out; 535 | } 536 | 537 | 538 | /*----------------------------------------------------------------------------*/ 539 | /*------------------------------ Gradient Angle ------------------------------*/ 540 | /*----------------------------------------------------------------------------*/ 541 | 542 | /*----------------------------------------------------------------------------*/ 543 | /* 544 | Computes the direction of the level line of 'in' at each point. 545 | It returns: 546 | 547 | - an image_double with the angle at each pixel, or NOTDEF if not defined. 548 | - the image_double 'modgrad' (a pointer is passed as argument) 549 | with the gradient magnitude at each point. 550 | - a list of pixels 'list_p' roughly ordered by gradient magnitude. 551 | (the order is made by classing points into bins by gradient magnitude. 552 | the parameters 'n_bins' and 'max_grad' specify the number of 553 | bins and the gradient modulus at the highest bin.) 554 | - a pointer 'mem_p' to the memory used by 'list_p' to be able to 555 | free the memory. 556 | */ 557 | static image_double ll_angle( image_double in, double threshold, 558 | struct coorlist ** list_p, void ** mem_p, 559 | image_double * modgrad, unsigned int n_bins, 560 | double max_grad ) 561 | { 562 | image_double g; 563 | unsigned int n,p,x,y,adr,i; 564 | double com1,com2,gx,gy,norm,norm2; 565 | /* the rest of the variables are used for pseudo-ordering 566 | the gradient magnitude values */ 567 | int list_count = 0; 568 | struct coorlist * list; 569 | struct coorlist ** range_l_s; /* array of pointers to start of bin list */ 570 | struct coorlist ** range_l_e; /* array of pointers to end of bin list */ 571 | struct coorlist * start; 572 | struct coorlist * end; 573 | 574 | /* check parameters */ 575 | if( in == NULL || in->data == NULL || in->xsize <= 0 || in->ysize <= 0 ) 576 | error("ll_angle: invalid image."); 577 | if( threshold < 0.0 ) error("ll_angle: 'threshold' must be positive."); 578 | if( list_p == NULL ) error("ll_angle: NULL pointer 'list_p'."); 579 | if( mem_p == NULL ) error("ll_angle: NULL pointer 'mem_p'."); 580 | if( modgrad == NULL ) error("ll_angle: NULL pointer 'modgrad'."); 581 | if( n_bins <= 0 ) error("ll_angle: 'n_bins' must be positive."); 582 | if( max_grad <= 0.0 ) error("ll_angle: 'max_grad' must be positive."); 583 | 584 | n = in->ysize; 585 | p = in->xsize; 586 | 587 | /* allocate output image */ 588 | g = new_image_double(in->xsize,in->ysize); 589 | 590 | /* get memory for the image of gradient modulus */ 591 | *modgrad = new_image_double(in->xsize,in->ysize); 592 | 593 | /* get memory for "ordered" coordinate list */ 594 | list = (struct coorlist *) calloc(n*p,sizeof(struct coorlist)); 595 | *mem_p = (void *) list; 596 | range_l_s = (struct coorlist **) calloc(n_bins,sizeof(struct coorlist *)); 597 | range_l_e = (struct coorlist **) calloc(n_bins,sizeof(struct coorlist *)); 598 | if( list == NULL || range_l_s == NULL || range_l_e == NULL ) 599 | error("not enough memory."); 600 | for(i=0;idata[(n-1)*p+x] = NOTDEF; 604 | for(y=0;ydata[p*y+p-1] = NOTDEF; 605 | 606 | /*** remaining part ***/ 607 | for(x=0;xdata[adr+p+1] - in->data[adr]; 624 | com2 = in->data[adr+1] - in->data[adr+p]; 625 | gx = com1+com2; 626 | gy = com1-com2; 627 | norm2 = gx*gx+gy*gy; 628 | norm = sqrt( norm2 / 4.0 ); 629 | 630 | (*modgrad)->data[adr] = norm; 631 | 632 | if( norm <= threshold ) /* norm too small, gradient no defined */ 633 | g->data[adr] = NOTDEF; 634 | else 635 | { 636 | /* angle computation */ 637 | g->data[adr] = atan2(gx,-gy); 638 | 639 | /* store the point in the right bin according to its norm */ 640 | i = (unsigned int) (norm * (double) n_bins / max_grad); 641 | if( i >= n_bins ) i = n_bins-1; 642 | if( range_l_e[i] == NULL ) 643 | range_l_s[i] = range_l_e[i] = list+list_count++; 644 | else 645 | { 646 | range_l_e[i]->next = list+list_count; 647 | range_l_e[i] = list+list_count++; 648 | } 649 | range_l_e[i]->x = (int) x; 650 | range_l_e[i]->y = (int) y; 651 | range_l_e[i]->next = NULL; 652 | } 653 | } 654 | 655 | /* Make the list of points "ordered" by norm value. 656 | It starts by the larger bin, so the list starts by the 657 | pixels with higher gradient value. 658 | */ 659 | for(i=n_bins-1; i>0 && range_l_s[i]==NULL; i--); 660 | start = range_l_s[i]; 661 | end = range_l_e[i]; 662 | if( start != NULL ) 663 | for(i--;i>0; i--) 664 | if( range_l_s[i] != NULL ) 665 | { 666 | end->next = range_l_s[i]; 667 | end = range_l_e[i]; 668 | } 669 | *list_p = start; 670 | 671 | /* free memory */ 672 | free( (void *) range_l_s ); 673 | free( (void *) range_l_e ); 674 | 675 | return g; 676 | } 677 | 678 | /*----------------------------------------------------------------------------*/ 679 | /* 680 | Is point (x,y) aligned to angle theta, up to precision 'prec'? 681 | */ 682 | static int isaligned( int x, int y, image_double angles, double theta, 683 | double prec ) 684 | { 685 | double a; 686 | 687 | /* check parameters */ 688 | if( angles == NULL || angles->data == NULL ) 689 | error("isaligned: invalid image 'angles'."); 690 | if( x < 0 || y < 0 || x >= (int) angles->xsize || y >= (int) angles->ysize ) 691 | error("isaligned: (x,y) out of the image."); 692 | if( prec < 0.0 ) error("isaligned: 'prec' must be positive."); 693 | 694 | a = angles->data[ x + y * angles->xsize ]; 695 | 696 | if( a == NOTDEF ) return FALSE; /* there is no risk of double comparison 697 | problem here because we are only 698 | interested in the exact NOTDEF value */ 699 | 700 | /* it is assumed that 'theta' and 'a' are in the range [-pi,pi] */ 701 | theta -= a; 702 | if( theta < 0.0 ) theta = -theta; 703 | if( theta > M_3_2_PI ) 704 | { 705 | theta -= M_2__PI; 706 | if( theta < 0.0 ) theta = -theta; 707 | } 708 | 709 | return theta < prec; 710 | } 711 | 712 | /*----------------------------------------------------------------------------*/ 713 | /* 714 | Absolute value angle difference. 715 | */ 716 | static double angle_diff(double a, double b) 717 | { 718 | a -= b; 719 | while( a <= -M_PI ) a += M_2__PI; 720 | while( a > M_PI ) a -= M_2__PI; 721 | if( a < 0.0 ) a = -a; 722 | return a; 723 | } 724 | 725 | /*----------------------------------------------------------------------------*/ 726 | /* 727 | Signed angle difference. 728 | */ 729 | static double angle_diff_signed(double a, double b) 730 | { 731 | a -= b; 732 | while( a <= -M_PI ) a += M_2__PI; 733 | while( a > M_PI ) a -= M_2__PI; 734 | return a; 735 | } 736 | 737 | 738 | /*----------------------------------------------------------------------------*/ 739 | /*----------------------------- NFA computation ------------------------------*/ 740 | /*----------------------------------------------------------------------------*/ 741 | 742 | /*----------------------------------------------------------------------------*/ 743 | /* 744 | Calculates the natural logarithm of the absolute value of 745 | the gamma function of x using the Lanczos approximation, 746 | see http://www.rskey.org/gamma.htm 747 | 748 | The formula used is 749 | \Gamma(x) = \frac{ \sum_{n=0}^{N} q_n x^n }{ \Pi_{n=0}^{N} (x+n) } 750 | (x+5.5)^(x+0.5) e^{-(x+5.5)} 751 | so 752 | \log\Gamma(x) = \log( \sum_{n=0}^{N} q_n x^n ) + (x+0.5) \log(x+5.5) 753 | - (x+5.5) - \sum_{n=0}^{N} \log(x+n) 754 | and 755 | q0 = 75122.6331530 756 | q1 = 80916.6278952 757 | q2 = 36308.2951477 758 | q3 = 8687.24529705 759 | q4 = 1168.92649479 760 | q5 = 83.8676043424 761 | q6 = 2.50662827511 762 | */ 763 | static double log_gamma_lanczos(double x) 764 | { 765 | static double q[7] = { 75122.6331530, 80916.6278952, 36308.2951477, 766 | 8687.24529705, 1168.92649479, 83.8676043424, 767 | 2.50662827511 }; 768 | double a = (x+0.5) * log(x+5.5) - (x+5.5); 769 | double b = 0.0; 770 | int n; 771 | 772 | for(n=0;n<7;n++) 773 | { 774 | a -= log( x + (double) n ); 775 | b += q[n] * pow( x, (double) n ); 776 | } 777 | return a + log(b); 778 | } 779 | 780 | /*----------------------------------------------------------------------------*/ 781 | /* 782 | Calculates the natural logarithm of the absolute value of 783 | the gamma function of x using Robert H. Windschitl method, 784 | see http://www.rskey.org/gamma.htm 785 | 786 | The formula used is 787 | \Gamma(x) = \sqrt(\frac{2\pi}{x}) ( \frac{x}{e} 788 | \sqrt{ x\sinh(1/x) + \frac{1}{810x^6} } )^x 789 | so 790 | \log\Gamma(x) = 0.5\log(2\pi) + (x-0.5)\log(x) - x 791 | + 0.5x\log( x\sinh(1/x) + \frac{1}{810x^6} ). 792 | 793 | This formula is a good approximation when x > 15. 794 | */ 795 | static double log_gamma_windschitl(double x) 796 | { 797 | return 0.918938533204673 + (x-0.5)*log(x) - x 798 | + 0.5*x*log( x*sinh(1/x) + 1/(810.0*pow(x,6.0)) ); 799 | } 800 | 801 | /*----------------------------------------------------------------------------*/ 802 | /* 803 | Calculates the natural logarithm of the absolute value of 804 | the gamma function of x. When x>15 use log_gamma_windschitl(), 805 | otherwise use log_gamma_lanczos(). 806 | */ 807 | #define log_gamma(x) ((x)>15.0?log_gamma_windschitl(x):log_gamma_lanczos(x)) 808 | 809 | /*----------------------------------------------------------------------------*/ 810 | /* 811 | Computes -log10(NFA) 812 | 813 | NFA stands for Number of False Alarms: 814 | 815 | NFA = NT.b(n,k,p) 816 | 817 | NT - number of tests 818 | b(,,) - tail of binomial distribution with parameters n,k and p 819 | 820 | The value -log10(NFA) is equivalent but more intuitive than NFA: 821 | -1 corresponds to 10 mean false alarms 822 | 0 corresponds to 1 mean false alarm 823 | 1 corresponds to 0.1 mean false alarms 824 | 2 corresponds to 0.01 mean false alarms 825 | ... 826 | 827 | Used this way, the bigger the value, better the detection, 828 | and a logarithmic scale is used. 829 | 830 | Parameters: 831 | n,k,p - binomial parameters. 832 | logNT - logarithm of Number of Tests 833 | */ 834 | #define TABSIZE 100000 835 | static double nfa(int n, int k, double p, double logNT) 836 | { 837 | static double inv[TABSIZE]; /* table to keep computed inverse values */ 838 | double tolerance = 0.1; /* an error of 10% in the result is accepted */ 839 | double log1term,term,bin_term,mult_term,bin_tail,err,p_term; 840 | int i; 841 | 842 | if( n<0 || k<0 || k>n || p<=0.0 || p>=1.0 ) 843 | error("nfa: wrong n, k or p values."); 844 | 845 | if( n==0 || k==0 ) return -logNT; 846 | if( n==k ) return -logNT - (double) n * log10(p); 847 | 848 | p_term = p / (1.0-p); 849 | 850 | /* compute the first term of the series */ 851 | /* 852 | binomial_tail(n,k,p) = sum_{i=k}^n bincoef(n,i) * p^i * (1-p)^{n-i} 853 | where bincoef(n,i) are the binomial coefficients. 854 | But 855 | bincoef(n,k) = gamma(n+1) / ( gamma(k+1) * gamma(n-k+1) ). 856 | We use this to compute the first term. Actually the log of it. 857 | */ 858 | log1term = log_gamma( (double) n + 1.0 ) - log_gamma( (double) k + 1.0 ) 859 | - log_gamma( (double) (n-k) + 1.0 ) 860 | + (double) k * log(p) + (double) (n-k) * log(1.0-p); 861 | term = exp(log1term); 862 | 863 | /* in some cases no more computations are needed */ 864 | if( double_equal(term,0.0) ) /* the first term is almost zero */ 865 | { 866 | if( (double) k > (double) n * p ) /* at begin or end of the tail? */ 867 | return -log1term / M_LN10 - logNT; /* end: use just the first term */ 868 | else 869 | return -logNT; /* begin: the tail is roughly 1 */ 870 | } 871 | 872 | /* compute more terms if needed */ 873 | bin_tail = term; 874 | for(i=k+1;i<=n;i++) 875 | { 876 | /* 877 | As 878 | term_i = bincoef(n,i) * p^i * (1-p)^(n-i) 879 | and 880 | bincoef(n,i)/bincoef(n,i-1) = n-1+1 / i, 881 | then, 882 | term_i / term_i-1 = (n-i+1)/i * p/(1-p) 883 | and 884 | term_i = term_i-1 * (n-i+1)/i * p/(1-p). 885 | 1/i is stored in a table as they are computed, 886 | because divisions are expensive. 887 | p/(1-p) is computed only once and stored in 'p_term'. 888 | */ 889 | bin_term = (double) (n-i+1) * ( ii. 899 | Then, the error on the binomial tail when truncated at 900 | the i term can be bounded by a geometric series of form 901 | term_i * sum mult_term_i^j. */ 902 | err = term * ( ( 1.0 - pow( mult_term, (double) (n-i+1) ) ) / 903 | (1.0-mult_term) - 1.0 ); 904 | 905 | /* One wants an error at most of tolerance*final_result, or: 906 | tolerance * abs(-log10(bin_tail)-logNT). 907 | Now, the error that can be accepted on bin_tail is 908 | given by tolerance*final_result divided by the derivative 909 | of -log10(x) when x=bin_tail. that is: 910 | tolerance * abs(-log10(bin_tail)-logNT) / (1/bin_tail) 911 | Finally, we truncate the tail if the error is less than: 912 | tolerance * abs(-log10(bin_tail)-logNT) * bin_tail */ 913 | if( err < tolerance * fabs(-log10(bin_tail)-logNT) * bin_tail ) break; 914 | } 915 | } 916 | return -log10(bin_tail) - logNT; 917 | } 918 | 919 | 920 | /*----------------------------------------------------------------------------*/ 921 | /*--------------------------- Rectangle structure ----------------------------*/ 922 | /*----------------------------------------------------------------------------*/ 923 | 924 | /*----------------------------------------------------------------------------*/ 925 | struct rect /* line segment with width */ 926 | { 927 | double x1,y1,x2,y2; /* first and second point of the line segment */ 928 | double width; /* rectangle width */ 929 | double x,y; /* center of the rectangle */ 930 | double theta; /* angle */ 931 | double dx,dy; /* vector with the line segment angle */ 932 | double prec; /* tolerance angle */ 933 | double p; /* probability of a point with angle within 'prec' */ 934 | }; 935 | 936 | /*----------------------------------------------------------------------------*/ 937 | /* 938 | Copy one rectangle structure to another. 939 | */ 940 | static void rect_copy(struct rect * in, struct rect * out) 941 | { 942 | if( in == NULL || out == NULL ) error("rect_copy: invalid 'in' or 'out'."); 943 | out->x1 = in->x1; 944 | out->y1 = in->y1; 945 | out->x2 = in->x2; 946 | out->y2 = in->y2; 947 | out->width = in->width; 948 | out->x = in->x; 949 | out->y = in->y; 950 | out->theta = in->theta; 951 | out->dx = in->dx; 952 | out->dy = in->dy; 953 | out->prec = in->prec; 954 | out->p = in->p; 955 | } 956 | 957 | /*----------------------------------------------------------------------------*/ 958 | /* 959 | Rectangle points iterator. 960 | */ 961 | typedef struct 962 | { 963 | double vx[4]; 964 | double vy[4]; 965 | double ys,ye; 966 | int x,y; 967 | } rect_iter; 968 | 969 | /*----------------------------------------------------------------------------*/ 970 | /* 971 | Rectangle points iterator auxiliary function. 972 | */ 973 | static double inter_low(double x, double x1, double y1, double x2, double y2) 974 | { 975 | if( x1 > x2 || x < x1 || x > x2 ) 976 | { 977 | fprintf(stderr,"inter_low: x %g x1 %g x2 %g.\n",x,x1,x2); 978 | error("impossible situation."); 979 | } 980 | if( double_equal(x1,x2) && y1y2 ) return y2; 982 | return y1 + (x-x1) * (y2-y1) / (x2-x1); 983 | } 984 | 985 | /*----------------------------------------------------------------------------*/ 986 | /* 987 | Rectangle points iterator auxiliary function. 988 | */ 989 | static double inter_hi(double x, double x1, double y1, double x2, double y2) 990 | { 991 | if( x1 > x2 || x < x1 || x > x2 ) 992 | { 993 | fprintf(stderr,"inter_hi: x %g x1 %g x2 %g.\n",x,x1,x2); 994 | error("impossible situation."); 995 | } 996 | if( double_equal(x1,x2) && y1y2 ) return y1; 998 | return y1 + (x-x1) * (y2-y1) / (x2-x1); 999 | } 1000 | 1001 | /*----------------------------------------------------------------------------*/ 1002 | /* 1003 | Free memory used by a rectangle iterator. 1004 | */ 1005 | static void ri_del(rect_iter * iter) 1006 | { 1007 | if( iter == NULL ) error("ri_del: NULL iterator."); 1008 | free( (void *) iter ); 1009 | } 1010 | 1011 | /*----------------------------------------------------------------------------*/ 1012 | /* 1013 | Check if the iterator finished the full iteration. 1014 | */ 1015 | static int ri_end(rect_iter * i) 1016 | { 1017 | if( i == NULL ) error("ri_end: NULL iterator."); 1018 | return (double)(i->x) > i->vx[2]; 1019 | } 1020 | 1021 | /*----------------------------------------------------------------------------*/ 1022 | /* 1023 | Increment a rectangle iterator. 