├── .gitignore
├── LICENSE.txt
├── README.md
└── release
├── data
├── example1.mat
├── example2.mat
├── example3.mat
└── frontCam.mat
├── demo.m
├── models
└── mocapReducedModel.mat
├── setup.m
└── src
├── alignToCamera.m
├── cameraAndPose.m
├── drawCam.m
├── estimateWPCamera.m
├── leastsquareseqcon3.m
├── plot2Dskeleton.m
├── pointsVisualize.m
├── process_options.m
├── projectIntoAffineCam.m
├── reArrangeBasis.m
├── recon3DPose.m
├── setK.m
├── skelConnectionMatrix.m
└── visualizeGaussianModel.m
/.gitignore:
--------------------------------------------------------------------------------
1 | .m~
2 | .asv
3 |
4 |
--------------------------------------------------------------------------------
/LICENSE.txt:
--------------------------------------------------------------------------------
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--------------------------------------------------------------------------------
/README.md:
--------------------------------------------------------------------------------
1 | This repository contains code and examples for the paper:
2 |
3 | Reconstructing 3D Human Pose from 2D Image Landmarks.
4 | [Varun Ramakrishna](http://www.cs.cmu.edu/~vramakri), [Takeo Kanade](http://wwww.cs.cmu.edu/~tk), [Yaser Sheikh](http://www.cs.cmu.edu/~yaser)
5 | European Conference on Computer Vision, 2012.
6 |
7 | Please cite the above paper if you use the code in your work.
8 |
9 | ---
10 | **Copyright (C) 2012 by Varun Ramakrishna**
11 |
12 | camera_and_pose is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by (at your option) any later version.
13 |
14 | camera_and_pose is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.
15 |
16 | You should have received a copy of the GNU General Public licenses along with camera_and_pose. If not, see .
17 |
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/release/data/example1.mat:
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https://raw.githubusercontent.com/varunnr/camera_and_pose/2094baed10af928dc0d2215c1ff51e15a845dc76/release/data/example1.mat
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/release/data/example2.mat:
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https://raw.githubusercontent.com/varunnr/camera_and_pose/2094baed10af928dc0d2215c1ff51e15a845dc76/release/data/example2.mat
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/release/data/example3.mat:
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https://raw.githubusercontent.com/varunnr/camera_and_pose/2094baed10af928dc0d2215c1ff51e15a845dc76/release/data/example3.mat
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/release/data/frontCam.mat:
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https://raw.githubusercontent.com/varunnr/camera_and_pose/2094baed10af928dc0d2215c1ff51e15a845dc76/release/data/frontCam.mat
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/release/demo.m:
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1 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Demo %%%%%%%%%%%%%%%%%%%%%%%%%%%%
2 | disp('Reconstructing Example 1');
3 | load example1.mat;
4 | [X, R, t] = recon3DPose(im,xy,'viz',1);
5 | input('Continue?');
6 |
7 | disp('Reconstructing Example 2');
8 | load example2.mat;
9 | [X, R, t] = recon3DPose(im,xy,'viz',1);
10 | input('Continue?');
11 |
12 | disp('Reconstructing Example 3');
13 | load example3.mat;
14 | [X, R, t] = recon3DPose(im,xy,'viz',1);
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/release/models/mocapReducedModel.mat:
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https://raw.githubusercontent.com/varunnr/camera_and_pose/2094baed10af928dc0d2215c1ff51e15a845dc76/release/models/mocapReducedModel.mat
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/release/setup.m:
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1 | addpath src;
2 | addpath data;
3 | addpath models;
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/release/src/alignToCamera.m:
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1 | function [Xnew]=alignToCamera(X,R,t,Rnew,tnew)
2 | % [Xnew]=alignToCamera(X,R,t,Rnew,tnew)
3 | %
4 | % R, t - Current Camera
5 | % Rnew, tnew - Camera to be aligned to.
6 | %
7 | %
8 |
9 | Xnew = R*X' + repmat(t,1,length(X));
10 | Xnew = Rnew*Xnew+repmat(tnew,1,length(X));
11 |
12 | Xnew = Xnew';
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/release/src/cameraAndPose.m:
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1 | function [camera, pose] = cameraAndPose(pose)
2 | % Inputs: pose - Structure containing 2D annotations and algorithm
3 | % parameters. See recon3DPose.m
4 | %
5 | % Outputs: camera - Structure with estimated camera parameters.
6 | % pose - Structure with estimated 3D pose.
7 | %
8 | % Reconstructs the 3D Pose of a human figure given the locations of the 2D
9 | % anatomical landmarks.
10 | % Copyright (C) 2012 Varun Ramakrishna.
11 | %
12 | % This program is free software: you can redistribute it and/or modify
13 | % it under the terms of the GNU General Public License as published by
14 | % the Free Software Foundation, either version 3 of the License, or
15 | % (at your option) any later version.
16 | %
17 | % This program is distributed in the hope that it will be useful,
18 | % but WITHOUT ANY WARRANTY; without even the implied warranty of
19 | % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
20 | % GNU General Public License for more details.
21 | %
22 | % You should have received a copy of the GNU General Public License
23 | % along with this program. If not, see .
24 |
25 | % Compute lengths and skeleton connectivity matrix.
26 | pose = getLimbLengths(pose);
27 |
28 | %% Initialization
29 | % Scale input so that K = eye(3).
30 | pose = scaleInput(pose);
31 |
32 | % Reshape Basis
33 | pose = reshapeBasis(pose);
34 |
35 | % Estimate initial cameras
36 | rigidInds = [1 2 5 8]; % Use rigid landmarks to estimate initial cam.
