I am trying to implement a basic face recognition system using Uniform Circular LBP (8 Points in 1 unit radius neighborhood). I am taking an image, re-sizing it to 200 x 200 pixels and then splitting the image in 8x8 little images. I then compute the histogram for each little image and get a list of histograms. To compare 2 images, I compute chi-squared distance between the corresponding histograms and generate a score.
Here's my Uniform LBP implementation:
import numpy as np
import math
uniform = {0: 0, 1: 1, 2: 2, 3: 3, 4: 4, 5: 58, 6: 5, 7: 6, 8: 7, 9: 58, 10: 58, 11: 58, 12: 8, 13: 58, 14: 9, 15: 10, 16: 11, 17: 58, 18: 58, 19: 58, 20: 58, 21: 58, 22: 58, 23: 58, 24: 12, 25: 58, 26: 58, 27: 58, 28: 13, 29: 58, 30: 14, 31: 15, 32: 16, 33: 58, 34: 58, 35: 58, 36: 58, 37: 58, 38: 58, 39: 58, 40: 58, 41: 58, 42: 58, 43: 58, 44: 58, 45: 58, 46: 58, 47: 58, 48: 17, 49: 58, 50: 58, 51: 58, 52: 58, 53: 58, 54: 58, 55: 58, 56: 18, 57: 58, 58: 58, 59: 58, 60: 19, 61: 58, 62: 20, 63: 21, 64: 22, 65: 58, 66: 58, 67: 58, 68: 58, 69: 58, 70: 58, 71: 58, 72: 58, 73: 58, 74: 58, 75: 58, 76: 58, 77: 58, 78: 58, 79: 58, 80: 58, 81: 58, 82: 58, 83: 58, 84: 58, 85: 58, 86: 58, 87: 58, 88: 58, 89: 58, 90: 58, 91: 58, 92: 58, 93: 58, 94: 58, 95: 58, 96: 23, 97: 58, 98: 58, 99: 58, 100: 58, 101: 58, 102: 58, 103: 58, 104: 58, 105: 58, 106: 58, 107: 58, 108: 58, 109: 58, 110: 58, 111: 58, 112: 24, 113: 58, 114: 58, 115: 58, 116: 58, 117: 58, 118: 58, 119: 58, 120: 25, 121: 58, 122: 58, 123: 58, 124: 26, 125: 58, 126: 27, 127: 28, 128: 29, 129: 30, 130: 58, 131: 31, 132: 58, 133: 58, 134: 58, 135: 32, 136: 58, 137: 58, 138: 58, 139: 58, 140: 58, 141: 58, 142: 58, 143: 33, 144: 58, 145: 58, 146: 58, 147: 58, 148: 58, 149: 58, 150: 58, 151: 58, 152: 58, 153: 58, 154: 58, 155: 58, 156: 58, 157: 58, 158: 58, 159: 34, 160: 58, 161: 58, 162: 58, 163: 58, 164: 58, 165: 58, 166: 58, 167: 58, 168: 58, 169: 58, 170: 58, 171: 58, 172: 58, 173: 58, 174: 58, 175: 58, 176: 58, 177: 58, 178: 58, 179: 58, 180: 58, 181: 58, 182: 58, 183: 58, 184: 58, 185: 58, 186: 58, 187: 58, 188: 58, 189: 58, 190: 58, 191: 35, 192: 36, 193: 37, 194: 58, 195: 38, 196: 58, 197: 58, 198: 58, 199: 39, 200: 58, 201: 58, 202: 58, 203: 58, 204: 58, 205: 58, 206: 58, 207: 40, 208: 58, 209: 58, 210: 58, 211: 58, 212: 58, 213: 58, 214: 58, 215: 58, 216: 58, 217: 58, 218: 58, 219: 58, 220: 58, 221: 58, 222: 58, 223: 41, 224: 42, 225: 43, 226: 58, 227: 44, 228: 58, 229: 58, 230: 58, 231: 45, 232: 58, 233: 58, 234: 58, 235: 58, 236: 58, 237: 58, 238: 58, 239: 46, 240: 47, 241: 48, 242: 58, 243: 49, 244: 58, 245: 58, 246: 58, 247: 50, 248: 51, 249: 52, 250: 58, 251: 53, 252: 54, 253: 55, 254: 56, 255: 57}def bilinear_interpolation(i, j, y, x, img):fy, fx = int(y), int(x)cy, cx = math.ceil(y), math.ceil(x)# calculate the fractional partsty = y - fytx = x - fxw1 = (1 - tx) * (1 - ty)w2 = tx * (1 - ty)w3 = (1 - tx) * tyw4 = tx * tyreturn w1 * img[i + fy, j + fx] + w2 * img[i + fy, j + cx] + \w3 * img[i + cy, j + fx] + w4 * img[i + cy, j + cx]def thresholded(center, pixels):out = []for a in pixels:if a > center:out.append(1)else:out.append(0)return outdef uniform_circular(img, P, R):ysize, xsize = img.shapetransformed_img = np.zeros((ysize - 2 * R,xsize - 2 * R), dtype=np.uint8)for y in range(R, len(img) - R):for x in range(R, len(img[0]) - R):center = img[y,x]pixels = []for point in range(0, P):r = R * math.cos(2 * math.pi * point / P)c = R * math.sin(2 * math.pi * point / P)pixels.append(bilinear_interpolation(y, x, r, c, img))values = thresholded(center, pixels)res = 0for a in range(0, P):res += values[a] << atransformed_img.itemset((y - R,x - R), uniform[res])transformed_img = transformed_img[R:-R,R:-R]return transformed_img
I did an experiment on AT&T database taking 2 gallery images and 8 probe images per subject. The ROC for the experiment came out to be:
In the above ROC, x axis denotes the false accept rate and the y axis denotes the genuine accept rate. The accuracy seems to be poor according to Uniform LBP standards. I am sure there is something wrong with my implementation. It would great if someone could help me with it. Thanks for reading.
EDIT:
I think I made a mistake in the above code. I am going clockwise while the paper on LBP suggest that I should go anticlockwise while assigning weights. The line: c = R * math.sin(2 * math.pi * point / P) should be c = -R * math.sin(2 * math.pi * point / P). Results after the edit are even worse. This suggests something is way wrong with my code. I guess the way I am choosing the coordinates for interpolation is messed up.
Edit: next I tried to replicate @bytefish's code here and used the uniform hashmap to make the implementation Uniform Circular LBP.
def uniform_circular(img, P, R):ysize, xsize = img.shapetransformed_img = np.zeros((ysize - 2 * R,xsize - 2 * R), dtype=np.uint8)for point in range(0, P):x = R * math.cos(2 * math.pi * point / P)y = -R * math.sin(2 * math.pi * point / P)fy, fx = int(y), int(x)cy, cx = math.ceil(y), math.ceil(x)# calculate the fractional partsty = y - fytx = x - fxw1 = (1 - tx) * (1 - ty)w2 = tx * (1 - ty)w3 = (1 - tx) * tyw4 = tx * ty for i in range(R, ysize - R):for j in range(R, xsize - R):t = w1 * img[i + fy, j + fx] + w2 * img[i + fy, j + cx] + \w3 * img[i + cy, j + fx] + w4 * img[i + cy, j + cx]center = img[i,j]pixels = []res = 0transformed_img[i - R,j - R] += (t > center) << pointfor i in range(R, ysize - R):for j in range(R, xsize - R):transformed_img[i - R,j - R] = uniform[transformed_img[i - R,j - R]]
Here's the ROC for the same:
I tried to implement the same code in C++. Here is the code:
#include <stdio.h>
#include <stdlib.h>