1024 | */ 1025 | static void ri_inc(rect_iter * i) 1026 | { 1027 | if( i == NULL ) error("ri_inc: NULL iterator."); 1028 | 1029 | if( (double) (i->x) <= i->vx[2] ) i->y++; 1030 | 1031 | while( (double) (i->y) > i->ye && (double) (i->x) <= i->vx[2] ) 1032 | { 1033 | /* new x */ 1034 | i->x++; 1035 | 1036 | if( (double) (i->x) > i->vx[2] ) return; /* end of iteration */ 1037 | 1038 | /* update lower y limit for the line */ 1039 | if( (double) i->x < i->vx[3] ) 1040 | i->ys = inter_low((double)i->x,i->vx[0],i->vy[0],i->vx[3],i->vy[3]); 1041 | else i->ys = inter_low((double)i->x,i->vx[3],i->vy[3],i->vx[2],i->vy[2]); 1042 | 1043 | /* update upper y limit for the line */ 1044 | if( (double)i->x < i->vx[1] ) 1045 | i->ye = inter_hi((double)i->x,i->vx[0],i->vy[0],i->vx[1],i->vy[1]); 1046 | else i->ye = inter_hi((double)i->x,i->vx[1],i->vy[1],i->vx[2],i->vy[2]); 1047 | 1048 | /* new y */ 1049 | i->y = (int) ceil(i->ys); 1050 | } 1051 | } 1052 | 1053 | /*----------------------------------------------------------------------------*/ 1054 | /* 1055 | Create and initialize a rectangle iterator. 1056 | */ 1057 | static rect_iter * ri_ini(struct rect * r) 1058 | { 1059 | double vx[4],vy[4]; 1060 | int n,offset; 1061 | rect_iter * i; 1062 | 1063 | if( r == NULL ) error("ri_ini: invalid rectangle."); 1064 | 1065 | i = (rect_iter *) malloc(sizeof(rect_iter)); 1066 | if( i == NULL ) error("ri_ini: Not enough memory."); 1067 | 1068 | vx[0] = r->x1 - r->dy * r->width / 2.0; 1069 | vy[0] = r->y1 + r->dx * r->width / 2.0; 1070 | vx[1] = r->x2 - r->dy * r->width / 2.0; 1071 | vy[1] = r->y2 + r->dx * r->width / 2.0; 1072 | vx[2] = r->x2 + r->dy * r->width / 2.0; 1073 | vy[2] = r->y2 - r->dx * r->width / 2.0; 1074 | vx[3] = r->x1 + r->dy * r->width / 2.0; 1075 | vy[3] = r->y1 - r->dx * r->width / 2.0; 1076 | 1077 | if( r->x1 < r->x2 && r->y1 <= r->y2 ) offset = 0; 1078 | else if( r->x1 >= r->x2 && r->y1 < r->y2 ) offset = 1; 1079 | else if( r->x1 > r->x2 && r->y1 >= r->y2 ) offset = 2; 1080 | else offset = 3; 1081 | 1082 | for(n=0; n<4; n++) 1083 | { 1084 | i->vx[n] = vx[(offset+n)%4]; 1085 | i->vy[n] = vy[(offset+n)%4]; 1086 | } 1087 | 1088 | /* starting point */ 1089 | i->x = (int) ceil(i->vx[0]) - 1; 1090 | i->y = (int) ceil(i->vy[0]); 1091 | i->ys = i->ye = -DBL_MAX; 1092 | 1093 | /* advance to the first point */ 1094 | ri_inc(i); 1095 | 1096 | return i; 1097 | } 1098 | 1099 | /*----------------------------------------------------------------------------*/ 1100 | /* 1101 | Compute a rectangle's NFA value. 1102 | */ 1103 | static double rect_nfa(struct rect * rec, image_double angles, double logNT) 1104 | { 1105 | rect_iter * i; 1106 | int pts = 0; 1107 | int alg = 0; 1108 | 1109 | if( rec == NULL ) error("rect_nfa: invalid rectangle."); 1110 | if( angles == NULL ) error("rect_nfa: invalid 'angles'."); 1111 | 1112 | for(i=ri_ini(rec); !ri_end(i); ri_inc(i)) 1113 | if( i->x >= 0 && i->y >= 0 && 1114 | i->x < (int) angles->xsize && i->y < (int) angles->ysize ) 1115 | { 1116 | ++pts; 1117 | if( isaligned(i->x, i->y, angles, rec->theta, rec->prec) ) ++alg; 1118 | } 1119 | ri_del(i); 1120 | 1121 | return nfa(pts,alg,rec->p,logNT); 1122 | } 1123 | 1124 | 1125 | /*----------------------------------------------------------------------------*/ 1126 | /*---------------------------------- Regions ---------------------------------*/ 1127 | /*----------------------------------------------------------------------------*/ 1128 | 1129 | /*----------------------------------------------------------------------------*/ 1130 | /* 1131 | Compute a region's angle. 1132 | */ 1133 | static double get_theta( struct point * reg, int reg_size, double x, double y, 1134 | image_double modgrad, double reg_angle, double prec ) 1135 | { 1136 | double lambda1,lambda2,tmp,theta,weight,sum; 1137 | double Ixx = 0.0; 1138 | double Iyy = 0.0; 1139 | double Ixy = 0.0; 1140 | int i; 1141 | 1142 | /* check parameters */ 1143 | if( reg == NULL ) error("get_theta: invalid region."); 1144 | if( reg_size <= 1 ) error("get_theta: region size <= 1."); 1145 | if( modgrad == NULL || modgrad->data == NULL ) 1146 | error("get_theta: invalid 'modgrad'."); 1147 | if( prec < 0.0 ) error("get_theta: 'prec' must be positive."); 1148 | 1149 | /*----------- theta ---------------------------------------------------*/ 1150 | /* 1151 | Region inertia matrix A: 1152 | Ixx Ixy 1153 | Ixy Iyy 1154 | where 1155 | Ixx = \sum_i y_i^2 1156 | Iyy = \sum_i x_i^2 1157 | Ixy = -\sum_i x_i y_i 1158 | 1159 | lambda1 and lambda2 are the eigenvalues, with lambda1 >= lambda2. 1160 | They are found by solving the characteristic polynomial 1161 | det(\lambda I - A) = 0. 1162 | 1163 | To get the line segment direction we want to get the eigenvector of 1164 | the smaller eigenvalue. We have to solve a,b in: 1165 | a.Ixx + b.Ixy = a.lambda2 1166 | a.Ixy + b.Iyy = b.lambda2 1167 | We want the angle theta = atan(b/a). I can be computed with 1168 | any of the two equations: 1169 | theta = atan( (lambda2-Ixx) / Ixy ) 1170 | or 1171 | theta = atan( Ixy / (lambda2-Iyy) ) 1172 | 1173 | When |Ixx| > |Iyy| we use the first, otherwise the second 1174 | (just to get better numeric precision). 1175 | */ 1176 | sum = 0.0; 1177 | for(i=0; idata[ reg[i].x + reg[i].y * modgrad->xsize ]; 1180 | Ixx += ( (double) reg[i].y - y ) * ( (double) reg[i].y - y ) * weight; 1181 | Iyy += ( (double) reg[i].x - x ) * ( (double) reg[i].x - x ) * weight; 1182 | Ixy -= ( (double) reg[i].x - x ) * ( (double) reg[i].y - y ) * weight; 1183 | sum += weight; 1184 | } 1185 | if( sum <= 0.0 ) error("get_theta: weights sum less or equal to zero."); 1186 | Ixx /= sum; 1187 | Iyy /= sum; 1188 | Ixy /= sum; 1189 | lambda1 = ( Ixx + Iyy + sqrt( (Ixx-Iyy)*(Ixx-Iyy) + 4.0*Ixy*Ixy ) ) / 2.0; 1190 | lambda2 = ( Ixx + Iyy - sqrt( (Ixx-Iyy)*(Ixx-Iyy) + 4.0*Ixy*Ixy ) ) / 2.0; 1191 | if( fabs(lambda1) < fabs(lambda2) ) 1192 | { 1193 | fprintf(stderr,"Ixx %g Iyy %g Ixy %g lamb1 %g lamb2 %g - lamb1 < lamb2\n", 1194 | Ixx,Iyy,Ixy,lambda1,lambda2); 1195 | tmp = lambda1; 1196 | lambda1 = lambda2; 1197 | lambda2 = tmp; 1198 | } 1199 | 1200 | if( fabs(Ixx) > fabs(Iyy) ) 1201 | theta = atan2( lambda2-Ixx, Ixy ); 1202 | else 1203 | theta = atan2( Ixy, lambda2-Iyy ); 1204 | 1205 | /* The previous procedure don't cares about orientation, 1206 | so it could be wrong by 180 degrees. Here is corrected if necessary. */ 1207 | if( angle_diff(theta,reg_angle) > prec ) theta += M_PI; 1208 | 1209 | return theta; 1210 | } 1211 | 1212 | /*----------------------------------------------------------------------------*/ 1213 | /* 1214 | Computes a rectangle that covers a region of points. 1215 | */ 1216 | static void region2rect( struct point * reg, int reg_size, 1217 | image_double modgrad, double reg_angle, 1218 | double prec, double p, struct rect * rec ) 1219 | { 1220 | double x,y,dx,dy,l,w,theta,weight,sum,l_min,l_max,w_min,w_max; 1221 | int i; 1222 | 1223 | /* check parameters */ 1224 | if( reg == NULL ) error("region2rect: invalid region."); 1225 | if( reg_size <= 1 ) error("region2rect: region size <= 1."); 1226 | if( modgrad == NULL || modgrad->data == NULL ) 1227 | error("region2rect: invalid image 'modgrad'."); 1228 | if( rec == NULL ) error("region2rect: invalid 'rec'."); 1229 | 1230 | /* center */ 1231 | x = y = sum = 0.0; 1232 | for(i=0; idata[ reg[i].x + reg[i].y * modgrad->xsize ]; 1235 | x += (double) reg[i].x * weight; 1236 | y += (double) reg[i].y * weight; 1237 | sum += weight; 1238 | } 1239 | if( sum <= 0.0 ) error("region2rect: weights sum equal to zero."); 1240 | x /= sum; 1241 | y /= sum; 1242 | 1243 | /* theta */ 1244 | theta = get_theta(reg,reg_size,x,y,modgrad,reg_angle,prec); 1245 | 1246 | /* length and width */ 1247 | dx = cos(theta); 1248 | dy = sin(theta); 1249 | l_min = l_max = w_min = w_max = 0.0; 1250 | for(i=0; i l_max ) l_max = l; 1256 | if( l < l_min ) l_min = l; 1257 | if( w > w_max ) w_max = w; 1258 | if( w < w_min ) w_min = w; 1259 | } 1260 | 1261 | /* store values */ 1262 | rec->x1 = x + l_min * dx; 1263 | rec->y1 = y + l_min * dy; 1264 | rec->x2 = x + l_max * dx; 1265 | rec->y2 = y + l_max * dy; 1266 | rec->width = w_max - w_min; 1267 | rec->x = x; 1268 | rec->y = y; 1269 | rec->theta = theta; 1270 | rec->dx = dx; 1271 | rec->dy = dy; 1272 | rec->prec = prec; 1273 | rec->p = p; 1274 | 1275 | if( rec->width < 1.0 ) rec->width = 1.0; 1276 | } 1277 | 1278 | /*----------------------------------------------------------------------------*/ 1279 | /* 1280 | Found a region of points that share the same angle, up to a tolerance 'prec', 1281 | starting at point (x,y). 1282 | */ 1283 | static void region_grow( int x, int y, image_double angles, struct point * reg, 1284 | int * reg_size, double * reg_angle, image_char used, 1285 | double prec ) 1286 | { 1287 | double sumdx,sumdy; 1288 | int xx,yy,i; 1289 | 1290 | /* check parameters */ 1291 | if( x < 0 || y < 0 || x >= (int) angles->xsize || y >= (int) angles->ysize ) 1292 | error("region_grow: (x,y) out of the image."); 1293 | if( angles == NULL || angles->data == NULL ) 1294 | error("region_grow: invalid image 'angles'."); 1295 | if( reg == NULL ) error("region_grow: invalid 'reg'."); 1296 | if( reg_size == NULL ) error("region_grow: invalid pointer 'reg_size'."); 1297 | if( reg_angle == NULL ) error("region_grow: invalid pointer 'reg_angle'."); 1298 | if( used == NULL || used->data == NULL ) 1299 | error("region_grow: invalid image 'used'."); 1300 | 1301 | /* first point of the region */ 1302 | *reg_size = 1; 1303 | reg[0].x = x; 1304 | reg[0].y = y; 1305 | *reg_angle = angles->data[x+y*angles->xsize]; 1306 | sumdx = cos(*reg_angle); 1307 | sumdy = sin(*reg_angle); 1308 | used->data[x+y*used->xsize] = USED; 1309 | 1310 | /* try neighbors as new region points */ 1311 | for(i=0; i<*reg_size; i++) 1312 | for(xx=reg[i].x-1; xx<=reg[i].x+1; xx++) 1313 | for(yy=reg[i].y-1; yy<=reg[i].y+1; yy++) 1314 | if( xx>=0 && yy>=0 && xx<(int)used->xsize && yy<(int)used->ysize && 1315 | used->data[xx+yy*used->xsize] != USED && 1316 | isaligned(xx,yy,angles,*reg_angle,prec) ) 1317 | { 1318 | /* add point */ 1319 | used->data[xx+yy*used->xsize] = USED; 1320 | reg[*reg_size].x = xx; 1321 | reg[*reg_size].y = yy; 1322 | ++(*reg_size); 1323 | 1324 | /* update region's angle */ 1325 | sumdx += cos( angles->data[xx+yy*angles->xsize] ); 1326 | sumdy += sin( angles->data[xx+yy*angles->xsize] ); 1327 | *reg_angle = atan2(sumdy,sumdx); 1328 | } 1329 | } 1330 | 1331 | /*----------------------------------------------------------------------------*/ 1332 | /* 1333 | Try some rectangles variations to improve NFA value. 1334 | Only if the rectangle is not meaningful (i.e., log_nfa <= eps). 1335 | */ 1336 | static double rect_improve( struct rect * rec, image_double angles, 1337 | double logNT, double eps ) 1338 | { 1339 | struct rect r; 1340 | double log_nfa,log_nfa_new; 1341 | double delta = 0.5; 1342 | double delta_2 = delta / 2.0; 1343 | int n; 1344 | 1345 | log_nfa = rect_nfa(rec,angles,logNT); 1346 | 1347 | if( log_nfa > eps ) return log_nfa; 1348 | 1349 | /* try finer precisions */ 1350 | rect_copy(rec,&r); 1351 | for(n=0; n<5; n++) 1352 | { 1353 | r.p /= 2.0; 1354 | r.prec = r.p * M_PI; 1355 | log_nfa_new = rect_nfa(&r,angles,logNT); 1356 | if( log_nfa_new > log_nfa ) 1357 | { 1358 | log_nfa = log_nfa_new; 1359 | rect_copy(&r,rec); 1360 | } 1361 | } 1362 | 1363 | if( log_nfa > eps ) return log_nfa; 1364 | 1365 | /* try to reduce width */ 1366 | rect_copy(rec,&r); 1367 | for(n=0; n<5; n++) 1368 | { 1369 | if( (r.width - delta) >= 0.5 ) 1370 | { 1371 | r.width -= delta; 1372 | log_nfa_new = rect_nfa(&r,angles,logNT); 1373 | if( log_nfa_new > log_nfa ) 1374 | { 1375 | rect_copy(&r,rec); 1376 | log_nfa = log_nfa_new; 1377 | } 1378 | } 1379 | } 1380 | 1381 | if( log_nfa > eps ) return log_nfa; 1382 | 1383 | /* try to reduce one side of the rectangle */ 1384 | rect_copy(rec,&r); 1385 | for(n=0; n<5; n++) 1386 | { 1387 | if( (r.width - delta) >= 0.5 ) 1388 | { 1389 | r.x1 += -r.dy * delta_2; 1390 | r.y1 += r.dx * delta_2; 1391 | r.x2 += -r.dy * delta_2; 1392 | r.y2 += r.dx * delta_2; 1393 | r.width -= delta; 1394 | log_nfa_new = rect_nfa(&r,angles,logNT); 1395 | if( log_nfa_new > log_nfa ) 1396 | { 1397 | rect_copy(&r,rec); 1398 | log_nfa = log_nfa_new; 1399 | } 1400 | } 1401 | } 1402 | 1403 | if( log_nfa > eps ) return log_nfa; 1404 | 1405 | /* try to reduce the other side of the rectangle */ 1406 | rect_copy(rec,&r); 1407 | for(n=0; n<5; n++) 1408 | { 1409 | if( (r.width - delta) >= 0.5 ) 1410 | { 1411 | r.x1 -= -r.dy * delta_2; 1412 | r.y1 -= r.dx * delta_2; 1413 | r.x2 -= -r.dy * delta_2; 1414 | r.y2 -= r.dx * delta_2; 1415 | r.width -= delta; 1416 | log_nfa_new = rect_nfa(&r,angles,logNT); 1417 | if( log_nfa_new > log_nfa ) 1418 | { 1419 | rect_copy(&r,rec); 1420 | log_nfa = log_nfa_new; 1421 | } 1422 | } 1423 | } 1424 | 1425 | if( log_nfa > eps ) return log_nfa; 1426 | 1427 | /* try even finer precisions */ 1428 | rect_copy(rec,&r); 1429 | for(n=0; n<5; n++) 1430 | { 1431 | r.p /= 2.0; 1432 | r.prec = r.p * M_PI; 1433 | log_nfa_new = rect_nfa(&r,angles,logNT); 1434 | if( log_nfa_new > log_nfa ) 1435 | { 1436 | log_nfa = log_nfa_new; 1437 | rect_copy(&r,rec); 1438 | } 1439 | } 1440 | 1441 | return log_nfa; 1442 | } 1443 | 1444 | /*----------------------------------------------------------------------------*/ 1445 | /* 1446 | Reduce the region size, by elimination the points far from the 1447 | starting point, until that leads to rectangle with the right 1448 | density of region points or to discard the region if too small. 1449 | */ 1450 | static int reduce_region_radius( struct point * reg, int * reg_size, 1451 | image_double modgrad, double reg_angle, 1452 | double prec, double p, struct rect * rec, 1453 | image_char used, image_double angles, 1454 | double density_th, double logNT, double eps ) 1455 | { 1456 | double density,rad1,rad2,rad,xc,yc,log_nfa; 1457 | int i; 1458 | 1459 | /* check parameters */ 1460 | if( reg == NULL ) error("refine: invalid pointer 'reg'."); 1461 | if( reg_size == NULL ) error("refine: invalid pointer 'reg_size'."); 1462 | if( prec < 0.0 ) error("refine: 'prec' must be positive."); 1463 | if( rec == NULL ) error("refine: invalid pointer 'rec'."); 1464 | if( used == NULL || used->data == NULL ) 1465 | error("refine: invalid image 'used'."); 1466 | if( angles == NULL || angles->data == NULL ) 1467 | error("refine: invalid image 'angles'."); 1468 | 1469 | /* compute region points density */ 1470 | density = (double) *reg_size / 1471 | ( dist(rec->x1,rec->y1,rec->x2,rec->y2) * rec->width ); 1472 | 1473 | if( density >= density_th ) return TRUE; 1474 | 1475 | /* compute region radius */ 1476 | xc = (double) reg[0].x; 1477 | yc = (double) reg[0].y; 1478 | rad1 = dist( xc, yc, rec->x1, rec->y1 ); 1479 | rad2 = dist( xc, yc, rec->x2, rec->y2 ); 1480 | rad = rad1 > rad2 ? rad1 : rad2; 1481 | 1482 | while( density < density_th ) 1483 | { 1484 | rad *= 0.75; 1485 | 1486 | /* remove points from the region and update 'used' map */ 1487 | for(i=0; i<*reg_size; i++) 1488 | if( dist( xc, yc, (double) reg[i].x, (double) reg[i].y ) > rad ) 1489 | { 1490 | /* point not kept, mark it as NOTUSED */ 1491 | used->data[ reg[i].x + reg[i].y * used->xsize ] = NOTUSED; 1492 | /* remove point from the region */ 1493 | reg[i].x = reg[*reg_size-1].x; /* if i==*reg_size-1 copy itself */ 1494 | reg[i].y = reg[*reg_size-1].y; 1495 | --(*reg_size); 1496 | --i; /* to avoid skipping one point */ 1497 | } 1498 | 1499 | /* reject if the region is too small. 1500 | 2 is the minimal region size for 'region2rect' to work. */ 1501 | if( *reg_size < 2 ) return FALSE; 1502 | 1503 | /* re-compute rectangle */ 1504 | region2rect(reg,*reg_size,modgrad,reg_angle,prec,p,rec); 1505 | 1506 | /* try to improve the rectangle and compute NFA */ 1507 | log_nfa = rect_improve(rec,angles,logNT,eps); 1508 | 1509 | /* re-compute region points density */ 1510 | density = (double) *reg_size / 1511 | ( dist(rec->x1,rec->y1,rec->x2,rec->y2) * rec->width ); 1512 | } 1513 | 1514 | /* if the final rectangle is meaningful accept, otherwise reject */ 1515 | if( log_nfa > eps ) return TRUE; 1516 | else return FALSE; 1517 | } 1518 | 1519 | /*----------------------------------------------------------------------------*/ 1520 | /* 1521 | Refine a rectangle. For that, an estimation of the angle tolerance is 1522 | performed by the standard deviation of the angle at points near the 1523 | region's starting point. Then, a new region is grown starting from the 1524 | same point, but using the estimated angle tolerance. 