37 | xyMissing = pose.xyh(:,rigidInds);
38 | XMissing = pose.Xmu(rigidInds,1:3);
39 | [camera] = estimateWPCamera(xyMissing',XMissing);
40 |
41 | %Assemble projection matrix
42 | Msub = kron(eye(length(pose.annoids),length(pose.annoids)),camera.M);
43 | Mmu = Msub*pose.mureVis;
44 | xyt = pose.xyvisible(:) - kron(ones(length(pose.annoids),1),camera.taff);
45 | res = xyt - Mmu;
46 |
47 | %% Projected Matching Pursuit
48 | selectIdx = [];
49 | pose.numIters = 0;
50 | pose.repErr = inf;
51 | while (pose.repErr> pose.tol1 && length(selectIdx) < pose.ks)
52 |
53 | %Pick best basis vector
54 | A = Msub*pose.BreVis;
55 | A(:,selectIdx) = NaN;
56 | lambdas = res'*A;
57 | [~,imax] = max(abs(lambdas));
58 |
59 | % Add basis to collection
60 | selectIdx = [selectIdx imax];
61 | pose.selectIdx = selectIdx;
62 |
63 | % Minimize reconstruction error and compute residual
64 | [camera, pose, res] = minimizeReconError(pose, camera);
65 | Msub = kron(eye(length(pose.annoids),length(pose.annoids)),camera.M);
66 | end
67 |
68 | end
69 |
70 |
71 |
72 | function pose = scaleInput(pose)
73 | % Helper function to scale input so that K = eye(3)
74 | pose.xyunscaled = pose.xy;
75 | pose.xyh = pose.K\pose.xy;
76 | pose.xyvisible = pose.xyh(1:2,pose.annoids);
77 | end
78 |
79 |
80 | function pose = reshapeBasis(pose)
81 | % Helper function to reshape basis
82 |
83 | Bnew=[];
84 | for i =1:size(pose.BOMP,2);
85 | Bnew =cat(3,Bnew,reshape(pose.BOMP(:,i),pose.numPoints,3));
86 | end
87 | pose.Breshaped = Bnew;
88 | pose.mur = reshape(pose.mu,pose.numPoints,3);
89 | pose.Bfull = pose.BOMP;
90 | [pose.Bre,pose.mure] = reArrangeBasis(pose.BOMP,pose.mu,pose.numPoints);
91 |
92 | pose.BreTensor = reshape(pose.Bre,3,pose.numPoints,[]);
93 | pose.mureTensor = reshape(pose.mure,3,pose.numPoints,[]);
94 | pose.mureVis = pose.mureTensor(:,pose.annoids);
95 | pose.mureVis = pose.mureVis(:);
96 | pose.BreVis = pose.BreTensor(:,pose.annoids,:);
97 | pose.BreVis = reshape(pose.BreVis, 3*length(pose.annoids),[]);
98 |
99 | end
100 |
101 | function pose = getLimbLengths(pose)
102 | % Helper function to compute limblengths.
103 |
104 | connect = skelConnectionMatrix(pose.skel);
105 | [pose.I,pose.J] = ind2sub(size(connect), find(connect));
106 | Xmu = reshape(pose.mu,pose.numPoints,3);
107 | Xmu = [Xmu ones(length(pose.xy),1)];
108 | pose.lengths = squareform(pdist(Xmu));
109 | pose.Xmu = Xmu;
110 | pose.lengths = squareform(pdist(Xmu));
111 |
112 | end
113 |
114 |
115 | function [camera,pose,res] = minimizeReconError(pose,camera)
116 | selectIdx = pose.selectIdx;
117 | optType = pose.optType;
118 | mur = pose.mur;
119 | I = pose.I;
120 | J = pose.J;
121 | lengths = pose.lengths;
122 | Bnew = pose.Breshaped;
123 | xyvisible = pose.xyvisible;
124 | B = pose.Bfull;
125 | annoids = pose.annoids;
126 | epsxy = inf;
127 | xyprev = zeros(2,pose.numPoints);
128 | numIters = 0;
129 | while(epsxy>pose.tol2 && numIters < pose.numIters2)
130 | Msub = kron(eye(length(annoids),length(annoids)),camera.M);
131 | A = Msub*pose.BreVis(:,selectIdx);
132 | b = xyvisible(:) - kron(ones(length(annoids),1),camera.taff) - kron(eye(length(annoids),length(annoids)),camera.M)*pose.mureVis;
133 | %% Equality constrained
134 | switch optType
135 | case 1
136 | C = [];
137 | d = [];
138 | alphasq = 0;
139 | for i = 1:length(I)
140 | if(length(selectIdx)>1)
141 | Bi = (squeeze(Bnew(I(i),:,selectIdx)));
142 | Bj = (squeeze(Bnew(J(i),:,selectIdx)));
143 | else
144 |
145 | Bi = (squeeze(Bnew(I(i),:,selectIdx)))';
146 | Bj = (squeeze(Bnew(J(i),:,selectIdx)))';
147 | end
148 | mui = mur(I(i),:)';
149 | muj = mur(J(i),:)';
150 | C = [C; (Bi-Bj)] ;
151 | d = [d; -(mui-muj)];
152 | alphasq = alphasq + lengths(I(i),J(i))^2;
153 | end
154 | alpha = sqrt(alphasq);
155 | % alpha = sqrt(pose.lengthsum);
156 | [a,asolT] = leastsquareseqcon3(A,b,C,d,alpha);
157 | asol = asolT';
158 |
159 | end
160 |
161 | Xnew = B(:,selectIdx)*asol + pose.mu;
162 | XnewR= reshape(Xnew,pose.numPoints,3);
163 | pose.Xnew = Xnew;
164 | pose.XnewR = XnewR;
165 | pose.XnewRt = XnewR';
166 | pose.Xnewre = pose.XnewRt(:);
167 | pose.XnewreVis = pose.XnewRt(:,annoids);
168 | pose.XnewreVis = pose.XnewreVis(:);
169 |
170 | XMissing=XnewR(annoids,:);
171 | xyMissing = xyvisible;
172 | pose.asol = asol;
173 | pose.selectIdx = selectIdx;
174 |