#include <opencv2/opencv.hpp>using namespace cv;int* uniform_circular_LBP_histogram(Mat& src) {int i, j;int radius = 1;int neighbours = 8;Size size = src.size();int *hist_array = (int *)calloc(59,sizeof(int));int uniform[] = {0,1,2,3,4,58,5,6,7,58,58,58,8,58,9,10,11,58,58,58,58,58,58,58,12,58,58,58,13,58,14,15,16,58,58,58,58,58,58,58,58,58,58,58,58,58,58,58,17,58,58,58,58,58,58,58,18,58,58,58,19,58,20,21,22,58,58,58,58,58,58,58,58,58,58,58,58,58,58,58,58,58,58,58,58,58,58,58,58,58,58,58,58,58,58,58,23,58,58,58,58,58,58,58,58,58,58,58,58,58,58,58,24,58,58,58,58,58,58,58,25,58,58,58,26,58,27,28,29,30,58,31,58,58,58,32,58,58,58,58,58,58,58,33,58,58,58,58,58,58,58,58,58,58,58,58,58,58,58,34,58,58,58,58,58,58,58,58,58,58,58,58,58,58,58,58,58,58,58,58,58,58,58,58,58,58,58,58,58,58,58,35,36,37,58,38,58,58,58,39,58,58,58,58,58,58,58,40,58,58,58,58,58,58,58,58,58,58,58,58,58,58,58,41,42,43,58,44,58,58,58,45,58,58,58,58,58,58,58,46,47,48,58,49,58,58,58,50,51,52,58,53,54,55,56,57};Mat dst = Mat::zeros(size.height - 2 * radius, size.width - 2 * radius, CV_8UC1);for (int n = 0; n < neighbours; n++) {float x = static_cast<float>(radius) * cos(2.0 * M_PI * n / static_cast<float>(neighbours));float y = static_cast<float>(radius) * -sin(2.0 * M_PI * n / static_cast<float>(neighbours));int fx = static_cast<int>(floor(x));int fy = static_cast<int>(floor(y));int cx = static_cast<int>(ceil(x));int cy = static_cast<int>(ceil(x));float ty = y - fy;float tx = y - fx;float w1 = (1 - tx) * (1 - ty);float w2 = tx * (1 - ty);float w3 = (1 - tx) * ty;float w4 = 1 - w1 - w2 - w3;for (i = 0; i < 59; i++) {hist_array[i] = 0;}for (i = radius; i < size.height - radius; i++) {for (j = radius; j < size.width - radius; j++) {float t = w1 * src.at<uchar>(i + fy, j + fx) + \w2 * src.at<uchar>(i + fy, j + cx) + \w3 * src.at<uchar>(i + cy, j + fx) + \w4 * src.at<uchar>(i + cy, j + cx);dst.at<uchar>(i - radius, j - radius) += ((t > src.at<uchar>(i,j)) && \(abs(t - src.at<uchar>(i,j)) > std::numeric_limits<float>::epsilon())) << n;}}}for (i = radius; i < size.height - radius; i++) {for (j = radius; j < size.width - radius; j++) {int val = uniform[dst.at<uchar>(i - radius, j - radius)];dst.at<uchar>(i - radius, j - radius) = val;hist_array[val] += 1;}}return hist_array;
}int main( int argc, char** argv )
{Mat src;int i,j;src = imread( argv[1], 0 );if( argc != 2 || !src.data ){printf( "No image data \n" );return -1;}const int width = 200;const int height = 200;Size size = src.size();Size new_size = Size();new_size.height = 200;new_size.width = 200;Mat resized_src;resize(src, resized_src, new_size, 0, 0, INTER_CUBIC);int count = 1;for (i = 0; i <= width - 8; i += 25) {for (j = 0; j <= height - 8; j += 25) {Mat new_mat = resized_src.rowRange(i, i + 25).colRange(j, j + 25);int *hist = uniform_circular_LBP_histogram(new_mat);int z;for (z = 0; z < 58; z++) {std::cout << hist[z] << ",";}std::cout << hist[z] << "\n";count += 1;}}return 0;
}
ROC for the same:
I also did a rank based experiment. And got this CMC curve.
Some details about the CMC curve: X axis represents ranks. (1-10) and Y axis represents the accuracy (0-1). So, I got a 80%+ Rank1 accuracy.