1525 | If this fails to produce a rectangle with the right density of 1526 | region points, 'reduce_region_radius' is called to try to 1527 | satisfy this condition. 1528 | */ 1529 | static int refine( struct point * reg, int * reg_size, image_double modgrad, 1530 | double reg_angle, double prec, double p, struct rect * rec, 1531 | image_char used, image_double angles, double density_th, 1532 | double logNT, double eps ) 1533 | { 1534 | double angle,ang_d,mean_angle,tau,density,xc,yc,ang_c,sum,s_sum,log_nfa; 1535 | int i,n; 1536 | 1537 | /* check parameters */ 1538 | if( reg == NULL ) error("refine: invalid pointer 'reg'."); 1539 | if( reg_size == NULL ) error("refine: invalid pointer 'reg_size'."); 1540 | if( prec < 0.0 ) error("refine: 'prec' must be positive."); 1541 | if( rec == NULL ) error("refine: invalid pointer 'rec'."); 1542 | if( used == NULL || used->data == NULL ) 1543 | error("refine: invalid image 'used'."); 1544 | if( angles == NULL || angles->data == NULL ) 1545 | error("refine: invalid image 'angles'."); 1546 | 1547 | /* compute region points density */ 1548 | density = (double) *reg_size / 1549 | ( dist(rec->x1,rec->y1,rec->x2,rec->y2) * rec->width ); 1550 | 1551 | if( density >= density_th ) return TRUE; 1552 | 1553 | /*------ First try: reduce angle tolerance ------*/ 1554 | 1555 | /* compute the new mean angle and tolerance */ 1556 | xc = (double) reg[0].x; 1557 | yc = (double) reg[0].y; 1558 | ang_c = angles->data[ reg[0].x + reg[0].y * angles->xsize ]; 1559 | sum = s_sum = 0.0; 1560 | n = 0; 1561 | for(i=0; i<*reg_size; i++) 1562 | { 1563 | used->data[ reg[i].x + reg[i].y * used->xsize ] = NOTUSED; 1564 | if( dist( xc, yc, (double) reg[i].x, (double) reg[i].y ) < rec->width ) 1565 | { 1566 | angle = angles->data[ reg[i].x + reg[i].y * angles->xsize ]; 1567 | ang_d = angle_diff_signed(angle,ang_c); 1568 | sum += ang_d; 1569 | s_sum += ang_d * ang_d; 1570 | ++n; 1571 | } 1572 | } 1573 | mean_angle = sum / (double) n; 1574 | tau = 2.0 * sqrt( (s_sum - 2.0 * mean_angle * sum) / (double) n 1575 | + mean_angle*mean_angle ); /* 2 * standard deviation */ 1576 | 1577 | /* find a new region from the same starting point and new angle tolerance */ 1578 | region_grow(reg[0].x,reg[0].y,angles,reg,reg_size,®_angle,used,tau); 1579 | 1580 | /* if the region is too small, reject */ 1581 | if( *reg_size < 2 ) return FALSE; 1582 | 1583 | /* re-compute rectangle */ 1584 | region2rect(reg,*reg_size,modgrad,reg_angle,prec,p,rec); 1585 | 1586 | /* try to improve the rectangle and compute NFA */ 1587 | log_nfa = rect_improve(rec,angles,logNT,eps); 1588 | 1589 | /* re-compute region points density */ 1590 | density = (double) *reg_size / 1591 | ( dist(rec->x1,rec->y1,rec->x2,rec->y2) * rec->width ); 1592 | 1593 | /*------ Second try: reduce region radius ------*/ 1594 | if( density < density_th ) 1595 | return reduce_region_radius( reg, reg_size, modgrad, reg_angle, prec, p, 1596 | rec, used, angles, density_th, logNT, eps ); 1597 | 1598 | /* if the final rectangle is meaningful accept, otherwise reject */ 1599 | if( log_nfa > eps ) return TRUE; 1600 | else return FALSE; 1601 | } 1602 | 1603 | 1604 | /*----------------------------------------------------------------------------*/ 1605 | /*-------------------------- Line Segment Detector ---------------------------*/ 1606 | /*----------------------------------------------------------------------------*/ 1607 | 1608 | /*----------------------------------------------------------------------------*/ 1609 | /* 1610 | LSD full interface 1611 | */ 1612 | ntuple_list LineSegmentDetection( image_double image, double scale, 1613 | double sigma_scale, double quant, 1614 | double ang_th, double eps, double density_th, 1615 | int n_bins, double max_grad, 1616 | image_int * region ) 1617 | { 1618 | ntuple_list out = new_ntuple_list(5); 1619 | image_double scaled_image,angles,modgrad; 1620 | image_char used; 1621 | struct coorlist * list_p; 1622 | void * mem_p; 1623 | struct rect rec; 1624 | struct point * reg; 1625 | int reg_size,min_reg_size,i; 1626 | unsigned int xsize,ysize; 1627 | double rho,reg_angle,prec,p,log_nfa,logNT; 1628 | int ls_count = 0; /* line segments are numbered 1,2,3,... */ 1629 | 1630 | 1631 | /* check parameters */ 1632 | if( image==NULL || image->data==NULL || image->xsize<=0 || image->ysize<=0 ) 1633 | error("invalid image input."); 1634 | if( scale <= 0.0 ) error("'scale' value must be positive."); 1635 | if( sigma_scale <= 0.0 ) error("'sigma_scale' value must be positive."); 1636 | if( quant < 0.0 ) error("'quant' value must be positive."); 1637 | if( ang_th <= 0.0 || ang_th >= 180.0 ) 1638 | error("'ang_th' value must be in the range (0,180)."); 1639 | if( density_th < 0.0 || density_th > 1.0 ) 1640 | error("'density_th' value must be in the range [0,1]."); 1641 | if( n_bins <= 0 ) error("'n_bins' value must be positive."); 1642 | if( max_grad <= 0.0 ) error("'max_grad' value must be positive."); 1643 | 1644 | 1645 | /* angle tolerance */ 1646 | prec = M_PI * ang_th / 180.0; 1647 | p = ang_th / 180.0; 1648 | rho = quant / sin(prec); /* gradient magnitude threshold */ 1649 | 1650 | 1651 | /* scale image (if necessary) and compute angle at each pixel */ 1652 | if( scale != 1.0 ) 1653 | { 1654 | scaled_image = gaussian_sampler( image, scale, sigma_scale ); 1655 | angles = ll_angle( scaled_image, rho, &list_p, &mem_p, 1656 | &modgrad, (unsigned int) n_bins, max_grad ); 1657 | free_image_double(scaled_image); 1658 | } 1659 | else 1660 | angles = ll_angle( image, rho, &list_p, &mem_p, &modgrad, 1661 | (unsigned int) n_bins, max_grad ); 1662 | xsize = angles->xsize; 1663 | ysize = angles->ysize; 1664 | logNT = 5.0 * ( log10( (double) xsize ) + log10( (double) ysize ) ) / 2.0; 1665 | min_reg_size = (int) (-logNT/log10(p)); /* minimal number of points in region 1666 | that can give a meaningful event */ 1667 | 1668 | 1669 | /* initialize some structures */ 1670 | if( region != NULL ) /* image to output pixel region number, if asked */ 1671 | *region = new_image_int_ini(angles->xsize,angles->ysize,0); 1672 | used = new_image_char_ini(xsize,ysize,NOTUSED); 1673 | reg = (struct point *) calloc(xsize * ysize, sizeof(struct point)); 1674 | if( reg == NULL ) error("not enough memory!"); 1675 | 1676 | 1677 | /* search for line segments */ 1678 | for(;list_p; list_p = list_p->next ) 1679 | if( used->data[ list_p->x + list_p->y * used->xsize ] == NOTUSED && 1680 | angles->data[ list_p->x + list_p->y * angles->xsize ] != NOTDEF ) 1681 | /* there is no risk of double comparison problem here 1682 | because we are only interested in the exact NOTDEF value */ 1683 | { 1684 | /* find the region of connected point and ~equal angle */ 1685 | region_grow( list_p->x, list_p->y, angles, reg, ®_size, 1686 | ®_angle, used, prec ); 1687 | 1688 | /* reject small regions */ 1689 | if( reg_size < min_reg_size ) continue; 1690 | 1691 | /* construct rectangular approximation for the region */ 1692 | region2rect(reg,reg_size,modgrad,reg_angle,prec,p,&rec); 1693 | 1694 | /* Check if the rectangle exceeds the minimal density of 1695 | region points. If not, try to improve the region. 1696 | The rectangle will be rejected if the final one does 1697 | not fulfill the minimal density condition. 1698 | This is an addition to the original LSD algorithm published in 1699 | "LSD: A Fast Line Segment Detector with a False Detection Control" 1700 | by R. Grompone von Gioi, J. Jakubowicz, J.M. Morel, and G. Randall. 1701 | The original algorithm is obtained with density_th = 0.0. 1702 | */ 1703 | if( !refine( reg, ®_size, modgrad, reg_angle, prec, p, 1704 | &rec, used, angles, density_th, logNT, eps ) ) continue; 1705 | 1706 | /* compute NFA value */ 1707 | log_nfa = rect_improve(&rec,angles,logNT,eps); 1708 | if( log_nfa <= eps ) continue; 1709 | 1710 | /* A New Line Segment was found! */ 1711 | ++ls_count; /* increase line segment counter */ 1712 | 1713 | /* 1714 | The gradient was computed with a 2x2 mask, its value corresponds to 1715 | points with an offset of (0.5,0.5), that should be added to output. 1716 | The coordinates origin is at the center of pixel (0,0). 1717 | */ 1718 | rec.x1 += 0.5; rec.y1 += 0.5; 1719 | rec.x2 += 0.5; rec.y2 += 0.5; 1720 | 1721 | /* scale the result values if a subsampling was performed */ 1722 | if( scale != 1.0 ) 1723 | { 1724 | rec.x1 /= scale; rec.y1 /= scale; 1725 | rec.x2 /= scale; rec.y2 /= scale; 1726 | rec.width /= scale; 1727 | } 1728 | 1729 | /* add line segment found to output */ 1730 | add_5tuple(out, rec.x1, rec.y1, rec.x2, rec.y2, rec.width); 1731 | 1732 | /* add region number to 'region' image if needed */ 1733 | if( region != NULL ) 1734 | for(i=0; idata[reg[i].x+reg[i].y*(*region)->xsize] = ls_count; 1736 | } 1737 | 1738 | 1739 | /* free memory */ 1740 | free_image_double(angles); 1741 | free_image_double(modgrad); 1742 | free_image_char(used); 1743 | free( (void *) reg ); 1744 | free( (void *) mem_p ); 1745 | 1746 | return out; 1747 | } 1748 | 1749 | /*----------------------------------------------------------------------------*/ 1750 | /* 1751 | LSD Simple Interface 1752 | */ 1753 | ntuple_list lsd(image_double image) 1754 | { 1755 | /* LSD parameters */ 1756 | // double scale = 0.8; /* Scale the image by Gaussian filter to 'scale'. */ 1757 | // double sigma_scale = 0.6; /* Sigma for Gaussian filter is computed as 1758 | // sigma = sigma_scale/scale. */ 1759 | // double quant = 2.0; /* Bound to the quantization error on the 1760 | // gradient norm. */ 1761 | // double ang_th = 22.5; /* Gradient angle tolerance in degrees. */ 1762 | // double eps = 0.0; /* Detection threshold, -log10(NFA). */ 1763 | // double density_th = 0.7; /* Minimal density of region points in rectangle. */ 1764 | // int n_bins = 1024; /* Number of bins in pseudo-ordering of gradient 1765 | // modulus. */ 1766 | //double max_grad = 255.0; /* Gradient modulus in the highest bin. The 1767 | // default value corresponds to the highest 1768 | // gradient modulus on images with gray 1769 | // levels in [0,255]. 1770 | // */ 1771 | 1772 | double scale = 0.8; /* Scale the image by Gaussian filter to 'scale'. */ 1773 | double sigma_scale = 0.6; /* Sigma for Gaussian filter is computed as 1774 | sigma = sigma_scale/scale. */ 1775 | double quant = 2.0; /* Bound to the quantization error on the 1776 | gradient norm. */ 1777 | double ang_th = 22.5; /* Gradient angle tolerance in degrees. */ 1778 | double eps = 0.0; /* Detection threshold, -log10(NFA). */ 1779 | double density_th = 0.7; /* Minimal density of region points in rectangle. */ 1780 | int n_bins = 1024; /* Number of bins in pseudo-ordering of gradient 1781 | modulus. */ 1782 | double max_grad = 255.0; /* Gradient modulus in the highest bin. The 1783 | default value corresponds to the highest 1784 | gradient modulus on images with gray 1785 | levels in [0,255]. */ 1786 | 1787 | return LineSegmentDetection( image, scale, sigma_scale, quant, ang_th, eps, 1788 | density_th, n_bins, max_grad, NULL ); 1789 | } 1790 | /*----------------------------------------------------------------------------*/ 1791 | -------------------------------------------------------------------------------- /TestLMDll/TestLMDll/lsd.h: -------------------------------------------------------------------------------- 1 | /*---------------------------------------------------------------------------- 2 | 3 | LSD - Line Segment Detector on digital images 4 | 5 | Copyright 2007,2008,2009,2010 rafael grompone von gioi (grompone@gmail.com) 6 | 7 | This program is free software: you can redistribute it and/or modify 8 | it under the terms of the GNU Affero General Public License as 9 | published by the Free Software Foundation, either version 3 of the 10 | License, or (at your option) any later version. 11 | 12 | This program is distributed in the hope that it will be useful, 13 | but WITHOUT ANY WARRANTY; without even the implied warranty of 14 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 15 | GNU Affero General Public License for more details. 16 | 17 | You should have received a copy of the GNU Affero General Public License 18 | along with this program. If not, see . 19 | 20 | ----------------------------------------------------------------------------*/ 21 | #ifndef LSD_HEADER 22 | #define LSD_HEADER 23 | 24 | 25 | /*----------------------------------------------------------------------------*/ 26 | /*----------------------- 'list of n-tuple' data type ------------------------*/ 27 | /*----------------------------------------------------------------------------*/ 28 | 29 | /* 30 | The i component, of the n-tuple number j, of an n-tuple list 'ntl' 31 | is accessed with: 32 | 33 | ntl->values[ i + j * ntl->dim ] 34 | 35 | The dimension of the n-tuple (n) is: 36 | 37 | ntl->dim 38 | 39 | The number of number of n-tuples in the list is: 40 | 41 | ntl->size 42 | 43 | The maximum number of n-tuples that can be stored in the 44 | list with the allocated memory at a given time is given by: 45 | 46 | ntl->max_size 47 | */ 48 | typedef struct ntuple_list_s 49 | { 50 | unsigned int size; 51 | unsigned int max_size; 52 | unsigned int dim; 53 | double * values; 54 | } * ntuple_list; 55 | 56 | void free_ntuple_list(ntuple_list in); 57 | ntuple_list new_ntuple_list(unsigned int dim); 58 | 59 | 60 | /*----------------------------------------------------------------------------*/ 61 | /*----------------------------- Image Data Types -----------------------------*/ 62 | /*----------------------------------------------------------------------------*/ 63 | /* 64 | The pixel value at (x,y) is accessed by: 65 | 66 | image->data[ x + y * image->xsize ] 67 | 68 | with x and y integer. 69 | */ 70 | 71 | /*----------------------------------------------------------------------------*/ 72 | /* 73 | char image data type 74 | */ 75 | typedef struct image_char_s 76 | { 77 | unsigned char * data; 78 | unsigned int xsize,ysize; 79 | } * image_char; 80 | 81 | void free_image_char(image_char i); 82 | image_char new_image_char(unsigned int xsize, unsigned int ysize); 83 | image_char new_image_char_ini( unsigned int xsize, unsigned int ysize, 84 | unsigned char fill_value ); 85 | 86 | /*----------------------------------------------------------------------------*/ 87 | /* 88 | int image data type 89 | */ 90 | typedef struct image_int_s 91 | { 92 | int * data; 93 | unsigned int xsize,ysize; 94 | } * image_int; 95 | 96 | void free_image_int(image_int i); 97 | image_int new_image_int(unsigned int xsize, unsigned int ysize); 98 | image_int new_image_int_ini( unsigned int xsize, unsigned int ysize, 99 | int fill_value ); 100 | 101 | /*----------------------------------------------------------------------------*/ 102 | /* 103 | double image data type 104 | */ 105 | typedef struct image_double_s 106 | { 107 | double * data; 108 | unsigned int xsize,ysize; 109 | } * image_double; 110 | 111 | void free_image_double(image_double i); 112 | image_double new_image_double(unsigned int xsize, unsigned int ysize); 113 | image_double new_image_double_ini( unsigned int xsize, unsigned int ysize, 114 | double fill_value ); 115 | 116 | 117 | /*----------------------------------------------------------------------------*/ 118 | /*-------------------------- Line Segment Detector ---------------------------*/ 119 | /*----------------------------------------------------------------------------*/ 120 | 121 | /*----------------------------------------------------------------------------*/ 122 | /* LSD Full Interface */ 123 | /*----------------------------------------------------------------------------*/ 124 | /* 125 | Input: 126 | 127 | image: Input image 128 | 129 | scale: When different than 1.0, LSD will scale the image by 130 | Gaussian filtering. 131 | Example: is scale=0.8, the input image will be subsampled 132 | to 80% of its size, and then the line segment detector 133 | will be applied. 134 | Suggested value: 0.8 135 | 136 | sigma_scale: When scale!