175 | xyrep1 = projectIntoAffineCam(XnewR,pose.K,camera.R,camera.t,camera.S,pose.skel);
176 | repErr1 = sum(sum((xyrep1(1:2,annoids)-pose.xyunscaled(1:2,annoids)).^2,1));
177 |
178 | %Estimate camera
179 | [cameraHyp]= estimateWPCamera(xyMissing',XMissing);
180 |
181 | %Compute reprojection error
182 | xyrep2 = projectIntoAffineCam(XnewR,pose.K,cameraHyp.R,cameraHyp.t,cameraHyp.S,pose.skel);
183 | repErr2 = sum(sum((xyrep2(1:2,annoids)-pose.xyunscaled(1:2,annoids)).^2,1));
184 |
185 |
186 | camera =cameraHyp;
187 | xyrep = xyrep2;
188 | repErr = repErr2;
189 |
190 | epsxy = sum(sum((xyrep(1:2,annoids)-xyprev(1:2,annoids)).^2,1));
191 | xyprev = xyrep;
192 | pose.repErr = repErr;
193 |
194 | % Visualize
195 | if(pose.viz)
196 | figure(4);clf;
197 | pointsVisualize(XnewR,pose.skel,'texton',0);hold on;
198 | drawCam(cameraHyp.R,cameraHyp.t,'gt',1);
199 |
200 | figure(3);clf;
201 | imshow(pose.im);hold on;
202 | plot2Dskeleton(xyrep',pose.skel,1,'texton',0);
203 | hold on;
204 | plot2Dskeleton(pose.xyunscaled',pose.skel,1,'texton',0,'gt',1);
205 | axis ij;
206 | end
207 |
208 | numIters = numIters + 1;
209 | pose.numIters = pose.numIters +1;
210 | end
211 |
212 | res = xyvisible(:) - kron(ones(length(annoids),1),camera.taff) - kron(eye(length(annoids),length(annoids)),camera.M)*pose.XnewreVis;
213 | res = res- ((kron(eye(length(annoids),length(annoids)),camera.M))*B(:,selectIdx))*((kron(eye(length(annoids),length(annoids)),camera.M))*B(:,selectIdx))'*res;
214 | end
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/release/src/drawCam.m:
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1 | function drawCam(R,t,varargin)
2 | [gt]= process_options(varargin,'gt',0);
3 | scale =5;
4 | P = scale*[0 0 0;0.5 0.5 0.8; 0.5 -0.5 0.8; -0.5 0.5 0.8;-0.5 -0.5 0.8];
5 |
6 | %P = scale*[0 0 0;0.5 0.5 -0.8; 0.5 -0.5 -0.8; -0.5 0.5 -0.8;-0.5 -0.5 -0.8];
7 |
8 | P1=R'*(P'-repmat(t,[1,5]));
9 | %P1=R*P'+repmat(t,[1,5]);
10 | P1=P1';
11 | maxp=max(max(P1));
12 | %axis(2*[-maxp maxp -maxp maxp -maxp maxp]);
13 | if(~gt)
14 | line([P1(1,1) P1(2,1)],[P1(1,3) P1(2,3)],[P1(1,2) P1(2,2)],'color','k')
15 | line([P1(1,1) P1(3,1)],[P1(1,3) P1(3,3)],[P1(1,2) P1(3,2)],'color','k')
16 | line([P1(1,1) P1(4,1)],[P1(1,3) P1(4,3)],[P1(1,2) P1(4,2)],'color','k')
17 | line([P1(1,1) P1(5,1)],[P1(1,3) P1(5,3)],[P1(1,2) P1(5,2)],'color','k')
18 |
19 | line([P1(2,1) P1(3,1)],[P1(2,3) P1(3,3)],[P1(2,2) P1(3,2)],'color','k')
20 | line([P1(3,1) P1(5,1)],[P1(3,3) P1(5,3)],[P1(3,2) P1(5,2)],'color','k')
21 | line([P1(5,1) P1(4,1)],[P1(5,3) P1(4,3)],[P1(5,2) P1(4,2)],'color','k')
22 | line([P1(4,1) P1(2,1)],[P1(4,3) P1(2,3)],[P1(4,2) P1(2,2)],'color','k')
23 |
24 |
25 | cameraPlane =[P1(2,1) P1(2,3) P1(2,2); P1(4,1) P1(4,3) P1(4,2); P1(3,1) P1(3,3) P1(3,2);P1(5,1) P1(5,3) P1(5,2)];
26 | faces =[2 1 3 4];
27 | patch('Vertices',cameraPlane,'Faces',faces,'FaceVertexCData',hsv(6),'FaceColor','k','FaceAlpha',0.1);
28 | else
29 | line([P1(1,1) P1(2,1)],[P1(1,3) P1(2,3)],[P1(1,2) P1(2,2)],'color','k','LineStyle','--')
30 | line([P1(1,1) P1(3,1)],[P1(1,3) P1(3,3)],[P1(1,2) P1(3,2)],'color','k','LineStyle','--')
31 | line([P1(1,1) P1(4,1)],[P1(1,3) P1(4,3)],[P1(1,2) P1(4,2)],'color','k','LineStyle','--')
32 | line([P1(1,1) P1(5,1)],[P1(1,3) P1(5,3)],[P1(1,2) P1(5,2)],'color','k','LineStyle','--')
33 |
34 | line([P1(2,1) P1(3,1)],[P1(2,3) P1(3,3)],[P1(2,2) P1(3,2)],'color','k','LineStyle','--')
35 | line([P1(3,1) P1(5,1)],[P1(3,3) P1(5,3)],[P1(3,2) P1(5,2)],'color','k','LineStyle','--')
36 | line([P1(5,1) P1(4,1)],[P1(5,3) P1(4,3)],[P1(5,2) P1(4,2)],'color','k','LineStyle','--')
37 | line([P1(4,1) P1(2,1)],[P1(4,3) P1(2,3)],[P1(4,2) P1(2,2)],'color','k','LineStyle','--')
38 |
39 | %
40 | % cameraPlane =[P1(2,1) P1(2,3) P1(2,2); P1(4,1) P1(4,3) P1(4,2); P1(3,1) P1(3,3) P1(3,2);P1(5,1) P1(5,3) P1(5,2)];
41 | % faces =[2 1 3 4];
42 | % patch('Vertices',cameraPlane,'Faces',faces,'FaceVertexCData',hsv(6),'FaceColor','k','FaceAlpha',0.05);
43 |
44 | end
45 |
46 |
47 | C1=[P1(2,1) P1(2,3) P1(2,2)];
48 | C2=[P1(3,1) P1(3,3) P1(3,2)];
49 | C3=[P1(4,1) P1(4,3) P1(4,2)];
50 | C4=[P1(5,1) P1(5,3) P1(5,2)];
51 |
52 | O=[P1(1,1) P1(1,3) P1(1,2)];
53 | Cmid =0.25*(C1+C2+C3+C4);
54 |
55 | % Lz = [O; O+0.5*(Cmid-O)];
56 | % Lx = [O; O+0.5*(C2-C1)];
57 | % Ly = [O; O+0.5*(C3-C1)];
58 |
59 | Lz = [O; O+0.5*(Cmid-O)];
60 | Lx = [O; O+0.5*(C1-C3)];
61 | Ly = [O; O+0.5*(C1-C2)];
