1 Histogram Comparison {#tutorial_histogram_comparison} 2 ==================== 3 4 Goal 5 ---- 6 7 In this tutorial you will learn how to: 8 9 - Use the function @ref cv::compareHist to get a numerical parameter that express how well two 10 histograms match with each other. 11 - Use different metrics to compare histograms 12 13 Theory 14 ------ 15 16 - To compare two histograms ( \f$H_{1}\f$ and \f$H_{2}\f$ ), first we have to choose a *metric* 17 (\f$d(H_{1}, H_{2})\f$) to express how well both histograms match. 18 - OpenCV implements the function @ref cv::compareHist to perform a comparison. It also offers 4 19 different metrics to compute the matching: 20 -# **Correlation ( CV_COMP_CORREL )** 21 \f[d(H_1,H_2) = \frac{\sum_I (H_1(I) - \bar{H_1}) (H_2(I) - \bar{H_2})}{\sqrt{\sum_I(H_1(I) - \bar{H_1})^2 \sum_I(H_2(I) - \bar{H_2})^2}}\f] 22 where 23 \f[\bar{H_k} = \frac{1}{N} \sum _J H_k(J)\f] 24 and \f$N\f$ is the total number of histogram bins. 25 26 -# **Chi-Square ( CV_COMP_CHISQR )** 27 \f[d(H_1,H_2) = \sum _I \frac{\left(H_1(I)-H_2(I)\right)^2}{H_1(I)}\f] 28 29 -# **Intersection ( method=CV_COMP_INTERSECT )** 30 \f[d(H_1,H_2) = \sum _I \min (H_1(I), H_2(I))\f] 31 32 -# **Bhattacharyya distance ( CV_COMP_BHATTACHARYYA )** 33 \f[d(H_1,H_2) = \sqrt{1 - \frac{1}{\sqrt{\bar{H_1} \bar{H_2} N^2}} \sum_I \sqrt{H_1(I) \cdot H_2(I)}}\f] 34 35 Code 36 ---- 37 38 - **What does this program do?** 39 - Loads a *base image* and 2 *test images* to be compared with it. 40 - Generate 1 image that is the lower half of the *base image* 41 - Convert the images to HSV format 42 - Calculate the H-S histogram for all the images and normalize them in order to compare them. 43 - Compare the histogram of the *base image* with respect to the 2 test histograms, the 44 histogram of the lower half base image and with the same base image histogram. 45 - Display the numerical matching parameters obtained. 46 - **Downloadable code**: Click 47 [here](https://github.com/Itseez/opencv/tree/master/samples/cpp/tutorial_code/Histograms_Matching/compareHist_Demo.cpp) 48 - **Code at glance:** 49 50 @include cpp/tutorial_code/Histograms_Matching/compareHist_Demo.cpp 51 52 Explanation 53 ----------- 54 55 -# Declare variables such as the matrices to store the base image and the two other images to 56 compare ( BGR and HSV ) 57 @code{.cpp} 58 Mat src_base, hsv_base; 59 Mat src_test1, hsv_test1; 60 Mat src_test2, hsv_test2; 61 Mat hsv_half_down; 62 @endcode 63 -# Load the base image (src_base) and the other two test images: 64 @code{.cpp} 65 if( argc < 4 ) 66 { printf("** Error. Usage: ./compareHist_Demo <image_settings0> <image_setting1> <image_settings2>\n"); 67 return -1; 68 } 69 70 src_base = imread( argv[1], 1 ); 71 src_test1 = imread( argv[2], 1 ); 72 src_test2 = imread( argv[3], 1 ); 73 @endcode 74 -# Convert them to HSV format: 75 @code{.cpp} 76 cvtColor( src_base, hsv_base, COLOR_BGR2HSV ); 77 cvtColor( src_test1, hsv_test1, COLOR_BGR2HSV ); 78 cvtColor( src_test2, hsv_test2, COLOR_BGR2HSV ); 79 @endcode 80 -# Also, create an image of half the base image (in HSV format): 81 @code{.cpp} 82 hsv_half_down = hsv_base( Range( hsv_base.rows/2, hsv_base.rows - 1 ), Range( 0, hsv_base.cols - 1 ) ); 83 @endcode 84 -# Initialize the arguments to calculate the histograms (bins, ranges and channels H and S ). 