├── LICENSE ├── README.md ├── bicubic.py ├── bicubic_butterfly.png ├── butterfly.png ├── formulation.png └── formulation2.png /LICENSE: -------------------------------------------------------------------------------- 1 | Apache License 2 | Version 2.0, January 2004 3 | http://www.apache.org/licenses/ 4 | 5 | TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION 6 | 7 | 1. Definitions. 8 | 9 | "License" shall mean the terms and conditions for use, reproduction, 10 | and distribution as defined by Sections 1 through 9 of this document. 11 | 12 | "Licensor" shall mean the copyright owner or entity authorized by 13 | the copyright owner that is granting the License. 14 | 15 | "Legal Entity" shall mean the union of the acting entity and all 16 | other entities that control, are controlled by, or are under common 17 | control with that entity. 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We also recommend that a 185 | file or class name and description of purpose be included on the 186 | same "printed page" as the copyright notice for easier 187 | identification within third-party archives. 188 | 189 | Copyright [yyyy] [name of copyright owner] 190 | 191 | Licensed under the Apache License, Version 2.0 (the "License"); 192 | you may not use this file except in compliance with the License. 193 | You may obtain a copy of the License at 194 | 195 | http://www.apache.org/licenses/LICENSE-2.0 196 | 197 | Unless required by applicable law or agreed to in writing, software 198 | distributed under the License is distributed on an "AS IS" BASIS, 199 | WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. 200 | See the License for the specific language governing permissions and 201 | limitations under the License. 202 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # Bicubic-interpolation 2 | This repository is for simple implementation of 'Bicubic-interpolation for images' (Python3). 3 | 4 | ## Table of contents 5 | * [Formulation](#Formulation) 6 | * [Example](#Example) 7 | * [Requirement](#Requirement) 8 | * [Installation](#Installation) 9 | * [Usage](#Usage) 10 | * [Reference](#Reference) 11 | * [Author](#Author) 12 | 13 | ## Formulation 14 | * Interpolation kernel [1] 15 | ![Formulation](./formulation.png) 16 | 17 | * Interpolation 18 | Use the values of 16 pixels around the new pixel dst(x,y) [1][2]. (x,y) shows the location of pixels. 19 | ![Formulation2](./formulation2.png) 20 | Here, f means the values of pixels. x1, x2, x3, x4 are the distance of x direction from new pixel to near 16 pixels. y1, ... are the distance of y direction. 21 | 22 | ## Example 23 | * Upscale input image 2 times (ratio = 2) 24 | The 'butterfly' image is from [3]. 25 | ![Input image](./butterfly.png) 26 | ↑ Input image (256x256) 27 | ![Output image](./bicubic_butterfly.png) 28 | ↑ Output image (512x512) 29 | 30 | ## Requirement 31 | * Python 3.5.2 or more 32 | 33 | ## Installation 34 | `$ git clone https://github.com/rootpine/Bicubic-interpolation.git` 35 | 36 | ## Usage 37 | 1. `$ python3 bicubic.py` 38 | 39 | ## Reference 40 | 1. R. Keys, "Cubic convolution interpolation for digital image processing," in IEEE Transactions on Acoustics, Speech, and Signal Processing, vol. 29, no. 6, pp. 1153-1160, December 1981. URL: 41 | 2. 奥富正敏ら, "ディジタル画像処理[改定新版]", CG-ARTS協会, pp. 170-171, 2016. 42 | 3. M. Bevilacqua, A. Roumy, C. Guillemot and ML. Alberi, "Low-Complexity Single-Image Super-Resolution based on Nonnegative Neighbor Embedding",BMVC 2012. 43 | 4. https://github.com/yunabe/codelab/blob/master/misc/terminal_progressbar/progress.py to show the progress. 