62 |
63 | if(~gt)
64 |
65 | line(Lz(:,1),Lz(:,2),Lz(:,3),'color','b','linewidth',2)
66 | line(Lx(:,1),Lx(:,2),Lx(:,3),'color','g','linewidth',2)
67 | line(Ly(:,1),Ly(:,2),Ly(:,3),'color','r','linewidth',2)
68 |
69 | else
70 | line(Lz(:,1),Lz(:,2),Lz(:,3),'color','b','linewidth',1)
71 | line(Lx(:,1),Lx(:,2),Lx(:,3),'color','g','linewidth',1)
72 | line(Ly(:,1),Ly(:,2),Ly(:,3),'color','r','linewidth',1)
73 |
74 |
75 |
76 | end
77 |
78 | axis tight;
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/release/src/estimateWPCamera.m:
--------------------------------------------------------------------------------
1 | function [camera]= estimateWPCamera(xy,XY)
2 | %[Raff, taff, R, scale,t,Rproc,tproc]=
3 | %estimateOrthoCamera(xy,XY,scaleFactor)
4 | xy=xy(:,1:2);
5 | % xy=scaleFactor*xy;
6 | taff= mean(xy,1);
7 | xy=xy-repmat(taff,[size(xy,1) 1]);
8 |
9 |
10 | numPoints = size(xy,1);
11 | A = zeros(2*numPoints,size(XY,2)+3);
12 | b = zeros(2*numPoints,1);
13 |
14 | for i=1:numPoints
15 |
16 | A((i-1)*2+1,:) = [ XY(i,:) 0 0 0];
17 | A(i*2,:) = [ 0 0 0 XY(i,:)];
18 |
19 | b((i-1)*2+1) = xy(i,1);
20 | b(i*2) = xy(i,2);
21 |
22 | end
23 |
24 | %% Procrustes solution as initial point
25 |
26 | x=xy;
27 | X=XY';
28 | meanX=mean(X,2);
29 | X=X-repmat(meanX,1,size(X,2));
30 |
31 | M=x'*X'*inv(X*X');
32 | % M = x'/X;
33 | [U,S,V]=svd(M);
34 |
35 | Inew=[1 0 0; 0 1 0];
36 | R = U*Inew*V';
37 |
38 | r3=cross(R(1,:),R(2,:));
39 | r3=r3/norm(r3);
40 | rinit =[R(1,:) R(2,:)]';
41 |
42 |
43 | Raff=R;
44 | R=[R; r3];
45 | scaleFactor=0.5*(S(2,2)+S(1,1));
46 |
47 | t=[taff';1/scaleFactor];
48 | det(R);
49 | if(sum(abs(diag(U)))>1)
50 | S = S(1:2,1:2);
51 | else
52 | S = S(1:2,1:2);
53 | S = flipud(fliplr(S));
54 | % disp('Flip scales');
55 | end
56 | % S = U*S;
57 |
58 |
59 | %%
60 | % %Solve non-linear optimization using fmincon
61 | % options = optimset('Algorithm','interior-point');
62 | % r=fmincon(@(x) objective(x,A,b),rinit,[],[],[],[],[],[], @(x) orthoConstraints(x),options);
63 | % %
64 | % Raff=[ r(1) r(2) r(3);...
65 | % r(4) r(5) r(6);];
66 | % %
67 | % % Find full rotation matrix
68 | % r1=Raff(1,:);
69 | % r2=Raff(2,:);
70 | % r3=cross(Raff(1,:),Raff(2,:));
71 | % r3=r3/norm(r3);
72 | % R=[r1;r2;r3];
73 | %
74 | % %Estimate average scale
75 | % %scale = mean(r2*XY'./xyunscaled(:,2)');
76 | % %t=[taff';scale];
77 | %
78 | camera.Raff = Raff;
79 | camera.taff = taff';
80 | camera.R = R;
81 | camera.t = t;
82 | camera.S = S;
83 | camera.M = S*Raff;
84 |
85 |
86 |
87 |
88 |
89 |
90 |
91 | end
92 |
93 |
94 | function f=objective(x,A,b)
95 | f= (A*x-b)'*(A*x-b);
96 | end
97 |
98 | function [c,ceq] = orthoConstraints(x)
99 |
100 | ceq = [[x(1) x(2) x(3)]*[x(4) x(5) x(6)]';...
101 | [x(1) x(2) x(3)]*[x(1) x(2) x(3)]'-1;...
102 | [x(4) x(5) x(6)]*[x(4) x(5) x(6)]'-1;];
103 | c=[];
104 |
105 | end
--------------------------------------------------------------------------------
/release/src/leastsquareseqcon3.m:
--------------------------------------------------------------------------------
1 | function [x, xsol] = leastsquareseqcon3(A,b,C,d,alpha)
2 |
3 | % Solve generalized SVD to get gammas and alphas. Please refer Gander et al, for description of the algorithm.
4 |
5 | [U,V,X,Da,Dc] = gsvd(A,C);
6 | c = U'*b;
7 | e = V'*d;
8 | p = size(C,1);
9 | r = sum(diag(Dc)>0);
10 | lambda = sym('lambda','real');
11 | i=1;
12 | % tic;
13 | f=Da(i,i)^2 *(Dc(i,i)*c(i)-Da(i,i)*e(i))^2/(Da(i,i)^2+lambda*Dc(i,i)^2)^2;
14 | for i = 2:r
15 | a=Da(i,i)^2 *(Dc(i,i)*c(i)-Da(i,i)*e(i))^2/(Da(i,i)^2+lambda*Dc(i,i)^2)^2;
16 | f = f+ a;
17 | end
18 | % toc;
19 |
20 | if(length(e)>r)
21 | for i =r+1:p
22 | f = f+e(i)^2;
23 | end
24 | end
25 | f = f-alpha^2;
26 | [num,den] = numden(f);
27 | c = coeffs(num);
28 | numNorm = vpa(num/c(end));
29 | % lambdaSol = roots(coeff);
30 |
31 | if(diff(f)~=0)
32 |
33 | lambdaSol = solve(numNorm);
34 | lambdaSol = double(lambdaSol);
35 |
36 | realLambdaSol = lambdaSol(~(abs(imag(lambdaSol))>0));
37 | ind = find(realLambdaSol == max(realLambdaSol));
38 | ind =ind(1);
39 |
40 | xsol = (A'*A+realLambdaSol(ind)*(C'*C))\(A'*b+realLambdaSol(ind)*C'*d);
41 | xsol = xsol';
42 | x = xsol;
43 | if(sum(isnan(xsol)))
44 | xsol(isnan(xsol))=0;
45 | end
46 | % disp(xsol');
47 | else
48 |
49 | end
50 |
51 |
52 |
53 |
54 |
55 |
56 | %% Solve completely symbolically.