=1.0, the sigma of the Gaussian filter is: 137 | sigma = sigma_scale / scale, if scale < 1.0 138 | sigma = sigma_scale, if scale >= 1.0 139 | Suggested value: 0.6 140 | 141 | quant: Bound to the quantization error on the gradient norm. 142 | Example: if gray level is quantized to integer steps, 143 | the gradient (computed by finite differences) error 144 | due to quantization will be bounded by 2.0, as the 145 | worst case is when the error are 1 and -1, that 146 | gives an error of 2.0. 147 | Suggested value: 2.0 148 | 149 | ang_th: Gradient angle tolerance in the region growing 150 | algorithm, in degrees. 151 | Suggested value: 22.5 152 | 153 | eps: Detection threshold, -log10(NFA). 154 | The bigger, the more strict the detector is, 155 | and will result in less detections. 156 | (Note that the 'minus sign' makes that this 157 | behavior is opposite to the one of NFA.) 158 | The value -log10(NFA) is equivalent but more 159 | intuitive than NFA: 160 | -1.0 corresponds to 10 mean false alarms 161 | 0.0 corresponds to 1 mean false alarm 162 | 1.0 corresponds to 0.1 mean false alarms 163 | 2.0 corresponds to 0.01 mean false alarms 164 | Suggested value: 0.0 165 | 166 | density_th: Minimal proportion of region points in a rectangle. 167 | Suggested value: 0.7 168 | 169 | n_bins: Number of bins used in the pseudo-ordering of gradient 170 | modulus. 171 | Suggested value: 1024 172 | 173 | max_grad: Gradient modulus in the highest bin. For example, 174 | for images with integer gray levels in [0,255], 175 | the maximum possible gradient value is 255.0. 176 | Suggested value: 255.0 177 | 178 | region: Optional output: an int image where the pixels used 179 | in some line support region are marked. Unused pixels 180 | have the value '0' while the used ones have the 181 | number of the line segment, numbered 1,2,3,... If desired, 182 | a non NULL pointer to an image_int should be used. 183 | The resulting image has the size of the image used 184 | for the processing, that is, the size of the input 185 | image scaled by the given factor 'scale'. 186 | Suggested value: NULL 187 | 188 | Return value: A 5-tuple list, where each 5-tuple corresponds to a 189 | detected line segment. The five values are: 190 | x1,y1,x2,y2,width 191 | for a line segment from (x1,y1) to (x2,y2) and 192 | a width 'width'. 193 | */ 194 | ntuple_list LineSegmentDetection( image_double image, double scale, 195 | double sigma_scale, double quant, 196 | double ang_th, double eps, double density_th, 197 | int n_bins, double max_grad, 198 | image_int * region ); 199 | 200 | /*----------------------------------------------------------------------------*/ 201 | /* LSD Simple Interface */ 202 | /*----------------------------------------------------------------------------*/ 203 | /* 204 | input: an image 205 | output: a 5-tuple list of detected line segments. 206 | */ 207 | ntuple_list lsd(image_double image); 208 | 209 | 210 | #endif /* !LSD_HEADER */ 211 | /*----------------------------------------------------------------------------*/ 212 | -------------------------------------------------------------------------------- /TestLMDll/TestLMDll/main.cpp: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/dlut-dimt/LineMatching/e05eb15c06303d724b9334f96ab2c6deb723deb2/TestLMDll/TestLMDll/main.cpp -------------------------------------------------------------------------------- /addpointsnearby.m: -------------------------------------------------------------------------------- 1 | 2 | function [canlines] = addpointsnearby(lines,pointlist,sublinds,charap) 3 | 4 | canlines=lines(sublinds); 5 | len=length(sublinds); 6 | for i=1:len 7 | 8 | [canlines(i).intsect1, canlines(i).intsect2] = get2imps(sublinds(i),lines,pointlist); 9 | 10 | [canlines(i).pleft, canlines(i).pright]=addcharapsrect(lines(sublinds(i)),charap); 11 | end 12 | 13 | end 14 | 15 | 16 | function [p1,p2]=get2imps(lind,lines,pointlist) 17 | 18 | subline=lines(lind); 19 | lnum=length(subline); 20 | p1=zeros(lnum,2); 21 | p2=zeros(lnum,2); 22 | [pinds]=getpoints(lind,pointlist); 23 | n=length(pinds); 24 | 25 | 26 | points=zeros(n,2); 27 | dist1=zeros(1,n); 28 | dist2=zeros(1,n); 29 | for j=1:n 30 | p=pointlist(pinds(j)).point; 31 | points(j,:)=p; 32 | dist1(j)=norm(p-subline.point1); 33 | dist2(j)=norm(p-subline.point2); 34 | end 35 | 36 | [d1,id1]=min(dist1); 37 | [d2,id2]=min(dist2); 38 | if isempty(d1) 39 | d1=Inf; 40 | end 41 | if isempty(d2) 42 | d2=Inf; 43 | end 44 | linelen=norm(subline.point1-subline.point2)/10; 45 | if d1>linelen &&d2<=linelen 46 | p1 = subline.point1; 47 | p2=points(id2,:); 48 | elseif d2>linelen && d1<=linelen 49 | p2 = subline.point2; 50 | p1=points(id1,:); 51 | elseif d1<=linelen &&d2<=linelen 52 | p1=points(id1,:); 53 | p2=points(id2,:); 54 | else 55 | p1 = subline.point1; 56 | p2 = subline.point2; 57 | end 58 | mid=(subline.point1+subline.point2)/2; 59 | endp= mid + subline.gradient; 60 | cp=crossproduct(p1,endp,mid); 61 | if cp<0 62 | t=p1; 63 | p1=p2; 64 | p2=t; 65 | end 66 | end 67 | 68 | function [pleft, pright] = addcharapsrect(line,charap) 69 | d2line=2; 70 | d2midline=0.5; 71 | pleft=[]; 72 | pright=[]; 73 | mid=(line.point1+line.point2)/2; 74 | pg=mid+line.gradient; 75 | linelen= norm(line.point1-line.point2); 76 | midline=line; 77 | if line.k ~=0 78 | midline.k = -1/line.k; 79 | if line.k == Inf 80 | midline.b=line.point1(1); 81 | else 82 | midline.b=(line.k * mid(2) + mid(1))/line.k; 83 | end 84 | else 85 | midline.k=Inf; 86 | midline.b=Inf; 87 | end 88 | pointnum=size(charap,1); 89 | for i=1:pointnum 90 | p=charap(i,:); 91 | if disp2line(p,line) < d2line * linelen && disp2line(p,midline) < d2midline * linelen 92 | if sameside(line,p,pg) 93 | pright=[ pright; [p i] ]; 94 | else 95 | pleft=[ pleft; [p i] ]; 96 | end 97 | end 98 | end 99 | end 100 | 101 | function dis=disp2line(point,line) 102 | k=line.k; 103 | b=line.b; 104 | if k~=Inf 105 | dis=abs(k*point(1)-point(2)+b)/sqrt(k*k+1); 106 | else 107 | dis = abs(point(1)-line.point1(1)); 108 | end 109 | end 110 | -------------------------------------------------------------------------------- /charanums5.m: -------------------------------------------------------------------------------- 1 | 2 | function CN=charanums5(a,b,c,d,e,f,g,h,i,j) 3 | CN=((a*d - b*c - a*j + b*i + c*j - d*i)*(a*f - b*e - a*h + b*g + e*h - f*g)*(c*h - d*g - c*j + d*i + g*j - h*i))/... 4 | ((a*d - b*c - a*h + b*g + c*h - d*g)*(a*h - b*g - a*j + b*i + g*j - h*i)*(c*f - d*e - c*j + d*i + e*j - f*i)); 5 | end 6 | 7 | % function CN=charanums5(p5) 8 | % p5=[p5,[1;1;1;1;1]]; 9 | % cn51=1-det(p5([1,3,5],:))*det(p5([2,4,5],:))/det(p5([1,4,5],:))/det(p5([2,3,5],:)); 10 | % cn52=det(p5([2,3,4],:))*det(p5([1,4,5],:))/det(p5([1,3,4],:))/det(p5([2,4,5],:))-1; 11 | % CN=cn51/cn52; 12 | % end 13 | % -------------------------------------------------------------------------------- /crossproduct.m: -------------------------------------------------------------------------------- 1 | 2 | function cp=crossproduct(p1,p2,o) 3 | % if~(exist('o','var')) 4 | % o=[0 0]; 5 | % end 6 | cp=(p1(1)-o(1))*(p2(2)-o(2))-(p2(1)-o(1))*(p1(2)-o(2)); 7 | 8 | end -------------------------------------------------------------------------------- /distline.p: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/dlut-dimt/LineMatching/e05eb15c06303d724b9334f96ab2c6deb723deb2/distline.p -------------------------------------------------------------------------------- /getHpoints1L.m: -------------------------------------------------------------------------------- 1 | 2 | function [p1,p2] = getHpoints1L(line1,line2,side) 3 | minnum=10; 4 | p1=[];p2=[]; 5 | if side == 1 6 | [C,ind1,ind2]=intersect( line1.pleft(:,3), line2.pleft(:,3)); 7 | n=length(C); 8 | if n>=minnum 9 | p1= [line1.pleft(ind1,1:2)]; %line1.intsect1;line1.intsect2; 10 | p2= [line2.pleft(ind2,1:2)];%line2.intsect1;line2.intsect2; 11 | end 12 | 13 | elseif side == 2 14 | [C,ind1,ind2]=intersect( line1.pright(:,3), line2.pright(:,3)); 15 | n=length(C); 16 | if n>=minnum 17 | p1= [line1.pright(ind1,1:2)];%line1.intsect1;line1.intsect2; 18 | p2= [line2.pright(ind2,1:2)];%line2.intsect1;line2.intsect2; 19 | end 20 | end 21 | 22 | 23 | end -------------------------------------------------------------------------------- /getgoodpair.m: -------------------------------------------------------------------------------- 1 | 2 | function [ind1,ind2] = getgoodpair(plines1,lines2,dist) 3 | 4 | len1=length(plines1); 5 | len2=length(lines2); 6 | ind1=[]; 7 | ind2=[]; 8 | for i=1:len1 9 | for j=1:len2 10 | if isclose(plines1(i),lines2(j),dist) 11 | ind1 = [ind1 plines1(i).ind]; 12 | ind2 = [ind2 j]; 13 | end 14 | end 15 | end 16 | 17 | 18 | end 19 | 20 | function [isc] = isclose(line1,line2,dist) 21 | 22 | 23 | if disp2line(line1.point1,line2)> dist || disp2line(line1.point2,line2)> dist || ... 24 | disp2line(line2.point1,line1)> dist || disp2line(line2.point2,line1)> dist || ... 25 | (norm((line1.point1 + line1.point2)/2 - (line2.point1 + line2.point2)/2 )> ... 26 | ((norm(line1.point1 - line1.point2)+norm(line2.point1 - line2.point2))/2)) 27 | isc=false; 28 | return; 29 | else 30 | isc = true; 31 | return; 32 | end 33 | 34 | end 35 | function dis=disp2line(point,line) 36 | k=line.k; 37 | b=line.b; 38 | if k~=Inf 39 | dis=abs(k*point(1)-point(2)+b)/sqrt(k*k+1); 40 | else 41 | dis = abs(point(1)-line.point1(1)); 42 | end 43 | end -------------------------------------------------------------------------------- /getpoints.m: -------------------------------------------------------------------------------- 1 | 2 | function [inds]=getpoints(linenum,pointlist,except) 3 | 4 | if~(exist('except','var')) 5 | except=0; 6 | end 7 | 8 | inds=[]; 9 | len=length(pointlist); 10 | for i=1:len 11 | if( (~isempty(find(pointlist(i).lines==linenum)))&& ... 12 | (isempty(find(pointlist(i).lines==except)))) 13 | inds=[inds i]; 14 | 15 | end 16 | end 17 | 18 | end -------------------------------------------------------------------------------- /imgs/1_A.jpg: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/dlut-dimt/LineMatching/e05eb15c06303d724b9334f96ab2c6deb723deb2/imgs/1_A.jpg -------------------------------------------------------------------------------- /imgs/1_B.jpg: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/dlut-dimt/LineMatching/e05eb15c06303d724b9334f96ab2c6deb723deb2/imgs/1_B.jpg -------------------------------------------------------------------------------- /intspoints.m: -------------------------------------------------------------------------------- 1 | 2 | function pointlist=intspoints(lines,imsize) 3 | len=length(lines); 4 | k=1; 5 | pointlist(k).point=[0 0]; 6 | pointlist(k).lines=[0 0]; 7 | for i = 1:len 8 | for j =i+1:len 9 | [a,b]=Itspoint(lines(i),lines(j)); 10 | 11 | if (a>0) && (a0) && (b-1 && k1<1 13 | for ii=min(p1(1),p2(1)):max(p1(1),p2(1)) 14 | jj = round(k1 * ii+b1); 15 | [dx,dy]=pointgrad(I, ii, jj); 16 | ldx=ldx+dx; 17 | ldy=ldy+dy; 18 | end 19 | else 20 | for jj=min(p1(2),p2(2)):max(p1(2),p2(2)) 21 | if k1~=Inf 22 | ii = round((jj-b1)/k1); 23 | else 24 | ii = p1(1); 25 | end 26 | [dx,dy]=pointgrad(I, ii, jj); 27 | ldx=ldx+dx; 28 | ldy=ldy+dy; 29 | end 30 | end 31 | 32 | lines(i).gradient=[ldx,ldy]./max(abs(ldx),abs(ldy))*15;%,atan(ldy/ldx) 33 | end 34 | 35 | end 36 | function [dx,dy] = pointgrad(I, i, j) 37 | 38 | i=floor(i); 39 | j=floor(j); 40 | s=size(I); 41 | if j<2||j>=s(1)||i<2||i>=s(2) 42 | dx=0; 43 | dy=0; 44 | else 45 | dx = [I(j,i+1) - I(j,i-1)]/2; 46 | dy = [I(j+1,i) - I(j-1,i)]/2; 47 | end 48 | end 49 | 50 | -------------------------------------------------------------------------------- /linematch.m: -------------------------------------------------------------------------------- 1 | 2 | function linematch 3 | clc; 4 | clear; 5 | close all; 6 | 7 | img1='.\imgs\1_A.jpg'; 8 | img2='.\imgs\1_B.jpg'; 9 | pmfile=strcat('.\pts&lines\1ABpoint.txt'); 10 | ltxt1='.\pts&lines\1Aline.txt'; 11 | ltxt2='.\pts&lines\1Bline.txt'; 12 | 13 | 14 | disp(' Reading files and preparing...'); 15 | [lines1, pointlist1]=paras(img1,ltxt1); 16 | [lines2, pointlist2]=paras(img2,ltxt2); 17 | 18 | P = load(pmfile); 19 | len1=length(lines1); 20 | len2=length(lines2); 21 | sublinds1=1:length(lines1); 22 | sublinds2=1:length(lines2); 23 | 24 | lines1=addpointsnearby(lines1,pointlist1,sublinds1,P(:,1:2)); 25 | lines2=addpointsnearby(lines2,pointlist2,sublinds2,P(:,3:4)); 26 | 27 | simL=zeros(len1,len2); 28 | simR=zeros(len1,len2); 29 | 30 | disp(' Calculating similarities between line neighborhoods...'); 31 | for i=1:len1 32 | t=lines1(i); 33 | for j=1:len2 34 | [simL(i,j),simR(i,j)]=distline(t,lines2(j)); 35 | end 36 | end 37 | 38 | k=[]; 39 | for i=1:len1 40 | for j=1:len2 41 | if simL(i,j)>0.95&&( simL(i,j)==max(simL(i,:)) && simL (i,j) == max(simL(:,j)) ) 42 | k=[k;[i,j]]; 43 | break; 44 | end 45 | end 46 | end 47 | simside1=ones(1,size(k,1)); 48 | 49 | for i=1:len1 50 | for j=1:len2 51 | if simR(i,j)>0.95&&( simR(i,j)==max(simR(i,:)) && simR (i,j) == max(simR(:,j)) ) 52 | k=[k;[i,j]]; 53 | break; 54 | end 55 | end 56 | end 57 | simeside1=[ simside1 2*ones(1,size(k,1))]; 58 | 59 | len=size(k,1); 60 | votecan=zeros(len2,len1); 61 | 62 | disp(' Matching lines ...'); 63 | for i=1:len 64 | 65 | [p1,p2]=getHpoints1L(lines1(k(i,1)),lines2(k(i,2)),simeside1(i)); 66 | 67 | if ~isempty(p1) 68 | [F1,~,~] = estimateGeometricTransform(p1,p2,'projective'); 69 | plines = projline(F1.T,lines1); 70 | [ind11,ind12]=getgoodpair(plines,lines2,3); 71 | 72 | plines = projline(inv(F1.T),lines2); 73 | [ind22,ind21]=getgoodpair(plines,lines1,3); 74 | 75 | if isempty(ind11)||isempty(ind22) 76 | continue; 77 | end 78 | 79 | [indfinal]=intersect([ind11;ind12]',[ind21;ind22]','rows'); 80 | 81 | if ~isempty(indfinal) 82 | indfinal=indfinal'; 83 | ind1=indfinal(1,:); 84 | ind2=indfinal(2,:); 85 | else 86 | ind1=[];ind2=[]; 87 | end 88 | 89 | if simeside1(i)==1 90 | v=simL(k(i,1),k(i,2)); 91 | elseif simeside1(i)==2 92 | v=simR(k(i,1),k(i,2)); 93 | end 94 | 95 | votecan(ind2+(ind1-1)*len2)=votecan(ind2+(ind1-1)*len2)+v; 96 | end 97 | end 98 | 99 | [num,ind]=sort(votecan,'descend'); 100 | num=num(1,:); 101 | ind=ind(1,:); 102 | votecan=votecan'; 103 | [num2,ind2]=sort(votecan,'descend'); 104 | num2=num2(1,:); 105 | ind2=ind2(1,:); 106 | k=[]; 107 | for i=1:length(ind) 108 | if i==ind2(ind(i)) && (num(i) > 0.9 && num2(ind(i))> 0.9) 109 | k=[k,i]; 110 | end 111 | end 112 | nummatch=length(k); 113 | draw(img1,lines1(k),1:nummatch,num2str(nummatch)); 114 | draw(img2,lines2(ind(k)),1:nummatch,num2str(nummatch)); 115 | 116 | end 117 | 118 | 119 | 120 | function draw(img,lines,orders,name) 121 | 122 | I=imread(img); 123 | len=length(orders); 124 | 125 | figure, imshow(I),hold on 126 | if exist('name','var') 127 | title(name); 128 | end 129 | for k = 1:len 130 | if orders(k)~=0 131 | xy = [lines(orders(k)).point1; lines(orders(k)).point2]; 132 | plot(xy(:,1),xy(:,2),'LineWidth',2,'Color','red'); 133 | text((xy(1,1)+xy(2,1))/2,(xy(1,2)+xy(2,2))/2,num2str(k)); 134 | end 135 | end 136 | hold off; 137 | 138 | end 139 | -------------------------------------------------------------------------------- /paras.m: -------------------------------------------------------------------------------- 1 | 2 | function [llines, pointlist]=paras(img,endpotxt) 3 | 4 | I=imread(img); 5 | imsize=size(I); 6 | if numel(imsize)>2 7 | I = rgb2gray(I); 8 | end 9 | 10 | points=load(endpotxt); 11 | for i=1:length(points) 12 | llines(i).point1=[points(i,1),points(i,2)]; 13 | llines(i).point2=[points(i,3),points(i,4)]; 14 | 15 | if (llines(i).point2(1)~=llines(i).point1(1)) 16 | llines(i).k=(llines(i).point2(2)-llines(i).point1(2))/(llines(i).point2(1)-llines(i).point1(1)); 17 | llines(i).b=llines(i).point1(2)-llines(i).k*llines(i).point1(1); 18 | else 19 | llines(i).k=Inf; 20 | llines(i).b=Inf; 21 | end 22 | 23 | end 24 | pointlist=intspoints(llines,imsize); 25 | llines=linegradient(I,llines); 26 | 27 | end 28 | 29 | 30 | -------------------------------------------------------------------------------- /projline.m: -------------------------------------------------------------------------------- 1 | 2 | function [plines] = projline(H,lines) 3 | 4 | n=length(lines); 5 | j=1; 6 | for i=1:n 7 | 8 | plines(j).point1 = projpoint(H,lines(i).point1); 9 | plines(j).point2 = projpoint(H,lines(i).point2); 10 | if (plines(j).point2(1)~=plines(j).point1(1)) 11 | plines(j).k=(plines(j).point2(2)-plines(j).point1(2))/(plines(j).point2(1)-plines(j).point1(1)); 12 | plines(j).b=plines(j).point1(2)-plines(j).k*plines(j).point1(1); 13 | else 14 | plines(j).k=Inf; 15 | plines(j).b=Inf; 16 | end 17 | plines(j).ind=i; 18 | j=j+1; 19 | end 20 | 21 | end 22 | 23 | function [p]= projpoint(H,point) 24 | 25 | p=[point 1]; 26 | 27 | p=p*H; 28 | p=p./p(3); 29 | p=p(1:2); 30 | end -------------------------------------------------------------------------------- /pts&lines/1ABpoint.txt: -------------------------------------------------------------------------------- 1 | 357.272 19.4215 752.302 465.991 2 | 475.431 19.9165 432.857 108.109 3 | 383.436 22.4496 695.635 310.41 4 | 388.938 22.2615 633.547 254.386 5 | 384.058 47.9601 261.078 340.946 6 | 344.071 59.7557 381.118 109.885 7 | 374.139 60.5778 783.164 406.9 8 | 367.573 63.2305 360.309 136.521 9 | 341.806 76.0132 161.508 240.382 10 | 434.082 92.111 459.459 448.658 11 | 448.127 92.1349 298.059 398.97 12 | 402.094 118.235 775.03 279.375 13 | 418.005 118.057 739.394 364.402 14 | 425.638 117.895 80.1125 449.05 15 | 400.406 121.299 770.603 310.737 16 | 344.617 123.983 345.184 177.345 17 | 382.603 124.267 370.523 178.575 18 | 314.895 124.716 324.213 177.953 19 | 320.91 124.611 128.374 474.116 20 | 533.236 136.598 293.225 287.529 21 | 367.244 146.415 35.895 530.829 22 | 421.745 146.68 756.443 442.12 23 | 463.406 146.542 672.086 573.026 24 | 319.63 147.086 46.7926 438.761 25 | 304.702 147.473 35.3651 411.459 26 | 414.839 149.713 782.515 359.644 27 | 496.83 150.429 299.309 512.363 28 | 327.305 152.993 794.294 212.066 29 | 468.549 157.066 152.396 231.222 30 | 323.459 158.515 771.488 340.735 31 | 348.127 170.09 794.76 454.792 32 | 353.604 174.126 50.0574 439.027 33 | 402.952 177.806 686.964 403.36 34 | 376.322 179.121 339.327 238.732 35 | 265.908 184.48 762.668 221.409 36 | 358.153 189.946 464.757 517.092 37 | 393.309 193.919 89.724 355.537 38 | 240.668 201.886 288.44 383.149 39 | 148.656 202.917 511.794 386.163 40 | 408.483 204.539 402.004 415.524 41 | 130.668 204.977 198.908 231.755 42 | 133.602 205.967 201.638 233.369 43 | 528.939 206.733 639.491 575.85 44 | 362.677 208.068 356.557 235.437 45 | 394.083 211.016 522.828 549.022 46 | 100.601 213.416 179.36 238.377 47 | 47.7245 216.024 143.006 240.605 48 | 660.731 216.17 677.237 287.074 49 | 404.704 224.338 780.835 337.118 50 | 553.924 224.639 289.129 276.84 51 | 21.1282 226.853 112.925 372.463 52 | 781.654 227.317 641.37 249.04 53 | 237.439 227.822 448.933 459.306 54 | 226.438 229.438 787.552 195.843 55 | 287.345 229.345 777.597 472.719 56 | 674.958 230.238 670.001 331.313 57 | 217.573 231.568 744.567 310.397 58 | 706.01 232.463 740.226 369.932 59 | 217.908 234.222 743.593 288.618 60 | 122.053 237.388 357.387 105.858 61 | 453.036 241.02 383.276 530.144 62 | 528.317 241.479 469.083 288.264 63 | 455.567 243.06 419.572 226.774 64 | 365.343 243.702 565.565 507.87 65 | 358.232 244.533 425.294 318.266 66 | 637.758 244.349 770.063 536.995 67 | 266.505 245.06 503.678 230.948 68 | 208.142 245.523 249.044 528.81 69 | 287.049 250.585 306.133 264.688 70 | 457.836 251.886 33.2871 564.689 71 | 95.6933 261.321 13.1579 497.259 72 | 287.719 263.27 305.841 272.59 73 | 696.842 266.045 139.103 515.127 74 | 519.03 267.148 751.457 227.789 75 | 323.349 267.818 791.217 192 76 | 317.188 270.184 684.555 547.319 77 | 85.805 271.74 168.478 278.207 78 | 372.444 274.03 37.8156 469.059 79 | 554.586 275.439 736.435 340.934 80 | 726.362 281.449 602.686 286.059 81 | 698.495 282.392 446.369 528.399 82 | 655.258 283.913 555.099 286.957 83 | 290.143 288.936 499.734 288.121 84 | 508.743 292.363 456.494 323.419 85 | 707.111 293.571 61.7097 586.336 86 | 482.274 298.489 766.492 534.662 87 | 707.454 298.975 633.714 274.974 88 | 214.181 300.644 255.339 268.967 89 | 306.724 304.422 556.225 495.653 90 | 29.936 306.089 693.903 345.509 91 | 133.558 305.879 151.628 240.883 92 | 90.8192 307.706 398.804 205.338 93 | 324.163 307.408 783.265 338.977 94 | 235.345 309.406 316.808 523.784 95 | 108.752 310.527 229.354 264.952 96 | 352.345 313.407 349.656 306.506 97 | 653.55 313.765 737.946 421.853 98 | 505.967 319.912 457.211 177.343 99 | 248.317 324.253 779.059 288.032 100 | 89.8432 330.25 170.969 322.888 101 | 111.076 329.867 21.6273 291.17 102 | 737.519 332.582 191.604 563.202 103 | 89.7312 337.65 459.755 205.688 104 | 658.818 338.391 768.434 327.002 105 | 235.584 347.171 269.996 330.26 106 | 713.471 349.592 8.96313 557.999 107 | 679.739 349.818 22.7731 582.754 108 | 84.486 352.608 300.916 592.981 109 | 736.928 354.133 757.406 482.04 110 | 391.906 354.977 788.515 232.676 111 | 327.917 356.511 340.505 394.606 112 | 690.543 356.904 486.203 554.013 113 | 51.8693 360.376 63.2901 435.817 114 | 740.939 360.598 771.79 209.058 115 | 100.291 362.839 82.3296 495.043 116 | 131.355 365.269 199.215 341.587 117 | 15.1396 368.569 118.702 344.081 118 | 74.0338 368.594 621.447 550.725 119 | 653.879 369.565 172.523 302.673 120 | 105.479 373.088 79.8553 554.198 121 | 745.54 374.217 290.847 565.569 122 | 27.3072 374.261 407.816 518.306 123 | 59.0754 374.42 549.408 532.338 124 | 123.626 376.493 147.935 453.392 125 | 645.3 377.287 169.229 338.03 126 | 112.459 377.677 580.934 446.951 127 | 46.4426 379.726 649.204 372.209 128 | 59.2797 379.759 69.6206 566.129 129 | 392.106 384.113 377.424 531.015 130 | 354.912 391.071 105.525 465.458 131 | 352.341 396.493 417.274 272.339 132 | 673.143 398.085 366.672 557.319 133 | 754.389 398.065 629.447 585.079 134 | 65.7479 398.523 569.084 332.02 135 | 29.7867 400.705 114.268 239.297 136 | 67.9958 400.821 492.794 588.639 137 | 506.905 406.397 795.867 273.679 138 | 392.146 409.721 22.8692 445.703 139 | 33.7673 410.127 265.086 542.17 140 | 394.747 410.798 41.7222 512.374 141 | 514.544 414.712 599.358 428.191 142 | 531.896 415.864 665.989 329.822 143 | 496.926 419.928 445.155 409.106 144 | 473.846 420.333 430.592 318.976 145 | 18.2086 421.734 421.671 553.957 146 | 64.8885 422.736 308.818 525.27 147 | 555.707 422.945 699.216 240.879 148 | 447.047 426.697 549.665 497.488 149 | 119.339 426.778 226.446 565.946 150 | 711.199 428.995 736.144 568.177 151 | 273.586 431.012 794.573 257.132 152 | 113.776 437.097 686.053 490.417 153 | 355.526 436.935 86.4115 470.84 154 | 723.024 437.016 409.626 588.439 155 | 705.877 438.07 401.266 540.638 156 | 330.307 439.539 790.445 459.887 157 | 476.257 440.54 402.485 178.124 158 | 483.255 441.947 393.2 360.024 159 | 786.334 442.52 751.898 394.228 160 | 705.995 445.31 361.363 465.577 161 | 789.057 445.352 756.493 544.403 162 | 419.777 445.943 346.481 450.075 163 | 681.732 445.838 789.992 350.698 164 | 134.488 446.489 456.462 167.066 165 | 132.023 447.756 680.719 240.935 166 | 51.8051 452.76 277.586 522.979 167 | 301.041 455.84 102.475 233.051 168 | 375.231 456.733 163.013 376.874 169 | 365.023 462.802 775.019 257.215 170 | 659.97 464.002 79.006 445.686 171 | 125.935 465.566 542.423 572.079 172 | 559.342 469.088 491.588 350.063 173 | 460.275 470.323 446.177 193.367 174 | 688.302 474.345 99.8851 558.387 175 | 696.094 475.799 669.749 591.999 176 | 104.734 476.715 591.092 561.607 177 | 370.126 478.573 436.062 354.043 178 | 719.794 478.185 560.89 520.907 179 | 550.089 479.32 769.969 228.032 180 | 279.04 482.974 475.683 455.794 181 | 97.163 485.179 45.9591 399.431 182 | 76.3821 486.656 121.633 259.64 183 | 700.953 490.952 595.358 429.01 184 | 303.468 491.595 316.909 520.305 185 | 312.779 492.162 324.878 521.163 186 | 422.475 492.252 404.445 461.425 187 | 490.638 493.862 255.529 303.441 188 | 44.9763 495.909 42.884 428.532 189 | 516.082 496.338 288.222 303.823 190 | 373.354 501.501 25.5374 342.465 191 | 57.4039 503.966 734.444 458.38 192 | 298.182 507.466 490.432 231.125 193 | 32.8255 509.456 638.152 564.03 194 | 100.803 510.546 170.808 579.503 195 | 381.443 516.469 788.408 417.674 196 | 430.25 517.449 742.22 317.062 197 | 684.424 518.688 684.773 549.466 198 | 9.38383 519.095 18.6529 509.428 199 | 313.18 519.599 322.819 446.704 200 | 322.432 519.333 336.552 446.848 201 | 11.6804 521.045 18.8142 512.194 202 | 58.2045 522.642 356.513 549.22 203 | 443.502 523.504 796.226 233.633 204 | 63.5945 524.527 175.318 580.356 205 | 535.98 524.366 474.099 449.549 206 | 459.956 526.628 751.37 204.642 207 | 65.2361 526.795 119.452 560.369 208 | 47.4979 529.345 720.174 568.458 209 | 487.03 529.432 332.706 300.353 210 | 16.1141 529.916 356.104 490.874 211 | 306.174 530.539 258.19 244.477 212 | 345.204 535.837 794.428 416.364 213 | 97.447 536.797 480.364 500.233 214 | 318.062 537.888 349.921 454.949 215 | 58.8859 538.326 664.548 390.228 216 | 16.3857 543.176 248.779 513.797 217 | 750.17 545.605 307.569 573.887 218 | 65.232 546.492 596.273 364.145 219 | 106.757 549.777 73.6842 560.878 220 | 19.6024 550.573 111.902 341.518 221 | 225.058 551.672 453.747 380.139 222 | 26.0081 551.951 246.33 542.99 223 | 360.185 553.215 157.885 595.542 224 | 38.5258 554.159 26.8658 467.869 225 | 135.033 554.341 202.417 469.552 226 | 23.0745 559.472 749.356 407.305 227 | 196.885 560.871 504.052 292.881 228 | 132.624 562.571 622.25 264.272 229 | 356.381 562.638 53.7811 552.689 230 | 236.799 565.527 270.627 477.96 231 | 602.115 566.001 227.037 503.994 232 | 345.43 571.093 764.938 494.97 233 | 356.248 571.808 165.99 492.157 234 | 538.78 571.875 688.33 296.941 235 | 298.873 573.658 760.412 236.008 236 | 496.327 574.376 62.3766 451.787 237 | 399.864 575.458 305.009 548.157 238 | 539.045 576.8 766.648 363.862 239 | 650.262 579.412 433.823 373.355 240 | 342.981 582.424 788.887 312.347 241 | 120.942 582.898 682.83 397.39 242 | 267.888 582.952 292.101 366.87 243 | 343.901 585.053 333.931 309.507 244 | 508.432 593.278 284.514 535.925 245 | 282.427 594.904 775.31 290.808 246 | 487.982 74.9712 442.089 143.979 247 | 341.51 101.428 341.908 161.982 248 | 441.41 102.59 410.842 164.002 249 | 477.467 114.454 435.228 171.431 250 | 344.64 118.386 345.057 173.91 251 | 560.736 129.638 491.685 182.401 252 | 566.381 140.453 495.332 189.864 253 | 468.672 142.909 429.582 191.341 254 | 376.424 144.588 366.707 192.036 255 | 379.937 144.637 369.237 192.007 256 | 454.22 146.213 19.9548 563.128 257 | 403.138 147.088 384.583 193.794 258 | 224.783 150.176 541.322 369.428 259 | 459.616 150.532 309.685 499.824 260 | 194.065 150.923 540.984 365.519 261 | 354.27 157.61 351.298 201.337 262 | 420.225 161.566 395.815 203.408 263 | 450.947 162.226 617.579 558.232 264 | 353.808 165.102 380.325 532.722 265 | 417.474 165.436 394.213 206.064 266 | 370.562 171.097 361.948 210.981 267 | 465.536 172.303 426.951 213.439 268 | 492.861 172.314 102.416 429.296 269 | 280.52 176.42 300.784 213.745 270 | 451.277 178.382 416.941 215.222 271 | 399.77 179.227 788.508 392.31 272 | 380.077 188.687 434.293 553.761 273 | 395.997 188.868 379.413 222.255 274 | 364.844 192.612 752.064 351.977 275 | 218.906 195.796 259.187 226.484 276 | 284.878 196.644 303.864 227.342 277 | 661.093 196.994 559.457 228.177 278 | 493.872 197.745 426.221 379.101 279 | 642.088 199.34 774.932 250.908 280 | 524.968 199.892 466.982 229.941 281 | 159.964 202.349 241.753 470.157 282 | 213.945 205.05 431.855 291.261 283 | 220.188 204.912 436.879 475.105 284 | 433.79 205.006 405.411 233.199 285 | 156.082 205.627 525.289 511.679 286 | 354.182 206.151 420.103 323.137 287 | 460.406 208.782 423.467 235.804 288 | 471.351 209.678 430.666 236.734 289 | 460.522 215.262 423.379 240.474 290 | 454.591 217.313 792.456 534.538 291 | 532.307 220.876 472.558 429.927 292 | 284.112 227.864 303.513 248.387 293 | 217.26 228.596 742.874 306.523 294 | 754.761 229.552 443.809 111.28 295 | 759.469 231.108 625.973 252.397 296 | 681.984 231.473 50.8853 221.825 297 | 790.003 232.826 645.458 253.181 298 | 111.89 234.195 42.0078 336.971 299 | 793.477 235.594 648.557 254.069 300 | 495.313 237.491 446.834 255.398 301 | 531.567 239.021 471.313 225.6 302 | 620.174 239.697 498.2 292.833 303 | 657.604 239.236 556.922 256.902 304 | 492.84 241.931 444.995 258.494 305 | 654.661 241.827 554.535 258.334 306 | 630.969 242.593 538.562 228.03 307 | 644.176 242.839 547.793 259.515 308 | 213.839 245.43 255.152 260.111 309 | 463.714 245.756 427.409 351.311 310 | 99.8268 248.179 177.657 262.402 311 | 502.842 248.763 452.347 263.193 312 | 531.306 248.529 471.168 263.099 313 | 648.006 248.994 767.82 483.63 314 | 451.566 249.853 417.203 263.716 315 | 457.986 249.779 772.911 189.509 316 | 217.709 251.551 434.506 233.075 317 | 178.347 252.163 498.87 262.087 318 | 262.939 255.99 288.905 358.757 319 | 714.665 257.039 154.423 552.893 320 | 272.612 258.722 320.514 440.301 321 | 272.534 263.589 721.41 205.521 322 | 371.381 264.482 110.691 530.317 323 | 417.92 266.112 394.07 243.987 324 | 310.038 266.232 409.597 489.502 325 | 116.425 267.783 189.946 274.629 326 | 127.521 267.694 197.136 275.489 327 | 488.022 269.309 442.021 307.432 328 | 220.315 274.91 781.043 449.723 329 | 651.754 275.871 552.999 281.471 330 | 299.289 282.079 486.116 235.774 331 | 113.913 282.291 187.296 285.273 332 | 221.852 284.498 261.514 286.57 333 | 592.138 285.664 234.492 528.755 334 | 96.6635 285.91 181.106 282.714 335 | 658.661 286.453 557.517 288.984 336 | 486.945 286.845 439.463 288.928 337 | 280.067 288.583 301.801 289.465 338 | 215.961 288.939 256.6 289.904 339 | 601.618 288.834 523.394 228.22 340 | 114.244 289.616 187.582 290.352 341 | 134.192 289.48 201.971 289.784 342 | 647.672 289.62 550.206 291.201 343 | 640.186 292.06 495.44 287.406 344 | 272.897 295.222 262.585 294.534 345 | 704.618 296.326 95.1279 394.203 346 | 113.864 296.73 170.724 290.247 347 | 284.938 298.823 303.97 448.782 348 | 94.748 300.733 175.456 297.741 349 | 790.897 301.839 6.55702 384.533 350 | 446.177 302.57 354.691 484.612 351 | 108.163 307.863 142.452 508.324 352 | 59.1385 311.323 150.204 305.023 353 | 331.141 311.554 791.396 430.387 354 | 452.372 312.151 417.588 306.146 355 | 704.287 312.854 667.766 302.952 356 | 395.597 317.161 379.164 309.676 357 | 355.378 320.395 351.665 253.312 358 | 556.01 321.475 487.971 311.676 359 | 64.1024 323.07 175.554 277.737 360 | 68.8166 322.946 182.009 277.71 361 | 456.367 324.648 420.828 375.54 362 | 506.533 325.879 454.237 315.348 363 | 400.132 332.385 382.834 318.073 364 | 523.87 334.328 465.773 351.767 365 | 527.22 334.312 247.227 232.638 366 | 486.088 337.669 440.636 323.536 367 | 68.9239 337.893 156.469 323.218 368 | 222.235 339.093 296.372 504.885 369 | 232.86 339.069 268.396 323.94 370 | 268.641 338.886 259.205 353.615 371 | 134.601 339.525 202.572 324.679 372 | 452.458 339.427 417.626 324.961 373 | 73.1999 353.527 160.393 333.461 374 | 532.311 353.715 472.035 461.931 375 | 352.045 356.919 349.441 335.919 376 | 441.854 358.138 336.422 395.833 377 | 431.741 358.296 397.484 492.285 378 | 698.304 360.921 583.77 339.109 379 | 531.998 361.269 472.198 467.241 380 | 39.3612 365.52 138.198 341.624 381 | 13.0984 365.842 121.887 341.575 382 | 506.579 368.824 454.185 344.742 383 | 554.882 369.275 396.6 106.417 384 | 358.92 370.241 353.923 227.247 385 | 509.631 370.374 457.012 436.757 386 | 532.024 371.837 259.623 546.741 387 | 127.509 374.274 197.029 347.596 388 | 226.07 376.071 674.754 300.917 389 | 115.432 378.959 238.935 548.214 390 | 557.737 380.491 489.074 228.68 391 | 234.355 382.24 267.45 353.478 392 | 401.263 384.19 382.751 355.056 393 | 49.7003 384.469 617.029 548.835 394 | 404.884 384.991 385.458 355.332 395 | 204.775 386.868 249.696 357.736 396 | 392.507 396.755 377.33 481.955 397 | 701.944 400.761 456.643 185.599 398 | 398.615 400.923 380.383 366.584 399 | 546.637 401.355 370.739 362.644 400 | 706.318 402.01 197.99 562.267 401 | 355.745 403.133 352.666 491.255 402 | 421.536 402.755 335.729 366.331 403 | 543.745 403.761 769.708 376.449 404 | 349.533 404.484 346.992 249.461 405 | 303.578 404.98 316.866 461.668 406 | 395.331 405.768 378.773 369.937 407 | 460.505 405.216 423.135 367.136 408 | 653.534 405.714 274.618 319.137 409 | 90.2195 408.427 70.0308 558.155 410 | 352.547 409.07 349.527 372.829 411 | 528.924 409.557 469.464 373.798 412 | 303.406 411.649 316.453 372.975 413 | 796.657 413.306 650.736 374.937 414 | 71.6206 418.228 160.696 376.969 415 | 131.508 417.814 484.968 348.747 416 | 702.936 417.941 585.556 253.195 417 | 27.6838 419.748 650.715 338.417 418 | 300.112 