85 @code{.cpp} 86 int h_bins = 50; int s_bins = 60; 87 int histSize[] = { h_bins, s_bins }; 88 89 float h_ranges[] = { 0, 180 }; 90 float s_ranges[] = { 0, 256 }; 91 92 const float* ranges[] = { h_ranges, s_ranges }; 93 94 int channels[] = { 0, 1 }; 95 @endcode 96 -# Create the MatND objects to store the histograms: 97 @code{.cpp} 98 MatND hist_base; 99 MatND hist_half_down; 100 MatND hist_test1; 101 MatND hist_test2; 102 @endcode 103 -# Calculate the Histograms for the base image, the 2 test images and the half-down base image: 104 @code{.cpp} 105 calcHist( &hsv_base, 1, channels, Mat(), hist_base, 2, histSize, ranges, true, false ); 106 normalize( hist_base, hist_base, 0, 1, NORM_MINMAX, -1, Mat() ); 107 108 calcHist( &hsv_half_down, 1, channels, Mat(), hist_half_down, 2, histSize, ranges, true, false ); 109 normalize( hist_half_down, hist_half_down, 0, 1, NORM_MINMAX, -1, Mat() ); 110 111 calcHist( &hsv_test1, 1, channels, Mat(), hist_test1, 2, histSize, ranges, true, false ); 112 normalize( hist_test1, hist_test1, 0, 1, NORM_MINMAX, -1, Mat() ); 113 114 calcHist( &hsv_test2, 1, channels, Mat(), hist_test2, 2, histSize, ranges, true, false ); 115 normalize( hist_test2, hist_test2, 0, 1, NORM_MINMAX, -1, Mat() ); 116 @endcode 117 -# Apply sequentially the 4 comparison methods between the histogram of the base image (hist_base) 118 and the other histograms: 119 @code{.cpp} 120 for( int i = 0; i < 4; i++ ) 121 { int compare_method = i; 122 double base_base = compareHist( hist_base, hist_base, compare_method ); 123 double base_half = compareHist( hist_base, hist_half_down, compare_method ); 124 double base_test1 = compareHist( hist_base, hist_test1, compare_method ); 125 double base_test2 = compareHist( hist_base, hist_test2, compare_method ); 126 127 printf( " Method [%d] Perfect, Base-Half, Base-Test(1), Base-Test(2) : %f, %f, %f, %f \n", i, base_base, base_half , base_test1, base_test2 ); 128 } 129 @endcode 130 131 Results 132 ------- 133 134 -# We use as input the following images: 135  136  137  138 where the first one is the base (to be compared to the others), the other 2 are the test images. 139 We will also compare the first image with respect to itself and with respect of half the base 140 image. 141 142 -# We should expect a perfect match when we compare the base image histogram with itself. Also, 143 compared with the histogram of half the base image, it should present a high match since both 144 are from the same source. For the other two test images, we can observe that they have very 145 different lighting conditions, so the matching should not be very good: 146 147 -# Here the numeric results: 148 *Method* | Base - Base | Base - Half | Base - Test 1 | Base - Test 2 149 ----------------- | ------------ | ------------ | -------------- | --------------- 150 *Correlation* | 1.000000 | 0.930766 | 0.182073 | 0.120447 151 *Chi-square* | 0.000000 | 4.940466 | 21.184536 | 49.273437 152 *Intersection* | 24.391548 | 14.959809 | 3.889029 | 5.775088 153 *Bhattacharyya* | 0.000000 | 0.222609 | 0.646576 | 0.801869 154 For the *Correlation* and *Intersection* methods, the higher the metric, the more accurate the 155 match. As we can see, the match *base-base* is the highest of all as expected. Also we can observe 156 that the match *base-half* is the second best match (as we predicted). For the other two metrics, 157 the less the result, the better the match. We can observe that the matches between the test 1 and 158 test 2 with respect to the base are worse, which again, was expected. 159