57 | % syms x lambda;
58 | % x = inv(A'*A + lambda*C'*C)*(A'*b + lambda*C'*d);
59 | % f = (C*x-d)'*(C*x -d);
60 | % lambdaSol = solve(f-alpha^2);
61 | % for i = 1:length(lambdaSol)
62 | % xsol(:,i) = feval(matlabFunction(x),double(lambdaSol(i)));
63 | % end
64 | % x = xsol;
65 | % realLambdaSol = lambdaSol(~(abs(imag(lambdaSol))>0));
66 | % ind = find(realLambdaSol == max(realLambdaSol));
67 | % xsol = x(ind,:);
68 |
69 |
70 |
71 |
72 |
--------------------------------------------------------------------------------
/release/src/plot2Dskeleton.m:
--------------------------------------------------------------------------------
1 | function [hSkel,hSkelText] =plot2Dskeleton(xy,skel,type,varargin)
2 | %PLOT2DSKELETON Plots projection of skeleton
3 | % plot2Dskeleton(xy,skel)
4 | %
5 | % Description:
6 | %
7 | %
8 | % Inputs:
9 | %
10 | %
11 | % Outputs:
12 | %
13 | %
14 | % Example:
15 | % plot2Dskeleton
16 | %
17 | % See also
18 |
19 | % Author: Varun Ramakrishna
20 | % Created: Jan 31, 2011
21 | xy=xy';
22 | [texton,linewidth,gt,hparent] = process_options(varargin,'texton',1,'linewidth',2,'gt',0,'Parent',gca);
23 | numPts=size(xy,2);
24 | for i =1:numPts
25 | strs{i}={int2str(i)};
26 | end
27 |
28 |
29 | connect = skelConnectionMatrix(skel);
30 | indices = find(connect);
31 | [I, J] = ind2sub(size(connect), indices);
32 |
33 | % gca; hold on;
34 |
35 | %figure
36 | % hold on;
37 | % plot(xy(1,:),xy(2,:),'o','LineWidth',linewidth,'MarkerSize',5);
38 |
39 |
40 | colors=prism(6);
41 | if(type==2)
42 | M=[ colors(4:6,:); ...
43 | colors(4:6,:); ...
44 | colors(6,:); colors(6,:); colors(6,:); colors(5,:); colors(6,:); ...
45 | colors(1,:); colors(2,:); colors(1,:); ...
46 | colors(1,:); colors(2,:); colors(1,:); ...
47 | ];
48 | elseif(type==1)
49 | M= [colors(4:6,:); colors(1,:); ...
50 | colors(4:6,:); colors(1,:); ...
51 | colors(6,:); colors(6,:); colors(6,:); colors(5,:); colors(5,:); colors(5,:);...
52 | colors(1,:); colors(2,:); colors(1,:); colors(4,:); ...
53 | colors(1,:); colors(2,:); colors(1,:); colors(4,:);...
54 | ];
55 | elseif(type==3)
56 | M=[ colors(4:6,:); ...
57 | colors(4:6,:); ...
58 | colors(6,:); colors(6,:); colors(6,:); colors(5,:); colors(6,:); ...
59 | colors(1,:); colors(2,:); colors(1,:); ...
60 | colors(1,:);
61 | ];
62 | end
63 |
64 | if(texton)
65 | for i =1:size(xy,2)
66 | hSkelText(i) = text(xy(1,i),xy(2,i),strs{i});
67 | end
68 | end
69 | xy=xy';
70 | % axis equal
71 | hold on;
72 |
73 | for i = 1:length(indices)
74 | if(gt)
75 |
76 | hSkel(i) = line([xy(I(i),1) xy(J(i),1)], ...
77 | [xy(I(i),2) xy(J(i),2)],'color','k','Parent',hparent);
78 | set(hSkel(i), 'linewidth', linewidth,'LineStyle','--');
79 | else
80 |
81 | hSkel(i) = line([xy(I(i),1) xy(J(i),1)], ...
82 | [xy(I(i),2) xy(J(i),2)],'color',M(i,:),'Parent',hparent);
83 | set(hSkel(i), 'linewidth', linewidth);
84 | end
85 | end
86 |
--------------------------------------------------------------------------------
/release/src/pointsVisualize.m:
--------------------------------------------------------------------------------
1 | function pointsVisualize(vals,skel,varargin)
2 | %function pointsVisualize(vals,skel)
3 | [color,type,person,connect,missing,gt,texton,textsize,linewidth,showlines,marker]=process_options(varargin,'color','r','type',1,'person',1,'connect',[],'missing', [],'gt',0,'texton',1,'textsize',10,'linewidth',5,'showlines',1,'marker','o');
4 |
5 | for i =1:size(vals,1)
6 | strs{i}=num2str(i);
7 | end
8 | if isempty(connect)
9 | connect = skelConnectionMatrix(skel);
10 | end
11 |
12 | indices = find(connect);
13 | [I, J] = ind2sub(size(connect), indices);
14 | %handle(1)=figure;
15 | inds = ones(size(vals,1),1);
16 | inds(missing) = 0;
17 | inds = logical(inds);
18 |
19 | handle(1) = plot3(vals(inds, 1), vals(inds, 3), vals(inds, 2), marker, 'LineWidth', linewidth, 'MarkerSize', 5);
20 | hold on;
21 | if(texton)
22 | for i = 1: length(vals)
23 | h1 = text( vals(i, 1), vals(i, 3), vals(i, 2),strs{i},'FontSize',textsize,'FontWeight','bold');
24 | end
25 | end
26 | axis ij % make sure the left is on the left.
27 |
28 |
29 | grid on
30 |
31 | colors=prism(6);
32 | if(type==2)
33 | M=[ colors(4:6,:); ...
34 | colors(4:6,:); ...
35 | colors(6,:); colors(6,:); colors(6,:); colors(5,:); colors(6,:); ...
36 | colors(1,:); colors(2,:); colors(1,:); ...
37 | colors(1,:); colors(2,:); colors(1,:); ...
38 | ];
39 | elseif(type==1)
40 | if person ==1
41 | colors=prism(6);
42 | M= [colors(4:6,:); colors(1,:); ...
43 | colors(4:6,:); colors(1,:); ...
44 | colors(6,:); colors(6,:); colors(6,:); colors(5,:); colors(6,:); colors(5,:);...
45 | colors(1,:); colors(2,:); colors(1,:); colors(4,:); ...