419.47 313.221 288.717 419 | 490.887 420.033 443.335 378.986 420 | 243.529 422.6 276.247 472.909 421 | 518.594 423.825 462.739 321.269 422 | 388.928 429.085 373.521 241.245 423 | 236.014 429.724 445.991 386.748 424 | 401.716 429.693 383.253 415.979 425 | 218.235 431.234 258.305 386.346 426 | 532.471 431.014 737.873 564.25 427 | 333.066 433.92 769.367 526.272 428 | 479.345 434.38 762.849 431.52 429 | 58.6919 435.791 299.132 538.651 430 | 319.309 436.735 327.039 390.73 431 | 239.02 443.755 272.908 423.338 432 | 319.479 443.384 327.122 394.416 433 | 218.1 445.614 433.957 491.214 434 | 475.965 446.758 433.681 336.776 435 | 532.552 448.536 471.55 336.395 436 | 28.8211 459.844 31.5436 555.397 437 | 506.83 459.806 454.235 406.46 438 | 226.088 463.217 438.28 228.425 439 | 556.157 462.964 487.556 377.358 440 | 389.951 465.353 374.563 439.353 441 | 363.778 466.359 356.902 382.369 442 | 499.603 467.554 448.588 381.332 443 | 556.412 468.3 538.908 419.259 444 | 234.534 469.743 270.257 534.214 445 | 659.698 470.197 517.951 538.136 446 | 529.369 471.961 468.797 384.353 447 | 573.888 471.999 511.302 445.784 448 | 767.331 472.293 601.349 525.769 449 | 785.482 473.213 511.603 583.15 450 | 218.218 473.511 258.45 415.284 451 | 653.771 475.973 553.706 417.369 452 | 533.505 476.422 472.226 418.002 453 | 551.86 476.273 484.593 417.453 454 | 392.759 478.159 652.664 559.253 455 | 664.349 478.608 72.339 587.423 456 | 678.586 481.035 701.427 579.995 457 | 698.986 481.261 584.274 420.728 458 | 224.487 489.503 262.567 425.894 459 | 450.102 489.19 415.579 425.817 460 | 453.503 491.783 418.227 427.77 461 | 645.115 494.538 547.395 429.747 462 | 478.36 495.133 302.038 204.945 463 | 93.1212 496.448 8.75407 284.545 464 | 400.898 498.856 382.476 344.46 465 | 353.078 500.595 349.565 404.747 466 | 226.871 504.114 264.641 435.394 467 | 99.8769 504.975 118.306 553.106 468 | 496.598 512.056 249.654 292.225 469 | 507.37 512.169 454.128 441.75 470 | 619.464 514.993 241.883 474.81 471 | 350.472 516.868 347.861 444.503 472 | 529.398 517.234 469.257 445.349 473 | 269.215 518.768 272.959 450.663 474 | 602.509 521.389 238.264 469.98 475 | 330.497 521.842 791.157 270.464 476 | 489.647 524.021 438.3 427.947 477 | 551.544 530.265 484.185 454.416 478 | 405.311 531.021 385.29 454.179 479 | 7.45184 531.758 115.398 454.302 480 | 457.106 532.526 592.502 424.29 481 | 306.625 534.832 475.507 461.535 482 | 415.537 538.576 392.532 459.574 483 | 356.622 539.266 352.726 519.464 484 | 703.153 540.545 679.588 485.552 485 | 496.095 540.979 270.065 458.241 486 | 698.415 542.331 629.232 504.754 487 | 353.77 549.082 349.338 345.123 488 | 278.043 549.769 298.844 466.901 489 | 353.918 552.242 449.617 443.872 490 | 33.665 553.996 480.156 537.145 491 | 567.267 554.594 494.934 470.346 492 | 384.139 555.042 371.374 528.366 493 | 54.302 555.763 147.77 470.504 494 | 738.087 556.217 610.639 471.766 495 | 511.083 560.074 457.474 473.832 496 | 500.989 561.552 307.039 502.706 497 | 507.32 561.46 452.285 475.243 498 | 65.7665 561.967 155.406 474.266 499 | 282.641 562.151 302.149 475.441 500 | 516.383 563.429 445.229 381.266 501 | 522.389 563.486 463.962 381.968 502 | 526.718 563.481 467.988 476.602 503 | 129.292 565.512 525.242 539.601 504 | 571.301 565.276 497.84 477.538 505 | 219.167 566.052 259.044 478.087 506 | 629.123 569.287 537.227 352.62 507 | 112.789 572.169 375.983 268.55 508 | 691.78 574.457 579.618 484.531 509 | 118.512 577.192 189.292 485.879 510 | 264.529 579.008 288.701 246.332 511 | 223.392 581.538 437.394 276.386 512 | 518.906 581.856 461.912 519.949 513 | 539.107 583.674 766.989 468.693 514 | 483.979 584.744 438.32 491.177 515 | 360.236 588.889 354.383 372.31 516 | 123.858 589.661 155.354 477.453 517 | 726.847 594.068 617.005 473.823 518 | 401.989 595.167 382.982 498.316 519 | 361.107 19.1038 356.012 107.119 520 | 455.647 21.4806 419.774 108.653 521 | 487.394 41.1676 441.694 123.539 522 | 491.523 81.0052 444.537 149.062 523 | 491.725 98.1096 444.674 160.941 524 | 318.099 105.947 327.2 166.411 525 | 541.82 124.503 479.212 179.095 526 | 400.587 128.121 382.945 181.112 527 | 592.554 128.982 528.701 181.87 528 | 368.597 129.374 361.782 182.072 529 | 259.368 131.595 270.929 183.252 530 | 242.747 131.511 275.3 183.032 531 | 164.138 132.878 254.62 183.665 532 | 491.719 134.8 444.456 185.832 533 | 464.548 135.535 754.556 257.654 534 | 443.965 135.938 757.655 528.234 535 | 312.555 139.974 323.246 189.006 536 | 501.248 145.857 450.88 193.219 537 | 411.764 146.885 389.941 193.629 538 | 530.859 147.505 471.47 194.539 539 | 298.395 149.693 313.613 195.597 540 | 354.304 149.599 351.533 195.493 541 | 458.161 158.996 421.648 202.352 542 | 532.059 161.835 472.202 204.326 543 | 462.035 162.386 424.526 205.48 544 | 311.077 165.414 321.912 206.213 545 | 307.449 168.622 319.572 208.264 546 | 390.592 168.87 375.87 208.689 547 | 307.477 179.426 319.316 215.128 548 | 487.038 179.955 441.296 216.358 549 | 311.759 182.022 322.29 217.316 550 | 357.377 181.964 353.268 217.479 551 | 370.338 182.475 361.738 217.994 552 | 229.26 183.642 394.743 540.964 553 | 642.648 184.073 546.715 219.5 554 | 539.06 184.924 328.418 188.831 555 | 301.968 186.2 315.607 220.041 556 | 462.18 187.616 425.039 221.905 557 | 481.379 190.675 437.445 223.693 558 | 267.286 191.829 291.92 223.828 559 | 279.252 191.628 300.352 223.919 560 | 509.508 195.586 456.633 227.037 561 | 647.553 197.213 550.158 228.52 562 | 228.35 197.687 266.134 227.931 563 | 470.201 197.601 429.982 228.355 564 | 275.627 200.298 297.463 229.938 565 | 289.114 200.145 306.602 229.825 566 | 358.619 200.617 354.316 258.938 567 | 487.624 200.683 441.415 230.385 568 | 224.454 201.483 262.829 230.495 569 | 531.77 203.003 471.646 232.182 570 | 491.024 204.576 445.062 232.881 571 | 492.882 208.619 445.267 236.227 572 | 316.494 209.078 324.863 236.54 573 | 475.539 209.611 433.632 236.501 574 | 283.91 211.713 303.205 237.817 575 | 110.89 216.904 185.856 240.878 576 | 390.881 220.9 375.962 244.782 577 | 493.054 224.78 445.259 246.584 578 | 532.388 225.343 472.118 247.442 579 | 550.631 225.995 484.389 247.43 580 | 390.874 226.168 375.944 248.048 581 | 541.015 226.166 477.917 247.816 582 | 262.406 226.576 292.662 205.062 583 | 774.718 227.384 635.107 249.35 584 | 546.129 229.255 481.277 249.912 585 | 302.505 230.117 315.953 250.202 586 | 281.506 231.768 301.626 251.087 587 | 210.762 233.45 253.58 252.464 588 | 493.803 233.295 445.798 252.651 589 | 290.095 234.552 307.244 252.78 590 | 778.455 235.598 764.578 507.847 591 | 475.472 236.147 433.42 254.439 592 | 282.398 238.359 302.36 255.517 593 | 124.706 240.878 195.163 257.359 594 | 514.275 248.507 459.326 262.847 595 | 491.704 248.964 444.653 263.147 596 | 314.495 251.915 760.211 543.361 597 | 496.861 254.838 447.999 266.645 598 | 222.932 256.78 261.564 268.259 599 | 99.0689 262.985 177.822 272.528 600 | 129.376 263.196 748.028 306.549 601 | 222.874 264.209 261.831 273.173 602 | 319.854 263.918 327.67 273.114 603 | 407.667 265.429 387.225 274.404 604 | 85.0347 267.64 169.316 275.176 605 | 213.358 269.117 255.335 276.126 606 | 223.012 270.97 261.937 277.988 607 | 354.74 272.085 351.741 339.22 608 | 369.187 275.24 361.041 281.553 609 | 550.807 279.444 485.832 504.884 610 | 482.25 279.431 437.97 283.961 611 | 275.621 281.814 297.603 285.154 612 | 95.5298 282.385 174.555 280.479 613 | 101.044 282.399 179.592 280.251 614 | 527.794 285.424 468.679 257.82 615 | 499.546 286.048 449.784 288.243 616 | 129.989 286.901 198.853 288.784 617 | 208.639 288.505 252.515 289.65 618 | 224.347 288.652 262.59 289.764 619 | 630.722 288.63 538.706 290.356 620 | 108.942 289.654 183.92 290.126 621 | 505.77 289.553 453.977 290.875 622 | 562.615 292.882 492.48 293.035 623 | 491.666 293.564 444.766 293.365 624 | 513.389 293.27 459.358 293.274 625 | 396.766 295.409 380.018 294.519 626 | 224.025 295.849 295.365 294.292 627 | 88.7777 296.889 187.408 295.173 628 | 96.6891 297.092 177.316 285.346 629 | 488.49 297.596 443.005 450.074 630 | 89.2074 304.102 187.769 280.427 631 | 112.957 304.17 187.501 300.083 632 | 318.565 311.048 326.429 305.107 633 | 435.534 310.397 406.63 365.301 634 | 327.278 312.763 332.756 306.201 635 | 546.543 314.691 481.337 307.929 636 | 85.6212 315.114 766.252 529.449 637 | 556.042 315.122 487.642 305.887 638 | 354.971 316.2 351.74 308.789 639 | 479.284 317.207 435.835 279.255 640 | 369.062 317.619 361.08 366.693 641 | 654.092 318.502 554.115 310.619 642 | 63.0582 319.005 153.008 310.194 643 | 82.8475 318.977 166.896 310.188 644 | 481.218 323.793 437.098 313.836 645 | 240.272 325.623 273.466 314.748 646 | 551.356 326.113 484.797 315.686 647 | 81.6566 326.512 182.605 280.223 648 | 58.2357 327.031 149.672 315.334 649 | 63.1661 326.857 151.194 325.474 650 | 234.604 327.318 269.823 315.808 651 | 643.672 327.776 546.967 317.128 652 | 509.974 330.307 457.886 503.873 653 | 299.453 331.635 314.372 500.398 654 | 86.4534 333.93 169.231 315.584 655 | 506.071 333.943 454.025 320.897 656 | 479.911 338.033 436.277 384.004 657 | 497.918 338.116 448.979 323.39 658 | 401.296 340.985 382.795 296.258 659 | 87.5517 341.461 168.065 325.454 660 | 476.312 343.104 434.07 327.388 661 | 267.214 343.351 291.974 326.885 662 | 391.834 347.27 376.456 330.22 663 | 506.377 348.729 454.354 332.048 664 | 658.556 352.413 557.346 333.948 665 | 267.46 352.96 292.186 332.498 666 | 686.039 353.633 113.297 364.113 667 | 726.111 353.584 15.2528 551.967 668 | 304.457 354.657 316.965 334.997 669 | 656.493 357.402 555.933 337.094 670 | 267.408 358.548 291.952 337.384 671 | 456.448 360.363 420.295 338.889 672 | 506.868 361.136 454.453 339.424 673 | 551.563 362.193 484.828 340.029 674 | 273.098 366.841 295.682 342.952 675 | 352.067 373.251 349.05 286.832 676 | 288.612 374.558 307.045 348.109 677 | 461.348 374.813 423.336 408.896 678 | 119.767 378.91 191.764 350.739 679 | 506.362 378.855 453.612 351.413 680 | 728.867 381.827 604.509 353.727 681 | 213.306 382.777 254.822 353.581 682 | 238.914 382.532 305.668 323.912 683 | 268.788 382.313 292.736 353.509 684 | 461.172 382.535 424.007 444.471 685 | 686.099 383.749 595.88 272.994 686 | 235.167 386.381 269.634 237.282 687 | 493.974 386.434 445.885 356.335 688 | 277.603 397.449 298.517 363.753 689 | 304.795 398.359 317.207 364.538 690 | 326.447 398.316 332.009 364.156 691 | 493.789 402.465 270.302 488.435 692 | 555.95 409.454 488.468 403.474 693 | 13.3478 410.846 119.161 372.4 694 | 135.162 418.689 202.066 377.962 695 | 520.624 419.844 463.325 379.356 696 | 396.765 422.336 379.805 380.855 697 | 657.925 422.425 556.851 380.778 698 | 281.052 426.124 301.432 383.098 699 | 392.205 426.975 376.426 296.78 700 | 223.568 430.955 437.854 387.17 701 | 488.719 430.902 442.088 386.756 702 | 476.603 431.304 433.854 387.105 703 | 67.7924 433.558 156.828 387.26 704 | 392.18 438.783 376.462 334.384 705 | 656.065 445.285 555.053 397.163 706 | 671.042 452.383 564.634 400.574 707 | 529.012 454.654 469.456 403.824 708 | 692.975 454.482 757.317 372.512 709 | 226.322 455.939 263.841 403.265 710 | 131.201 459.074 199.514 405.276 711 | 216.98 462.677 257.342 407.887 712 | 232.912 462.75 268.099 408.034 713 | 702.01 462.387 252.338 542.561 714 | 52.7712 466.694 146.505 409.285 715 | 506.686 467.374 453.934 411.408 716 | 3.08335 472.936 113.488 414.279 717 | 224.46 474.344 262.541 416.101 718 | 702.514 475.204 586.591 416.781 719 | 556.802 476.029 487.865 416.975 720 | 304.782 478.515 317.219 419.918 721 | 103.159 482.77 180.335 421.464 722 | 718.97 482.523 597.933 421.674 723 | 460.915 483.996 422.955 456.847 724 | 656.384 485.603 555.436 423.953 725 | 306.977 486.614 318.518 424.133 726 | 61.1925 486.825 649.827 584.817 727 | 218.499 489.76 258.551 426.32 728 | 304.429 493.218 317.122 492.492 729 | 281.223 493.7 300.601 429.375 730 | 59.004 495.122 150.923 429.389 731 | 725.871 497.423 602.47 431.74 732 | 457.814 502.968 421.144 498.518 733 | 721.941 502.867 599.498 435.878 734 | 9.73729 504.788 114.598 436.569 735 | 27.0015 505.664 128.274 436.841 736 | 135.992 504.794 202.567 436.376 737 | 18.0968 505.794 122.982 436.66 738 | 59.2175 506.801 683.903 428.559 739 | 484.254 508.427 435.215 439.121 740 | 397.177 508.753 380.101 439.257 741 | 51.3178 510.663 145.427 440.208 742 | 109.107 513.941 652.238 326.536 743 | 300.694 514.082 314.381 442.98 744 | 349.228 515.434 415.537 446.619 745 | 713.436 516.22 593.881 444.314 746 | 86.3027 518.305 155.738 508.329 747 | 680.141 518.447 676.302 524.583 748 | 436.2 518.689 406.71 446.279 749 | 633.289 522.238 539.726 482.938 750 | 453.475 524.208 418.075 450.031 751 | 656.16 525.44 555.579 477.943 752 | 42.6308 528.216 139.497 452.097 753 | 393.063 527.942 376.39 392.131 754 | 660.286 529.262 557.966 453.046 755 | 37.4514 529.94 768.167 186.109 756 | 490.437 532.694 441.467 212.278 757 | 702.68 533.045 586.388 456.785 758 | 353.17 536.933 350.004 458.39 759 | 405.963 538.254 792.43 575.247 760 | 490.496 540.388 371.375 480.709 761 | 225.859 541.68 263.388 461.55 762 | 232.289 541.386 267.78 461.286 763 | 694.262 541.679 581.233 461.837 764 | 458.105 543.083 421.049 462.291 765 | 18.7482 546.3 122.549 464.361 766 | 282.017 547.545 301.75 465.609 767 | 575.702 547.844 501.229 466.295 768 | 738.509 549.037 48.0646 457.634 769 | 498.29 551.528 448.455 468.495 770 | 115.984 553.475 189.232 469.571 771 | 236.508 554.915 270.538 470.465 772 | 397.817 554.96 380.34 470.479 773 | 135.662 561.109 202.511 412.802 774 | 220.992 561.985 260.109 475.422 775 | 230.381 562.032 266.106 475.255 776 | 744.129 562.286 614.124 475.955 777 | 478.658 565.004 434.652 477.518 778 | 492.672 564.985 444.914 477.529 779 | 23.2231 565.934 11.2649 475.543 780 | 86.6686 566.646 293.492 571.58 781 | 273.763 566.632 295.852 478.495 782 | 518.525 571.072 461.918 481.674 783 | 522.231 572.917 464.562 483.198 784 | 78.8395 575.919 711.685 565.87 785 | 301.535 576.992 314.283 363.248 786 | 72.4878 577.715 681.366 389.247 787 | 109.908 581.111 184.432 487.929 788 | 437.362 583.814 406.927 490.384 789 | 276.74 589.956 298.007 494.417 790 | 81.3656 591.608 166.842 494.498 791 | 361.13 595.213 376.372 325.818 792 | 473.322 15.5397 432.018 104.145 793 | 344.931 24.8494 345.122 110.557 794 | 443.053 35.3092 411.73 117.506 795 | 382.03 49.1573 370.268 127.161 796 | 429.457 54.641 402.352 131.256 797 | 344.999 65.8381 199.549 364.297 798 | 436.63 92.6298 407.144 156.801 799 | 382.272 93.9166 370.37 157.93 800 | 429.954 99.6354 402.891 161.797 801 | 389.129 100.575 375.085 162.224 802 | 382.408 107.326 370.307 167.124 803 | 389.804 113.962 374.57 171.031 804 | 479.846 118.503 436.826 174.601 805 | 556.227 118.936 488.4 175.273 806 | 352.317 123.126 31.4231 333.137 807 | 467.6 123.318 428.407 177.846 808 | 517.047 124.358 461.385 178.561 809 | 389.852 128.456 374.328 181.083 810 | 339.653 129.907 341.449 182.115 811 | 461.398 131.048 424.337 182.988 812 | 265.717 131.77 259.607 182.857 813 | 337.112 139.422 339.761 188.554 814 | 489.247 143.441 442.995 191.777 815 | 341.222 143.837 342.437 191.489 816 | 526.461 145.146 468.206 192.668 817 | 202.248 145.761 247.865 192.526 818 | 233.35 151.351 269.291 196.879 819 | 425.552 156.492 399.703 200.051 820 | 395.152 160.902 379.047 203.39 821 | 537.168 161.337 475.482 204.262 822 | 316.833 168.817 325.787 208.097 823 | 429.288 169.33 401.921 208.606 824 | 237.816 171.15 207.818 178.064 825 | 547.662 172.098 482.503 211.324 826 | 311.658 172.815 547.633 461.611 827 | 537.753 172.674 475.743 211.471 828 | 336.234 174.38 688.128 449.835 829 | 364.812 173.945 358.296 211.993 830 | 435.194 175.714 406.126 213.737 831 | 395.191 176.963 379.166 213.89 832 | 475.874 179.738 433.619 216.353 833 | 656.113 180.477 555.083 216.512 834 | 283.1 181.992 302.876 217.374 835 | 364.832 182.069 358.532 216.513 836 | 218.428 183.441 258.989 217.675 837 | 647.89 186.28 550.091 220.928 838 | 475.894 188.314 433.699 221.99 839 | 369.013 191.589 361.433 223.964 840 | 504.902 191.906 453.605 224.406 841 | 213.422 192.548 255.383 224.453 842 | 267.199 199.86 292.239 229.494 843 | 275.357 199.956 262.495 318.846 844 | 482.625 205.347 438.404 233.431 845 | 518.972 204.647 463.025 233.279 846 | 536.558 205.175 475.089 233.509 847 | 297.684 208.554 312.779 235.76 848 | 266.731 212.412 291.467 237.978 849 | 308.117 211.966 319.925 237.739 850 | 435.492 220.547 406.472 243.452 851 | 129.253 222.252 