44 | 45 | ## Author 46 | [@rootpine](https://github.com/rootpine/) 47 | -------------------------------------------------------------------------------- /bicubic.py: -------------------------------------------------------------------------------- 1 | import cv2 2 | import numpy as np 3 | import math 4 | import sys, time 5 | 6 | # Interpolation kernel 7 | def u(s,a): 8 | if (abs(s) >=0) & (abs(s) <=1): 9 | return (a+2)*(abs(s)**3)-(a+3)*(abs(s)**2)+1 10 | elif (abs(s) > 1) & (abs(s) <= 2): 11 | return a*(abs(s)**3)-(5*a)*(abs(s)**2)+(8*a)*abs(s)-4*a 12 | return 0 13 | 14 | #Paddnig 15 | def padding(img,H,W,C): 16 | zimg = np.zeros((H+4,W+4,C)) 17 | zimg[2:H+2,2:W+2,:C] = img 18 | #Pad the first/last two col and row 19 | zimg[2:H+2,0:2,:C]=img[:,0:1,:C] 20 | zimg[H+2:H+4,2:W+2,:]=img[H-1:H,:,:] 21 | zimg[2:H+2,W+2:W+4,:]=img[:,W-1:W,:] 22 | zimg[0:2,2:W+2,:C]=img[0:1,:,:C] 23 | #Pad the missing eight points 24 | zimg[0:2,0:2,:C]=img[0,0,:C] 25 | zimg[H+2:H+4,0:2,:C]=img[H-1,0,:C] 26 | zimg[H+2:H+4,W+2:W+4,:C]=img[H-1,W-1,:C] 27 | zimg[0:2,W+2:W+4,:C]=img[0,W-1,:C] 28 | return zimg 29 | 30 | # https://github.com/yunabe/codelab/blob/master/misc/terminal_progressbar/progress.py 31 | def get_progressbar_str(progress): 32 | END = 170 33 | MAX_LEN = 30 34 | BAR_LEN = int(MAX_LEN * progress) 35 | return ('Progress:[' + '=' * BAR_LEN + 36 | ('>' if BAR_LEN < MAX_LEN else '') + 37 | ' ' * (MAX_LEN - BAR_LEN) + 38 | '] %.1f%%' % (progress * 100.)) 39 | 40 | # Bicubic operation 41 | def bicubic(img, ratio, a): 42 | #Get image size 43 | H,W,C = img.shape 44 | 45 | img = padding(img,H,W,C) 46 | #Create new image 47 | dH = math.floor(H*ratio) 48 | dW = math.floor(W*ratio) 49 | dst = np.zeros((dH, dW, 3)) 50 | 51 | h = 1/ratio 52 | 53 | print('Start bicubic interpolation') 54 | print('It will take a little while...') 55 | inc = 0 56 | for c in range(C): 57 | for j in range(dH): 58 | for i in range(dW): 59 | x, y = i * h + 2 , j * h + 2 60 | 61 | x1 = 1 + x - math.floor(x) 62 | x2 = x - math.floor(x) 63 | x3 = math.floor(x) + 1 - x 64 | x4 = math.floor(x) + 2 - x 65 | 66 | y1 = 1 + y - math.floor(y) 67 | y2 = y - math.floor(y) 68 | y3 = math.floor(y) + 1 - y 69 | y4 = math.floor(y) + 2 - y 70 | 71 | mat_l = np.matrix([[u(x1,a),u(x2,a),u(x3,a),u(x4,a)]]) 72 | mat_m = np.matrix([[img[int(y-y1),int(x-x1),c],img[int(y-y2),int(x-x1),c],img[int(y+y3),int(x-x1),c],img[int(y+y4),int(x-x1),c]], 73 | [img[int(y-y1),int(x-x2),c],img[int(y-y2),int(x-x2),c],img[int(y+y3),int(x-x2),c],img[int(y+y4),int(x-x2),c]], 74 | [img[int(y-y1),int(x+x3),c],img[int(y-y2),int(x+x3),c],img[int(y+y3),int(x+x3),c],img[int(y+y4),int(x+x3),c]], 75 | [img[int(y-y1),int(x+x4),c],img[int(y-y2),int(x+x4),c],img[int(y+y3),int(x+x4),c],img[int(y+y4),int(x+x4),c]]]) 76 | mat_r = np.matrix([[u(y1,a)],[u(y2,a)],[u(y3,a)],[u(y4,a)]]) 77 | dst[j, i, c] = np.dot(np.dot(mat_l, mat_m),mat_r) 78 | 79 | # Print progress 80 | inc = inc + 1 81 | sys.stderr.write('\r\033[K' + get_progressbar_str(inc/(C*dH*dW))) 82 | sys.stderr.flush() 83 | sys.stderr.write('\n') 84 | sys.stderr.flush() 85 | return dst 86 | 87 | # Read image 88 | img = cv2.imread('butterfly.png') 89 | 90 | # Scale factor 91 | ratio = 2 92 | # Coefficient 93 | a = -1/2 94 | 95 | dst = bicubic(img, ratio, a) 96 | print('Completed!') 97 | cv2.imwrite('bicubic_butterfly.png', dst) 98 | -------------------------------------------------------------------------------- /bicubic_butterfly.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/rootpine/Bicubic-interpolation/96fa34643258ed6d97e035a73171f3b2ecbad348/bicubic_butterfly.png -------------------------------------------------------------------------------- /butterfly.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/rootpine/Bicubic-interpolation/96fa34643258ed6d97e035a73171f3b2ecbad348/butterfly.png -------------------------------------------------------------------------------- /formulation.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/rootpine/Bicubic-interpolation/96fa34643258ed6d97e035a73171f3b2ecbad348/formulation.png -------------------------------------------------------------------------------- /formulation2.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/rootpine/Bicubic-interpolation/96fa34643258ed6d97e035a73171f3b2ecbad348/formulation2.png --------------------------------------------------------------------------------