46 | colors(1,:); colors(2,:); colors(1,:); colors(4,:);...
47 | ];
48 | elseif person ==2
49 | colors =jet(6);
50 | M= [colors(4:6,:); colors(1,:); ...
51 | colors(4:6,:); colors(1,:); ...
52 | colors(6,:); colors(6,:); colors(6,:); colors(5,:); colors(6,:); colors(5,:);...
53 | colors(1,:); colors(2,:); colors(1,:); colors(4,:); ...
54 | colors(1,:); colors(2,:); colors(1,:); colors(4,:);...
55 | ];
56 |
57 | end
58 | elseif(type==3)
59 | M=[ colors(4:6,:); ...
60 | colors(4:6,:); ...
61 | colors(6,:); colors(6,:); colors(6,:); ...
62 | colors(1,:); colors(2,:); colors(1,:); ...
63 | colors(1,:); colors(2,:); colors(1,:); ...
64 | ];
65 | else
66 | M = repmat(colors(2,:),length(indices),1);
67 | end
68 | if(showlines)
69 | if(type<4)
70 | for i = 1:length(indices)
71 |
72 | handle(i+1) = line([vals(I(i), 1) vals(J(i), 1)], ...
73 | [vals(I(i), 3) vals(J(i), 3)], ...
74 | [vals(I(i), 2) vals(J(i), 2)]);
75 | missI = logical(length(find(missing == I(i))));
76 | missJ = logical(length(find(missing == J(i))));
77 | if(missI || missJ)
78 | set(handle(i+1), 'linewidth', linewidth,'Color',M(i,:), 'LineStyle', '--');
79 | elseif(gt)
80 | set(handle(i+1), 'linewidth', linewidth,'Color','k', 'LineStyle', '--');
81 | else
82 | set(handle(i+1), 'linewidth', linewidth,'Color',M(i,:));
83 | end
84 | end
85 | axis equal
86 | else
87 |
88 | for i = 1:length(indices)
89 | handle(i+1) = line([vals(I(i), 1) vals(J(i), 1)],...
90 | [vals(I(i), 2) vals(J(i), 2)], ...
91 | [vals(I(i), 3) vals(J(i), 3)]);
92 | set(handle(i+1), 'linewidth', 5,'Color',M(i,:));
93 | end
94 | axis equal
95 | end
96 | end
97 |
98 | % xlabel('x','Interpreter','latex','fontsize',10);
99 | % ylabel('z','Interpreter','latex','fontsize',10);
100 | % zlabel('y','Interpreter','latex','fontsize',10);
101 |
102 |
103 |
104 | hold off
--------------------------------------------------------------------------------
/release/src/process_options.m:
--------------------------------------------------------------------------------
1 | % PROCESS_OPTIONS - Processes options passed to a Matlab function.
2 | % This function provides a simple means of
3 | % parsing attribute-value options. Each option is
4 | % named by a unique string and is given a default
5 | % value.
6 | %
7 | % Usage: [var1, var2, ..., varn[, unused]] = ...
8 | % process_options(args, ...
9 | % str1, def1, str2, def2, ..., strn, defn)
10 | %
11 | % Arguments:
12 | % args - a cell array of input arguments, such
13 | % as that provided by VARARGIN. Its contents
14 | % should alternate between strings and
15 | % values.
16 | % str1, ..., strn - Strings that are associated with a
17 | % particular variable
18 | % def1, ..., defn - Default values returned if no option
19 | % is supplied
20 | %
21 | % Returns:
22 | % var1, ..., varn - values to be assigned to variables
23 | % unused - an optional cell array of those
24 | % string-value pairs that were unused;
25 | % if this is not supplied, then a
26 | % warning will be issued for each
27 | % option in args that lacked a match.
28 | %
29 | % Examples:
30 | %
31 | % Suppose we wish to define a Matlab function 'func' that has
32 | % required parameters x and y, and optional arguments 'u' and 'v'.
33 | % With the definition
34 | %
35 | % function y = func(x, y, varargin)
36 | %
37 | % [u, v] = process_options(varargin, 'u', 0, 'v', 1);
38 | %
39 | % calling func(0, 1, 'v', 2) will assign 0 to x, 1 to y, 0 to u, and 2
40 | % to v. The parameter names are insensitive to case; calling
41 | % func(0, 1, 'V', 2) has the same effect. The function call
42 | %
43 | % func(0, 1, 'u', 5, 'z', 2);
44 | %
45 | % will result in u having the value 5 and v having value 1, but
46 | % will issue a warning that the 'z' option has not been used. On
47 | % the other hand, if func is defined as
48 | %
49 | % function y = func(x, y, varargin)
50 | %
51 | % [u, v, unused_args] = process_options(varargin, 'u', 0, 'v', 1);
52 | %
53 | % then the call func(0, 1, 'u', 5, 'z', 2) will yield no warning,
54 | % and unused_args will have the value {'z', 2}. This behaviour is
55 | % useful for functions with options that invoke other functions
56 | % with options; all options can be passed to the outer function and
57 | % its unprocessed arguments can be passed to the inner function.
58 |
59 | % Copyright (C) 2002 Mark A. Paskin
60 | %
61 | % This program is free software; you can redistribute it and/or modify
62 | % it under the terms of the GNU General Public License as published by
63 | % the Free Software Foundation; either version 2 of the License, or
64 | % (at your option) any later version.
65 | %
66 | % This program is distributed in the hope that it will be useful, but
67 | % WITHOUT ANY WARRANTY; without even the implied warranty of
68 | % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
69 | % General Public License for more details.
70 | %
71 | % You should have received a copy of the GNU General Public License
72 | % along with this program; if not, write to the Free Software
73 | % Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307
74 | % USA.