198.272 244.111 852 | 326.194 222.065 331.577 243.797 853 | 513.5 222.435 459.273 245.085 854 | 6.96945 225.911 113.332 379.128 855 | 298.48 226.067 313.154 247.405 856 | 266.942 227.032 292.047 247.55 857 | 470.576 233.196 430.206 252.337 858 | 216.173 236.359 257.062 254.193 859 | 276.727 236.207 298.499 254.094 860 | 555.839 238.514 487.682 256.387 861 | 510.19 240.346 456.74 257.546 862 | 499.592 241.182 449.721 257.876 863 | 229.414 243.667 267.477 258.83 864 | 753.87 243.685 621.95 260.307 865 | 632.838 247.298 540.419 230.653 866 | 554.285 248.443 487.17 263.229 867 | 298.642 252.458 313.352 265.097 868 | 233.62 256.268 269.265 267.675 869 | 83.8174 262.491 166.779 272.235 870 | 325.216 265.843 331.331 274.195 871 | 95.3103 266.902 174.147 274.957 872 | 133.646 267.188 201.358 274.094 873 | 233.876 267.438 269.147 276.807 874 | 514.843 267.664 460.066 275.813 875 | 547.238 269.203 482.215 276.707 876 | 118.087 271.994 191.064 278.5 877 | 129.929 271.961 199.213 277.652 878 | 542.588 272.653 478.982 279.249 879 | 226.884 275.404 264.243 280.855 880 | 476.751 277.38 434.385 282.497 881 | 213.875 279.099 255.693 283.148 882 | 556.257 283.858 488.095 287.077 883 | 208.067 288.076 254.18 528.232 884 | 355.725 291.525 351.92 351.136 885 | 630.602 293.09 539.266 323.912 886 | 435.584 295.117 406.382 294.338 887 | 288.43 296.268 307.448 505.973 888 | 416.81 296.263 393.413 294.748 889 | 135.357 297.304 202.195 295.493 890 | 118.741 306.758 191.572 301.472 891 | 396.565 310.574 379.834 304.515 892 | 426.277 309.628 399.948 304.067 893 | 514.242 311.643 459.762 306.232 894 | 533.184 317.407 472.396 310.48 895 | 542.787 318.542 479.128 310.727 896 | 231.499 319.52 267.62 310.663 897 | 475.741 321.471 433.619 312.085 898 | 243.092 321.101 303.948 282.601 899 | 548.411 321.721 482.895 312.562 900 | 556.166 330.1 487.72 318.825 901 | 520.76 339.194 464.102 324.287 902 | 555.241 339.444 487.132 324.677 903 | 407.218 341.305 386.948 326.257 904 | 436.627 341.353 406.929 325.631 905 | 391.574 342.259 375.849 239.618 906 | 284.084 343.186 303.522 326.808 907 | 396.811 345.31 379.904 328.3 908 | 101.594 348.827 180.301 330.683 909 | 396.96 352.037 379.865 332.238 910 | 721.836 353.584 157.694 325.604 911 | 737.675 353.259 161.101 325.553 912 | 436.886 354.184 407.208 334.951 913 | 446.551 353.928 413.659 334.144 914 | 326.813 354.853 331.834 334.911 915 | 426.52 354.733 399.876 334.742 916 | 62.8422 361.248 153.089 338.761 917 | 70.8912 360.442 158.353 338.311 918 | 651.531 365.604 552.57 342.919 919 | 24.8557 369.935 127.679 344.379 920 | 360.188 372.558 355.366 316.756 921 | 527.799 374.606 468.887 348.372 922 | 672.823 374.792 690.302 363.32 923 | 44.5111 379.132 141.284 350.821 924 | 23.2209 379.558 126.552 351.33 925 | 397.313 380.05 379.98 351.339 926 | 262.909 383.416 255.937 413.082 927 | 299.638 383.36 313.906 354.127 928 | 462.184 383.139 424.032 414.082 929 | 346.874 384.274 346.538 507.386 930 | 22.9151 384.991 125.771 354.581 931 | 32.0095 385.431 131.25 355.196 932 | 437.407 385.403 407.301 355.6 933 | 446.617 386.038 413.691 356.136 934 | 538.688 391.319 476.21 359.673 935 | 225.219 393.516 263.29 361.164 936 | 337.613 397.636 339.435 364.06 937 | 346.783 397.586 346.899 513.809 938 | 15.0068 400.152 120.826 365.138 939 | 538.966 399.483 476.392 365.976 940 | 479.52 406.735 435.838 370.235 941 | 278.543 412.039 299.554 373.64 942 | 686.271 415.004 752.528 343.922 943 | 240.157 427.486 273.008 383.75 944 | 347.949 427.464 346.576 385.074 945 | 317.493 427.922 325.839 384.488 946 | 234.893 430.901 269.749 386.207 947 | 338.129 431.135 339.662 385.497 948 | 397.347 430.722 380.028 386.223 949 | 447.953 431.084 414.148 386.767 950 | 556.59 431.54 487.702 386.676 951 | 493.591 431.869 445.16 417.993 952 | 515.949 432.215 460.61 387.58 953 | 667.356 434.321 563.597 389.455 954 | 338.424 440.795 339.966 393.389 955 | 447.242 443.245 413.923 395.096 956 | 706.224 446.374 790.511 158.63 957 | 233.974 450.909 269.113 399.933 958 | 551.674 454.674 484.872 403.507 959 | 663.83 455.268 560.504 402.804 960 | 697.54 458.051 582.891 405.113 961 | 370.395 465.042 360.899 409.412 962 | 131.704 466.027 200.02 409.623 963 | 706.82 467.544 771.716 588.148 964 | 673.778 469.613 566.409 412.586 965 | 299.953 471.239 313.673 414.216 966 | 338.198 472.277 339.749 414.551 967 | 691.507 472.464 579.148 415.067 968 | 235.247 475.244 270.019 416.341 969 | 447.924 475.322 414.475 416.858 970 | 703.379 476.62 586.916 419.956 971 | 275.404 478.919 296.85 419.335 972 | 655.526 481.724 554.792 420.996 973 | 338.868 484.642 339.978 423.08 974 | 438.07 484.916 407.461 423.269 975 | 289.982 485.93 307.047 333.758 976 | 344.398 488.764 343.728 425.722 977 | 438.707 491.317 407.422 427.485 978 | 650.029 492.591 551.495 428.322 979 | 222.556 493.827 261.051 428.916 980 | 14.7041 495.084 118.775 429.306 981 | 512.517 498.111 458.284 432.415 982 | 19.6047 500.498 123.792 433.428 983 | 664.04 501.138 560.587 434.131 984 | 745.799 502.287 777.812 350.693 985 | 727.638 503.68 603.736 435.848 986 | 52.7633 505.84 144.1 436.876 987 | 299.858 505.763 313.85 437.267 988 | 357.748 508.336 352.87 439.421 989 | 499.651 507.794 449.117 438.9 990 | 688.911 509.171 577.607 439.03 991 | 717.184 510.446 596.621 440.324 992 | 318.688 514.824 326.745 443.765 993 | 328.617 515.188 333.335 443.603 994 | 551.654 522.692 484.737 449.186 995 | 50.005 529.805 144.176 453.103 996 | 61.0132 530.697 151.705 453.716 997 | 655.515 530.483 554.75 454.496 998 | 708.902 533.25 591.491 453.988 999 | 318.718 533.599 326.751 455.914 1000 | 8.75057 538.332 116.577 458.574 1001 | 281.666 542.377 301.632 462.058 1002 | 59.1114 544.202 150.627 462.882 1003 | 479.924 545.238 259.516 222.243 1004 | 11.6476 548.425 117.657 465.572 1005 | 21.8894 550.462 9.56711 465.385 1006 | 492.83 549.775 444.58 467.516 1007 | 105.424 551.87 109.814 363.285 1008 | 737.675 556.109 257.003 583.006 1009 | 268.779 566.856 292.651 478.702 1010 | 285.559 567.46 303.953 479.006 1011 | 428.726 567.712 400.92 480.509 1012 | 409.069 569.354 387.973 480.884 1013 | 437.747 568.84 407.238 480.01 1014 | 403.66 570.108 384.143 481.568 1015 | 660.112 573.764 557.539 483.844 1016 | 487.829 575.855 441.057 485.369 1017 | 318.152 577.723 326.299 485.801 1018 | 327.648 579.147 77.1776 267.567 1019 | 268.884 581.682 292.484 489.082 1020 | 285.631 581.457 303.804 488.27 1021 | 409.381 582.653 387.929 489.134 1022 | 419.284 582.98 394.715 489.125 1023 | 428.409 583.113 401.16 489.535 1024 | 441.867 586.12 409.748 491.289 1025 | 281.614 587.686 301.338 492.671 1026 | 458.132 588.409 421.168 492.682 1027 | 479.68 589.646 435.644 494.322 1028 | 716.841 589.544 150.255 437.691 1029 | 479.98 595.391 435.82 497.831 1030 | 456.951 15.6565 422.065 105.362 1031 | 443.277 22.9791 411.798 110.287 1032 | 473.554 42.4634 432.532 119.99 1033 | 429.264 47.1411 402.346 126.199 1034 | 443.466 46.6459 411.969 125.935 1035 | 375.274 49.3249 365.737 127.444 1036 | 388.961 48.8432 374.959 127.234 1037 | 443.457 61.1998 411.906 135.76 1038 | 371.022 86.8644 362.575 152.212 1039 | 429.463 92.5016 402.476 156.889 1040 | 443.663 92.0672 412.081 156.592 1041 | 389.253 93.5328 375.146 157.544 1042 | 357.371 106.828 353.436 166.93 1043 | 389.337 107.263 375.21 166.788 1044 | 375.731 107.934 365.948 167.256 1045 | 455.978 117.747 420.491 174.433 1046 | 334.015 122.859 337.279 177.089 1047 | 579.745 135.632 503.733 186.536 1048 | 416.808 140.746 393.845 189.708 1049 | 468.161 141.424 428.307 190.266 1050 | 633.843 141.536 540.568 189.576 1051 | 327.235 143.511 332.964 190.986 1052 | 180.722 146.892 233.007 192.981 1053 | 548.452 151.74 482.851 197.437 1054 | 547.539 162.894 482.459 204.726 1055 | 435.04 167 406.094 207.304 1056 | 267.589 169.162 292.577 208.778 1057 | 281.754 169.546 302.074 209.024 1058 | 532.213 181.108 471.969 216.928 1059 | 481.241 185.179 437.447 220.266 1060 | 511.459 185.679 457.839 220.158 1061 | 633.454 191.421 540.205 223.858 1062 | 467.327 195.187 424.645 257.469 1063 | 650.557 202.616 552.197 231.976 1064 | 546.912 205.262 482.083 233.68 1065 | 260.133 210.483 287.138 236.468 1066 | 491.222 210.519 443.944 237.845 1067 | 95.6632 214.883 174.792 238.916 1068 | 537.714 215.767 475.632 240.716 1069 | 273.105 217.875 295.581 242.139 1070 | 425.764 219.619 399.859 243.284 1071 | 50.6682 222.097 144.814 243.634 1072 | 211.7 230.045 254.179 250.076 1073 | 271.294 232.676 295.282 251.4 1074 | 550.305 233.036 483.974 252.791 1075 | 368.89 234.433 361.059 252.515 1076 | 296.915 241.551 312.213 258.143 1077 | 209.045 242.805 252.575 258.779 1078 | 457.213 245.986 421.095 261.163 1079 | 520.052 250.376 465.443 510.696 1080 | 498.262 251.167 448.871 264.504 1081 | 360.16 253.343 354.866 265.663 1082 | 514.442 255.423 459.789 267.78 1083 | 426.346 255.571 400.025 268.195 1084 | 268.041 257.197 292.384 268.201 1085 | 548.278 262.127 482.819 272.598 1086 | 536.623 262.381 474.769 272.703 1087 | 304.764 264.861 317.349 274.096 1088 | 268.123 269.48 292.466 276.919 1089 | 360.369 285.61 355.256 287.888 1090 | 369.197 285.029 361.216 287.326 1091 | 297.729 285.874 312.846 288.205 1092 | 555.022 295.167 487.333 294.531 1093 | 530.817 295.857 470.941 294.908 1094 | 537.42 296.528 475.323 294.924 1095 | 261.768 297.501 288.074 295.726 1096 | 548.545 297.738 482.825 296.389 1097 | 333.742 299.618 337.08 297.912 1098 | 478.343 300.758 435.193 298.542 1099 | 283.087 301.25 302.783 297.949 1100 | 219.121 302.475 259.295 299.256 1101 | 457.24 301.598 420.817 298.59 1102 | 407.214 307.822 387.034 303.493 1103 | 129.352 313.455 198.437 306.135 1104 | 283.023 313.102 302.543 306.345 1105 | 456.584 316.814 420.524 308.596 1106 | 304.339 319.245 316.963 310.469 1107 | 511.949 319.82 458.315 311.536 1108 | 223.273 320.743 262.555 311.325 1109 | 641.043 320.925 545.44 311.981 1110 | 228.588 325.527 265.695 314.656 1111 | 526.733 328.419 468.229 317.785 1112 | 299.178 340.689 313.551 325.321 1113 | 316.354 340.899 325.255 325.258 1114 | 426.611 341.314 400.117 326.124 1115 | 538.111 341.433 475.781 326.129 1116 | 446.691 342.276 413.82 326.725 1117 | 515.483 344.174 460.464 327.423 1118 | 233.659 345.416 268.937 328.137 1119 | 690.823 352.171 580.056 334.004 1120 | 538.085 353.563 475.672 334.453 1121 | 762.275 353.099 627.45 334.187 1122 | 284.146 356.755 303.431 337.262 1123 | 515.521 356.844 460.369 336.793 1124 | 716.67 359.811 596.795 338.692 1125 | 282.705 364.73 302.277 341.644 1126 | 711.757 366.147 593.95 342.88 1127 | 721.597 366.138 181.081 498.571 1128 | 52.2229 371.24 147.124 344.684 1129 | 337.044 384.29 339.077 355.391 1130 | 136.261 384.784 202.72 354.753 1131 | 316.77 384.892 325.366 355.531 1132 | 416.656 384.925 393.482 355.481 1133 | 522.133 385.338 464.993 356.182 1134 | 427.05 386.175 400.371 355.778 1135 | 556.273 386.556 487.872 356.413 1136 | 219.344 389.698 259.154 358.075 1137 | 515.708 389.032 460.349 358.937 1138 | 549.352 392.359 483.218 360.594 1139 | 374.452 392.97 365.116 417.409 1140 | 13.9773 393.648 751.822 431.671 1141 | 427.286 399 400.332 364.879 1142 | 219.235 400.796 259.313 365.353 1143 | 532.44 400.82 471.788 365.818 1144 | 515.927 401.894 460.609 367.289 1145 | 674.138 405.122 567.927 368.823 1146 | 129.954 406.483 485.692 534.574 1147 | 699.093 407.261 584.747 370.909 1148 | 488.91 408.321 442.544 371.231 1149 | 2.98084 412.063 3.30851 216.336 1150 | 702.327 416.43 235.281 548.487 1151 | 23.3055 416.799 126.582 376.313 1152 | 527.422 417.828 468.296 377.823 1153 | 457.778 423.975 421.215 381.925 1154 | 307.007 430.232 318.932 385.699 1155 | 76.9765 432.542 181.541 566.897 1156 | 270.72 433.098 293.948 388.096 1157 | 282.197 433.375 301.957 388.082 1158 | 707.514 432.77 589.925 388.198 1159 | 385.63 435.742 371.795 387.886 1160 | 427.441 438.755 400.288 393.065 1161 | 307.121 440.106 318.947 393.067 1162 | 327.832 441.261 332.781 393.622 1163 | 282.244 443.571 301.876 394.784 1164 | 549.165 445.136 483.03 396.488 1165 | 515.44 446.419 460.276 397.395 1166 | 675.508 448.974 568.722 399.106 1167 | 659.466 449.972 557.39 399.988 1168 | 457.291 450.68 420.679 399.622 1169 | 700.692 451.163 584.963 400.611 1170 | 458.084 467.887 421.442 411.691 1171 | 317.299 472.062 325.775 414.253 1172 | 327.478 473.559 332.475 416.364 1173 | 438.006 474.865 407.395 416.865 1174 | 407.53 475.967 387.143 416.97 1175 | 715.421 476.015 596.123 417.604 1176 | 387.275 477.589 373.096 535.79 1177 | 492.577 478.285 444.899 451.388 1178 | 516.228 478.312 460.792 418.846 1179 | 417.991 486.151 393.57 424.202 1180 | 235.471 488.353 270.163 425.482 1181 | 268.82 488.956 292.346 425.926 1182 | 550.844 490.958 484.096 427.297 1183 | 658.444 491.33 556.903 427.788 1184 | 135.183 495.024 699.083 385.514 1185 | 217.537 499.828 257.954 433.092 1186 | 641.925 502.644 545.809 435.224 1187 | 85.482 504.165 167.758 435.967 1188 | 210.283 503.463 251.922 435.24 1189 | 458.365 511.986 421.509 441.613 1190 | 361.837 513.451 356.171 442.038 1191 | 273.496 516.313 435.348 413.931 1192 | 387.195 518.472 373.089 446.912 1193 | 514.365 519.763 459.325 446.986 1194 | 699.886 522.474 585.394 449.596 1195 | 270.314 523.282 293.617 449.046 1196 | 307.825 525.639 319.17 451.362 1197 | 714.255 524.991 594.463 450.457 1198 | 328.304 533.926 332.916 456.057 1199 | 664.865 534.334 561.043 456.337 1200 | 234.934 535.687 268.878 306.71 1201 | 56.6772 537.268 154.958 556.177 1202 | 428.164 536.401 400.736 458.618 1203 | 290.212 541.519 307.115 461.524 1204 | 361.946 548.351 355.892 466.885 1205 | 561.798 551.466 491.436 468.574 1206 | 37.8431 553.246 136.756 469.085 1207 | 318.081 565.062 326.223 477.201 1208 | 327.945 566.918 433.476 316.536 1209 | 500.807 566.949 450.109 478.914 1210 | 220.491 568.426 293.138 358.178 1211 | 553.15 568.175 498.183 557.38 1212 | 493.953 570.647 445.416 481.409 1213 | 307.117 576.458 318.725 485.11 1214 | 220.713 579.692 259.992 487.477 1215 | 447.949 581.659 413.944 488.668 1216 | 493.875 583.965 445.49 490.562 1217 | 709.501 586.64 591.884 492.854 1218 | 305.909 587.85 317.94 493.446 1219 | 647.102 588.248 548.861 493.431 1220 | 435.702 54.5235 406.809 131.2 1221 | 435.522 98.9747 406.309 161.217 1222 | 382.489 100.397 370.557 162.02 1223 | 396.651 112.185 381.135 169.87 1224 | 422.723 112.105 397.613 169.741 1225 | 501.169 117.003 450.066 173.462 1226 | 619.527 134.544 531.697 186.076 1227 | 284.771 143.585 303.729 191.16 1228 | 228.082 144.549 266.947 191.243 1229 | 326.54 156.924 332.29 200.663 1230 | 345.584 157.216 345.696 200.74 1231 | 304.899 159.451 317.121 202.727 1232 | 384.84 161.637 371.961 203.709 1233 | 230.638 170.02 743.373 331.391 1234 | 469.182 181.776 429.182 217.576 1235 | 211.141 184.203 253.826 218.527 1236 | 641.964 187.483 546.253 222.149 1237 | 557.1 190.942 488.987 223.963 1238 | 524.973 192.98 466.98 225.239 1239 | 227.599 194.91 686.898 295.772 1240 | 204.875 196.494 249.594 227.256 1241 | 295.305 197.336 311.155 227.709 1242 | 360.299 197.225 355.124 227.916 1243 | 658.484 203.361 557.504 232.558 1244 | 302.943 204.047 316.367 232.426 1245 | 210.224 211.841 253.141 237.816 1246 | 458.544 215.354 421.969 240.055 1247 | 218.933 215.848 259.45 240.231 1248 | 478.197 222.025 435.021 245.233 1249 | 455.127 228.623 419.804 248.449 1250 | 478.632 230.403 581.461 588.273 1251 | 642.076 235.809 546.386 254.652 1252 | 669.42 235.523 563.848 254.377 1253 | 754.855 236.536 621.891 254.053 1254 | 712.855 243.765 594.108 260.028 1255 | 260.141 256.106 286.633 268.309 1256 | 490.886 255.657 443.843 268.085 1257 | 661.321 258.774 581.799 441.099 1258 | 478.37 265.735 435.212 304.647 1259 | 195.405 272.179 242.526 277.601 1260 | 656.786 280.238 555.935 284.841 1261 | 733.647 281.437 608.186 285.752 1262 | 233.019 282.371 268.718 285.357 1263 | 465.768 283.622 427.139 286.737 1264 | 457.404 290.526 421.251 291.358 1265 | 491.4 300.285 444.205 297.823 1266 | 384.681 305.49 372.021 301.137 1267 | 538.221 306.138 475.642 302.482 1268 | 320.45 307.733 327.958 302.032 1269 | 491.313 311.232 444.118 305.579 1270 | 734.16 313.49 608.736 307.468 1271 | 475.27 324.82 433.015 314.6 1272 | 241.341 343.303 274.216 326.6 1273 | 260.656 342.574 287.587 326.399 1274 | 549.094 350.8 483.292 333.806 1275 | 211.952 351.222 254.04 332.049 1276 | 269.252 355.12 293.293 335.297 1277 | 232.961 356.087 