75 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
76 |
77 | function [varargout] = process_options(args, varargin)
78 |
79 | % Check the number of input arguments
80 | n = length(varargin);
81 | if (mod(n, 2))
82 | error('Each option must be a string/value pair.');
83 | end
84 |
85 | % Check the number of supplied output arguments
86 | if (nargout < (n / 2))
87 | error('Insufficient number of output arguments given');
88 | elseif (nargout == (n / 2))
89 | warn = 1;
90 | nout = n / 2;
91 | else
92 | warn = 0;
93 | nout = n / 2 + 1;
94 | end
95 |
96 | % Set outputs to be defaults
97 | varargout = cell(1, nout);
98 | for i=2:2:n
99 | varargout{i/2} = varargin{i};
100 | end
101 |
102 | % Now process all arguments
103 | nunused = 0;
104 | for i=1:2:length(args)
105 | found = 0;
106 | for j=1:2:n
107 | if strcmpi(args{i}, varargin{j})
108 | varargout{(j + 1)/2} = args{i + 1};
109 | found = 1;
110 | break;
111 | end
112 | end
113 | if (~found)
114 | if (warn)
115 | warning(sprintf('Option ''%s'' not used.', args{i}));
116 | args{i}
117 | else
118 | nunused = nunused + 1;
119 | unused{2 * nunused - 1} = args{i};
120 | unused{2 * nunused} = args{i + 1};
121 | end
122 | end
123 | end
124 |
125 | % Assign the unused arguments
126 | if (~warn)
127 | if (nunused)
128 | varargout{nout} = unused;
129 | else
130 | varargout{nout} = cell(0);
131 | end
132 | end
133 |
--------------------------------------------------------------------------------
/release/src/projectIntoAffineCam.m:
--------------------------------------------------------------------------------
1 | function xy=projectIntoAffineCam(X, K,R,t,S,skel,varargin )
2 | %xy=projectIntoAffineCam(X, K,R,t,S,skel )
3 | [viz,s]=process_options(varargin,'viz',0,'scale',1);
4 |
5 | %% Do projection
6 | numPts =size(X,1);
7 |
8 | %Create Affine camera
9 | Raff =[ R(1,:); R(2,:); zeros(1,3)];
10 | taff =K*[ t(1); t(2); 1]; % TODO: z-dim should be scaling
11 | M=K*Raff;
12 |
13 |
14 | %Project into affine camera
15 | xy = S*M(1:2,:)*X' + repmat(taff(1:2),[1,numPts]);
16 | xy(3,:) = ones(1,size(xy,2));
17 | %% Plot projection
18 |
19 | if(viz)
20 | connect = skelConnectionMatrix(skel);
21 | indices = find(connect);
22 | [I, J] = ind2sub(size(connect), indices);
23 | for i =1:numPts
24 | strs{i}={int2str(i)};
25 | end
26 |
27 | if(~isempty(skel))
28 |
29 | figure
30 | handle(1)=plot(xy(1,:),xy(2,:),'x');
31 | hold on
32 | for i =1:size(xy,2)
33 | text(xy(1,i),xy(2,i),strs{i});
34 | end
35 | axis equal
36 | hold off
37 |
38 | if(K(1,3)>0) &&(K(2,3)>0)
39 | axis([0 2*K(1,3) 0 2*K(2,3)]);
40 | end
41 | axis ij% make sure the left is on the left.
42 | set(handle(1), 'markersize', 20);
43 | hold on
44 | grid on
45 | for i = 1:length(indices)
46 | handle(i+1) = line([xy(1,I(i)) xy(1,J(i))], ...
47 | [xy(2,I(i)) xy(2,J(i))]);
48 | set(handle(i+1), 'linewidth', 2);
49 | end
50 | hold off
51 | end
52 | end
53 |
--------------------------------------------------------------------------------
/release/src/reArrangeBasis.m:
--------------------------------------------------------------------------------
1 | function [Bre,mure] = reArrangeBasis(B,mu,numPoints)
2 |
3 | for i = 1:size(B,2)
4 | Btemp = reshape(B(:,i),numPoints,3)';
5 | Bre(:,i) = Btemp(:);
6 | end
7 | mutemp = reshape(mu,numPoints,3)';
8 | mure = mutemp(:);
--------------------------------------------------------------------------------
/release/src/recon3DPose.m:
--------------------------------------------------------------------------------
1 | % [X, R, t] = function recon3DPose(xy,im,varargin)
2 | %
3 | % Inputs: xy - [2 x 14] matrix of 2D joint locations
4 | % im - Input image
5 | %
6 | %
7 | %
8 | % Outputs: X - [3 x 14] matrix of 3D joint locations.
9 | % R - [3 x 3] Relative Camera Rotation.
10 | % t - [3 x 1] Relative Camera translation.
11 | %
12 | % Wrapper for reconstruction of the 3D Pose of a human figure given the
13 | % locations of the 2D anatomical landmarks.
14 | % Copyright (C) 2012 Varun Ramakrishna.
15 | %
16 | % This program is free software: you can redistribute it and/or modify
17 | % it under the terms of the GNU General Public License as published by
18 | % the Free Software Foundation, either version 3 of the License, or
19 | % (at your option) any later version.
20 | %
21 | % This program is distributed in the hope that it will be useful,
22 | % but WITHOUT ANY WARRANTY; without even the implied warranty of
23 | % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
24 | % GNU General Public License for more details.
25 | %
26 | % You should have received a copy of the GNU General Public License
27 | % along with this program. If not, see .
28 |
29 | function [X, R, t] = recon3DPose(im,xy,varargin)
30 | % [X, R, t] = recon3DPose(xy,im,varargin)
31 |
32 | % Parse parameters.
33 | [pose.skel, pose.BOMP, pose.mu, pose.lambda1,...
34 | pose.lamda2, pose.K, pose.numIter,...
35 | pose.numIters2, pose.tol1, pose.tol2, pose.ks,...
36 | pose.optType, pose.viz, pose.annoids,pose.numPoints] = process_options(varargin,...
37 | 'skel','',...
38 | 'BOMP','',...
39 | 'mu' ,'',...
40 | 'lambda2',0.01,...
41 | 'lambda1',0.01,...
42 | 'K', setK(size(im,2),size(im,1),2),...
43 | 'numIter', 20,...
44 | 'numIters2',30,...
45 | 'tol1', 500, ...
46 | 'tol2', 1, ...
47 | 'ks', 15, ...
48 | 'optType', 1, ...
49 | 'viz', 0,...
50 | 'annoids',1:15,...
51 | 'numPoints',15);
52 | pose.im = im;
53 | pose.xy = [xy; ones(1,size(xy,2))];
54 |
55 | % Load default basis and skeleton
56 | if(isempty(pose.BOMP)||isempty(pose.mu)||isempty(pose.skel))
57 | basis = load('mocapReducedModel.mat');
58 | pose.BOMP = basis.B;
59 | pose.mu = basis.mu;
60 | pose.skel = basis.skel;
61 | pose.numPoints = length(pose.skel.tree);
62 | pose.annoids = [1:length(pose.skel.tree)];
63 | end
64 |
65 | % Reconstruct camera and pose.
66 | [camera, pose] = cameraAndPose(pose);
67 |
68 | % Assign outputs
69 | X = pose.XnewR;
70 | R = camera.R;
71 | t = camera.t;
72 |
73 | % Show aligned output
74 | if(pose.viz)
75 | load frontCam;
76 | Xnew1 = alignToCamera(pose.XnewR,camera.R,camera.t,R,t);
77 | figure(9);clf;
78 | visualizeGaussianModel(Xnew1,pose.skel);
79 | drawCam(R,t);
80 | end
81 |
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/release/src/setK.m:
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1 | function K=setK(x,y,f)
2 | K=eye(3);
3 | K(1,1) = f*x;
4 | K(2,2) =f*x;
5 | K(1,3) = x/2;
6 | K(2,3) =y/2;
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/release/src/skelConnectionMatrix.m:
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1 | function connection = skelConnectionMatrix(skel);
2 |
3 | % SKELCONNECTIONMATRIX Compute the connection matrix for the structure.
4 | %
5 | % Description:
6 | %
7 | % CONNECTION = SKELCONNECTIONMATRIX(SKEL) computes the connection
8 | % matrix for the structure. Returns a matrix which has zeros at all
9 | % entries except those that are connected in the skeleton.
10 | % Returns:
11 | % CONNECTION - connectivity matrix.
12 | % Arguments:
13 | % SKEL - the skeleton for which the connectivity is required.
14 | %
15 | %
16 | % See also
17 | % SKELVISUALISE, SKELMODIFY
18 |
19 |
20 | % Copyright (c) 2006 Neil D. Lawrence
21 | % skelConnectionMatrix.m CVS version 1.2
22 | % skelConnectionMatrix.m SVN version 42
23 | % last update 2008-08-12T20:23:47.000000Z
24 |
25 | connection = zeros(length(skel.tree));
26 | for i = 1:length(skel.tree);
27 | for j = 1:length(skel.tree(i).children)
28 | connection(i, skel.tree(i).children(j)) = 1;
29 | end
30 | end
31 |
32 |
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/release/src/visualizeGaussianModel.m:
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1 | function gaussianMan = visualizeGaussianModel(vals,skel,varargin)
2 |
3 | [color,type,person,connect]=process_options(varargin,'color','r','type',1,'person',1,'connect',[]);
4 |
5 | for i =1:size(vals,1)
6 | strs{i}={int2str(i)};
7 | end
8 | if isempty(connect)
9 | connect = skelConnectionMatrix(skel);
10 | end
11 |
12 | indices = find(connect);
13 | [I, J] = ind2sub(size(connect), indices);
14 | handle(1) = plot3(vals(:, 1), vals(:, 3), vals(:, 2), '.');
15 | axis ij % make sure the left is on the left.
16 | set(handle(1), 'markersize', 1);
17 | hold on
18 | grid on
19 |
20 | colors=prism(6);
21 | if(type==2)
22 | M=[ colors(4:6,:); ...
23 | colors(4:6,:); ...
24 | colors(6,:); colors(6,:); colors(6,:); colors(5,:); colors(6,:); ...
25 | colors(1,:); colors(2,:); colors(1,:); ...
26 | colors(1,:); colors(2,:); colors(1,:); ...
27 | ];
28 | elseif(type==1)
29 | if person ==1
30 | colors=prism(6);
31 | M= [colors(4:6,:); colors(1,:); ...
32 | colors(4:6,:); colors(1,:); ...
33 | colors(6,:); colors(6,:); colors(6,:); colors(5,:); colors(5,:); colors(5,:);...
34 | colors(1,:); colors(2,:); colors(1,:); colors(4,:); ...
35 | colors(1,:); colors(2,:); colors(1,:); colors(4,:);...
36 | ];
37 | elseif person ==2
38 | colors =jet(6);
39 | M= [colors(4:6,:); colors(1,:); ...
40 | colors(4:6,:); colors(1,:); ...
41 | colors(6,:); colors(6,:); colors(6,:); colors(5,:); colors(6,:); colors(5,:);...
42 | colors(1,:); colors(2,:); colors(1,:); colors(4,:); ...
43 | colors(1,:); colors(2,:); colors(1,:); colors(4,:);...
44 | ];
45 |
46 | end
47 | elseif(type==3)
48 | M=[ colors(4:6,:); ...
49 | colors(4:6,:); ...
50 | colors(6,:); colors(6,:); colors(6,:); ...
51 | colors(1,:); colors(2,:); colors(1,:); ...
52 | colors(1,:); colors(2,:); colors(1,:); ...
53 | ];
54 | else
55 | M = repmat(colors(2,:),length(indices),1);
56 | end
57 |
58 |
59 |
60 | if(type<4)
61 | for i = 1:length(indices)
62 | P1 = [vals(I(i),1) vals(I(i),3) vals(I(i),2)];
63 | P2 = [vals(J(i),1) vals(J(i),3) vals(J(i),2)];
64 | P = 0.5*(P1 + P2);
65 | U = [ null(P1 - P2)'; (P1 -P2)/norm(P1-P2)];
66 | S = eye(3); S(1,1) = 1.5*norm(P1-P2);
67 | C = U*S*U';
68 | [x,y,z] = ellipsoid(0,0,0,0.8,0.8,1.1*sqrt(1.5*norm(P1-P2)),8);
69 | axis equal;
70 | xv =x(:);
71 | yv = y(:);
72 | zv = z(:);
73 | newXYZ = U'*[xv';yv';zv'];
74 | xnew = reshape(newXYZ(1,:)+P(1),size(x,1),size(x,2));
75 | ynew = reshape(newXYZ(2,:)+P(2),size(x,1),size(x,2));
76 | znew = reshape(newXYZ(3,:)+P(3),size(x,1),size(x,2));
77 |
78 |
79 | handle(i+1) = patch(surf2patch(xnew,ynew,znew));
80 |
81 | set(handle(i+1),'EdgeColor','k','EdgeAlpha',0.1);
82 | set(handle(i+1),'FaceLighting','phong','AmbientStrength',0.6);
83 | set(handle(i+1),'FaceColor', M(i,:));
84 | set(handle(i+1),'BackfaceLighting','lit');
85 |
86 | gaussianMan(i).P = P;
87 | gaussianMan(i).C = C;
88 |
89 | end
90 | axis equal
91 |
92 | else
93 |
94 |
95 |
96 | end
97 |
98 | axis on
99 | hold off
100 |
101 |
102 |
103 |
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