268.535 335.717 1278 | 128.913 364.089 197.925 340.958 1279 | 645.363 366.108 548.268 343.064 1280 | 81.1041 368.087 165.766 343.692 1281 | 297.475 371.736 312.333 346.08 1282 | 457.453 378.751 421.265 351.384 1283 | 665.143 381.001 561.309 353.497 1284 | 52.5916 382.797 146.086 353.81 1285 | 723.573 382.506 600.736 354.161 1286 | 260.787 386.809 287.639 356.226 1287 | 283.242 389.002 302.562 358.152 1288 | 479.309 389.969 435.524 358.467 1289 | 720.031 391.443 599.504 360.068 1290 | 705.43 391.852 590.411 360.229 1291 | 654.788 399.404 555.098 364.308 1292 | 269.819 399.838 293.496 365.206 1293 | 283.182 399.966 302.517 365.666 1294 | 233.288 401.143 268.783 366.035 1295 | 666.131 404.543 160.864 438.249 1296 | 212.698 405.684 254.618 368.768 1297 | 513.412 411.591 459.314 373.33 1298 | 297.977 416.044 312.736 376.318 1299 | 32.009 416.448 593.777 386.28 1300 | 499.795 429.427 449.743 386.321 1301 | 271.079 443.231 294.473 395.223 1302 | 537.701 444.007 476.694 425.11 1303 | 129.187 445.551 196.929 394.901 1304 | 306.054 452.751 317.878 401.53 1305 | 212.236 473.285 254.394 415.413 1306 | 242.401 474.302 274.58 415.574 1307 | 479.435 477.504 435.522 418.41 1308 | 684.712 476.811 617.148 428.047 1309 | 557.993 478.907 489.063 419.318 1310 | 492.41 488.669 444.533 425.775 1311 | 516.433 490.891 460.728 427.66 1312 | 686.581 495.691 575.753 431.395 1313 | 129.893 502.415 198.025 434.817 1314 | 657.795 518.299 556.223 446.127 1315 | 234.311 524.489 269.213 450.042 1316 | 479.966 527.385 435.873 451.901 1317 | 263.065 527.969 288.844 452.477 1318 | 516.085 529.402 460.568 453.256 1319 | 307.935 531.417 319.333 454.434 1320 | 480.248 537.499 436.214 459.007 1321 | 516.259 539.542 460.507 459.948 1322 | 658.4 539.911 556.621 460.505 1323 | 229.15 549.591 265.433 466.944 1324 | 464.961 554.382 425.858 470.743 1325 | 386.953 565.21 372.953 477.786 1326 | 402.009 581.62 382.952 488.685 1327 | 516.862 583.413 460.835 490.448 1328 | 397.18 592.376 379.793 496.19 1329 | 451.859 54.447 417.104 131.265 1330 | 472.911 96.1164 431.58 159.264 1331 | 579.013 120.334 504.131 174.927 1332 | 639.807 151.314 544.693 197.438 1333 | 652.106 151.211 553.214 197.191 1334 | 361.641 155.253 356.113 199.098 1335 | 371.606 162.09 363.015 204.024 1336 | 500.946 174.93 450.683 213.145 1337 | 372.455 176.663 363.442 213.536 1338 | 199.931 178.247 36.4552 329.942 1339 | 386.031 182.577 373.314 217.837 1340 | 495.458 191.683 447.048 224.549 1341 | 458.444 201.414 421.715 230.925 1342 | 52.5488 213.506 146.399 238.8 1343 | 15.8872 223.242 121.598 245.04 1344 | 27.7852 227.43 130.365 248.265 1345 | 524.08 235.886 466.43 254.61 1346 | 117.62 238.16 190.525 255.681 1347 | 472.128 241.803 431.421 258.762 1348 | 755.822 252.023 150.351 560.874 1349 | 120.002 263.49 192.112 273.582 1350 | 315.341 266.645 325.031 274.88 1351 | 456.251 273.685 420.426 279.19 1352 | 295.441 282.096 311.583 285.647 1353 | 724.397 287.944 602.157 289.304 1354 | 241.507 300.853 274.217 297.688 1355 | 724.059 300.166 601.696 298.867 1356 | 60.5356 314.685 584.063 279.996 1357 | 241.391 316.169 274.057 309.008 1358 | 467.963 343.152 428.223 326.581 1359 | 210.19 345.116 252.932 329.036 1360 | 242.315 344.72 275.116 328.442 1361 | 666.712 346.008 562.84 328.128 1362 | 499.599 350.666 449.57 331.523 1363 | 513.717 367.493 459.012 343.569 1364 | 116.983 373.435 190.097 347.201 1365 | 704.662 375.807 587.712 349.91 1366 | 692.389 377.356 580.16 350.448 1367 | 128.102 382.006 196.839 354.121 1368 | 210.145 388.854 253.24 357.621 1369 | 259.682 388.631 287.566 387.274 1370 | 630.608 388.63 490.05 439.846 1371 | 689.096 406.622 577.436 370.33 1372 | 79.0925 414.219 24.9399 577.345 1373 | 137.964 413.811 203.225 375.619 1374 | 216.126 418.605 256.961 377.945 1375 | 477.311 417.725 434.381 378.106 1376 | 631.513 417.236 538.973 377.564 1377 | 283.06 419.597 302.392 378.406 1378 | 129.897 422.972 198.47 381.359 1379 | 210.904 432.42 253.497 386.884 1380 | 514.761 456.999 459.591 404.503 1381 | 666.812 461.076 562.366 405.487 1382 | 631.241 463.006 538.468 407.573 1383 | 550.048 504.232 483.751 436.003 1384 | 631.576 507.525 538.17 438.507 1385 | 138.739 518.843 204.356 445.522 1386 | 15.9708 523.585 120.932 448.999 1387 | 743.712 547.138 612.967 465.569 1388 | 644.454 557.879 547.173 472.759 1389 | 211.432 568.032 254.136 478.274 1390 | 559.606 576.874 489.645 485.558 1391 | 717.516 578.579 597.413 486.072 1392 | 340.547 579.654 341.517 487.689 1393 | 351.171 118.852 349.136 174.846 1394 | 450.952 129.399 417.439 181.86 1395 | 483.121 131.739 438.74 183.991 1396 | 636.045 132.64 542.453 184.67 1397 | 329.556 133.924 334.214 185.054 1398 | 525.685 171.483 467.218 211.203 1399 | 557.691 208.627 489.401 235.954 1400 | 369.221 209.483 361.289 236.032 1401 | 527.919 212.326 468.069 299.786 1402 | 542.493 210.772 478.818 237.209 1403 | 3.24935 215.119 2.11017 331.479 1404 | 468.312 222.669 428.461 244.926 1405 | 233.266 238.256 268.94 255.439 1406 | 265.935 237.869 291.088 255.558 1407 | 468.323 256.132 428.394 268.483 1408 | 293.172 259.192 309.582 269.998 1409 | 222.027 263.504 261.613 272.467 1410 | 384.645 264.35 372.357 272.959 1411 | 468.061 267.107 428.347 275.136 1412 | 492.456 278.897 444.878 283.875 1413 | 208.6 302.288 252.038 299.007 1414 | 258.575 302.703 286.059 299.33 1415 | 468.257 300.705 428.399 298.419 1416 | 502.06 302.744 451.196 299.299 1417 | 493.448 323.93 445.592 314.131 1418 | 217.901 325.665 258.706 315.001 1419 | 295.149 346.439 310.814 328.375 1420 | 527.485 347.438 468.611 330.607 1421 | 488.568 352.335 442.557 334.077 1422 | 231.274 368.722 267.653 344.046 1423 | 631.411 368.885 539.372 345.004 1424 | 41.7663 375.431 140.087 348.395 1425 | 13.7415 388.888 119.952 357.357 1426 | 295.08 390.685 310.667 359.46 1427 | 468.576 389.468 428.566 357.472 1428 | 502.671 392.693 451.527 360.327 1429 | 229.244 412.552 265.653 373.743 1430 | 267.799 412.541 292.4 373.931 1431 | 492.738 413.071 444.514 374.759 1432 | 643.748 411.693 547.068 374.022 1433 | 468.027 434.6 428.132 388.979 1434 | 138.893 454.618 204.337 402.6 1435 | 274.644 456.471 296.763 403.879 1436 | 441.163 479.019 409.416 419.318 1437 | 468.166 480.51 428.291 420.475 1438 | 527.753 482.312 468.569 421.055 1439 | 235.448 498.918 270.262 432.546 1440 | 276.259 499.452 298.543 432.857 1441 | 220.601 505.966 259.979 437.305 1442 | 503.858 535.455 452.185 457.483 1443 | 560.607 540.823 490.448 461.473 1444 | 109.315 557.722 184.473 472.243 1445 | 78.2298 569.202 163.754 480.251 1446 | 296.089 570.292 311.211 481.116 1447 | 469.22 573.121 428.741 482.672 1448 | 631.395 580.959 538.045 488.855 1449 | 352.017 28.4547 350.091 113.694 1450 | 434.656 77.1045 405.38 146.776 1451 | 335.454 96.3924 338.648 159.354 1452 | 309.145 120.108 320.347 175.698 1453 | 149.648 122.37 213.149 176.218 1454 | 370.346 123.854 362.266 178.014 1455 | 410.597 134.764 389.5 185.354 1456 | 203.731 141.843 249.009 190.092 1457 | 560.782 150.058 491.824 197.17 1458 | 520.14 152.111 463.917 197.578 1459 | 477.406 153.699 434.832 198.518 1460 | 289.473 159.172 307.395 202.368 1461 | 358.164 170.326 353.678 209.716 1462 | 484.801 171.812 439.53 210.835 1463 | 223.772 174.376 262.648 212.219 1464 | 274.181 174.305 297.178 212.172 1465 | 428.864 213.225 402.071 238.303 1466 | 447.606 214.121 414.739 239.456 1467 | 352.331 217.224 349.538 241.389 1468 | 370.773 254.632 362.415 266.745 1469 | 351.422 261.211 349.094 271.147 1470 | 485.63 261.459 440.615 271.525 1471 | 663.689 267.313 561.833 276.559 1472 | 123.875 277.794 194.589 282.331 1473 | 521.689 278.48 464.721 283.234 1474 | 295.614 305.125 311.043 300.956 1475 | 353.92 305.133 350.99 300.995 1476 | 487.05 305.423 440.469 301.271 1477 | 226.292 308.242 263.927 302.983 1478 | 520.341 322.346 463.724 312.799 1479 | 226.4 351.624 263.95 332.504 1480 | 489.352 369.144 442.695 344.832 1481 | 313.01 389.52 322.981 358.313 1482 | 353.3 392.45 350.246 360.298 1483 | 277.428 394.603 298.706 361.829 1484 | 486.767 393.834 440.682 361.279 1485 | 545.013 395.14 480.264 362.276 1486 | 469.063 402.604 428.697 367.661 1487 | 672.157 425.187 565.717 382.666 1488 | 295.151 434.496 310.736 388.753 1489 | 276.272 438.703 297.821 391.527 1490 | 486.837 440.073 440.816 392.854 1491 | 543.135 439.682 478.798 392.326 1492 | 490.067 458.054 442.659 405.058 1493 | 296.035 479.237 311.273 419.487 1494 | 227.632 481.791 264.768 420.969 1495 | 484.853 483.576 439.335 422.436 1496 | 545.8 486.034 480.659 423.983 1497 | 294.148 496.261 310.049 430.38 1498 | 470.679 498.166 430.479 433.047 1499 | 521.658 502.171 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231 463 204 358 | 468 542 462 519 359 | 90 309 125 309 360 | 26 360 109 355 361 | 69 420 91 419 362 | 249 327 250 300 363 | 682 229 660 232 364 | 646 293 646 326 365 | 113 277 89 277 366 | 519 278 525 253 367 | 638 519 636 545 368 | 89 280 114 280 369 | 89 272 114 272 370 | 177 261 191 280 371 | 391 441 371 442 372 | 331 512 305 512 373 | 646 335 647 358 374 | 364 254 363 281 375 | 113 291 89 291 376 | 368 102 345 103 377 | 751 231 751 266 378 | 65 310 86 310 379 | 88 321 55 321 380 | 57 324 89 324 381 | 199 196 197 173 382 | 398 574 376 574 383 | 716 259 716 238 384 | 89 302 114 302 385 | 463 594 463 569 386 | 637 573 636 598 387 | 359 170 360 200 388 | 90 336 55 336 389 | 114 298 88 298 390 | 89 287 114 287 391 | 634 446 635 466 392 | 88 294 114 294 393 | 647 253 645 285 394 | 102 217 36 218 395 | 114 306 88 306 396 | 76 343 55 343 397 | 77 588 58 595 398 | 737 280 737 315 399 | 648 421 647 443 400 | 648 464 648 486 401 | 658 469 658 449 402 | 365 472 363 495 403 | 464 48 463 21 404 | 476 51 475 28 405 | 634 339 634 375 406 | -------------------------------------------------------------------------------- /pts&lines/1Bline.txt: -------------------------------------------------------------------------------- 1 | 558 226 556 195 2 | 200 437 200 351 3 | 760 205 700 206 4 | 381 351 381 325 5 | 201 497 200 440 6 | 484 214 485 191 7 | 381 306 381 279 8 | 381 439 381 378 9 | 316 441 315 473 10 | 309 541 309 561 11 | 35 464 14 464 12 | 315 262 314 289 13 | 381 275 380 221 14 | 697 317 696 294 15 | 698 392 697 371 16 | 229 179 203 180 17 | 446 221 446 201 18 | 486 350 485 323 19 | 486 380 485 354 20 | 487 261 540 260 21 | 315 323 315 348 22 | 313 320 273 320 23 | 203 382 314 382 24 | 264 320 198 320 25 | 486 442 486 415 26 | 203 411 314 412 27 | 315 413 315 439 28 | 202 195 238 195 29 | 314 409 203 408 30 | 349 197 316 198 31 | 559 422 559 500 32 | 201 293 314 293 33 | 546 319 488 320 34 | 542 257 488 258 35 | 232 231 211 231 36 | 263 473 299 474 37 | 314 234 314 259 38 | 547 288 488 289 39 | 539 226 486 227 40 | 202 234 313 233 41 | 289 290 201 291 42 | 316 383 315 408 43 | 202 323 313 322 44 | 316 475 315 500 45 | 535 183 504 183 46 | 472 229 540 229 47 | 487 292 548 291 48 | 269 501 209 499 49 | 291 194 311 194 50 | 540 444 488 443 51 | 488 415 541 416 52 | 203 473 260 473 53 | 250 379 201 379 54 | 316 353 315 378 55 | 350 310 350 335 56 | 489 481 543 482 57 | 293 260 200 261 58 | 200 264 313 263 59 | 316 504 315 530 60 | 254 438 203 437 61 | 312 349 201 349 62 | 255 231 234 231 63 | 296 379 263 379 64 | 538 171 488 172 65 | 202 352 313 352 66 | 559 499 559 524 67 | 281 530 203 529 68 | 240 195 268 194 69 | 322 178 280 178 70 | 498 188 539 188 71 | 203 502 254 503 72 | 203 440 314 441 73 | 312 290 291 290 74 | 359 200 359 228 75 | 296 471 263 471 76 | 313 438 264 438 77 | 556 257 558 238 78 | 777 423 777 394 79 | 200 347 200 324 80 | 698 418 697 396 81 | 350 249 350 275 82 | 541 479 488 478 83 | 489 447 543 447 84 | 468 258 436 259 85 | 487 323 543 322 86 | 540 413 488 413 87 | 541 356 542 380 88 | 700 244 749 244 89 | 699 269 736 269 90 | 541 510 489 509 91 | 203 531 278 533 92 | 488 504 485 483 93 | 488 512 541 513 94 | 697 291 697 269 95 | 260 471 203 470 96 | 435 106 355 108 97 | 287 533 314 533 98 | 433 539 433 561 99 | 540 382 488 382 100 | 126 476 10 513 101 | 422 262 470 261 102 | 447 192 483 190 103 | 266 178 230 179 104 | 489 384 514 384 105 | 700 294 738 294 106 | 736 241 699 241 107 | 315 294 314 319 108 | 423 382 469 383 109 | 606 428 587 457 110 | 274 503 314 504 111 | 311 231 256 231 112 | 423 292 454 292 113 | 736 393 700 392 114 | 736 266 699 267 115 | 452 410 424 410 116 | 746 368 700 367 117 | 298 501 269 501 118 | 606 424 578 422 119 | 697 265 697 244 120 | 699 492 697 471 121 | 540 351 488 351 122 | 488 353 541 353 123 | 698 209 758 208 124 | 421 232 441 231 125 | 484 174 458 175 126 | 82 455 42 466 127 | 424 442 469 444 128 | 701 395 738 395 129 | 419 216 399 218 130 | 450 350 424 350 131 | 699 344 736 344 132 | 127 461 108 469 133 | 348 308 316 308 134 | 423 352 470 353 135 | 699 370 736 370 136 | 200 198 200 233 137 | 108 470 10 499 138 | 681 507 681 474 139 | 451 440 424 440 140 | 423 322 454 322 141 | 698 468 697 445 142 | 453 504 425 503 143 | 759 209 758 230 144 | 106 342 151 342 145 | 424 475 469 477 146 | 669 562 616 561 147 | 700 420 738 421 148 | 736 292 700 292 149 | 28 443 0 449 150 | 451 319 423 320 151 | 736 317 700 317 152 | 171 342 198 342 153 | 420 195 395 196 154 | 542 417 542 443 155 | 699 445 736 446 156 | 736 418 700 418 157 | 382 536 382 494 158 | 424 412 470 413 159 | 76 430 143 431 160 | 141 353 95 352 161 | 416 247 383 247 162 | 542 232 542 258 163 | 151 468 129 466 164 | 698 543 696 519 165 | 450 380 423 380 166 | 700 470 738 471 167 | 125 444 103 450 168 | 680 274 679 296 169 | 736 342 700 342 170 | 416 338 383 338 171 | 441 161 443 115 172 | 422 176 394 176 173 | 289 205 289 226 174 | 87 537 68 543 175 | 699 572 697 541 176 | 452 414 452 439 177 | 737 494 700 493 178 | 347 248 316 248 179 | 541 294 542 316 180 | 601 553 679 555 181 | 542 447 542 478 182 | 701 319 738 319 183 | 74 228 54 227 184 | 200 317 200 295 185 | 758 470 739 464 186 | 347 278 316 278 187 | 418 277 383 277 188 | 680 348 658 347 189 | 736 443 700 443 190 | 124 435 46 454 191 | 737 519 700 518 192 | 701 521 738 522 193 | 779 520 777 494 194 | 422 407 421 385 195 | 542 386 543 413 196 | 1 555 32 543 197 | 115 452 137 449 198 | 626 551 673 540 199 | 349 460 318 460 200 | 737 468 700 468 201 | 150 439 125 437 202 | 756 201 699 202 203 | 700 496 736 496 204 | 6 429 48 429 205 | 32 433 73 434 206 | 451 384 452 404 207 | 423 438 423 415 208 | 737 544 700 543 209 | 178 491 45 542 210 | 357 233 358 259 211 | 422 501 425 480 212 | 701 546 738 547 213 | 46 538 150 498 214 | 423 194 421 215 215 | 578 424 603 426 216 | 28 434 0 440 217 | 181 500 156 510 218 | 343 109 343 161 219 | 347 368 318 368 220 | 417 524 384 523 221 | 676 271 676 248 222 | 0 525 35 538 223 | 29 548 0 559 224 | 416 399 384 399 225 | 451 266 451 288 226 | 422 472 424 450 227 | 423 533 423 508 228 | 50 483 121 462 229 | 558 345 558 365 230 | 116 234 93 234 231 | 126 435 146 434 232 | 417 429 384 429 233 | 51 555 73 555 234 | 66 328 91 328 235 | 416 369 384 368 236 | 781 195 780 216 237 | 155 340 125 339 238 | 582 251 559 251 239 | 155 497 177 488 240 | 49 429 74 430 241 | 30 489 49 484 242 | 349 427 318 427 243 | 417 493 385 493 244 | 660 553 626 552 245 | 27 539 6 530 246 | 197 276 166 276 247 | 53 426 0 426 248 | 178 241 136 242 249 | 64 437 33 437 250 | 620 252 619 278 251 | 171 326 148 326 252 | 58 431 33 431 253 | 86 431 60 431 254 | 642 250 620 251 255 | 170 316 149 316 256 | 72 445 91 440 257 | 243 209 241 229 258 | 339 490 318 490 259 | 170 311 149 311 260 | 610 285 610 308 261 | 48 471 73 464 262 | 149 319 170 319 263 | 542 325 540 348 264 | 357 350 356 371 265 | 143 519 168 520 266 | 359 535 358 556 267 | 80 494 126 479 268 | 354 497 352 475 269 | 627 335 601 336 270 | 358 471 358 496 271 | -------------------------------------------------------------------------------- /sameside.m: -------------------------------------------------------------------------------- 1 | 2 | function ss=sameside(line,point1,point2) 3 | 4 | ss = false; 5 | if isnan(point2(1)) || isnan(point2(2)) 6 | return; 7 | end 8 | 9 | if (line.k~=Inf) 10 | s1=line.k*point1(1)+line.b-point1(2); 11 | s2=line.k*point2(1)+line.b-point2(2); 12 | else 13 | s1=point1(1)-line.point1(1); 14 | s2=point2(1)-line.point1(1); 15 | end 16 | 17 | if s1*s2>0 18 | ss = true; 19 | end 20 | 21 | end 22 | --------------------------------------------------------------------------------