1Histogram Equalization {#tutorial_histogram_equalization} 2====================== 3 4Goal 5---- 6 7In this tutorial you will learn: 8 9- What an image histogram is and why it is useful 10- To equalize histograms of images by using the OpenCV function @ref cv::equalizeHist 11 12Theory 13------ 14 15### What is an Image Histogram? 16 17- It is a graphical representation of the intensity distribution of an image. 18- It quantifies the number of pixels for each intensity value considered. 19 20 21 22### What is Histogram Equalization? 23 24- It is a method that improves the contrast in an image, in order to stretch out the intensity 25 range. 26- To make it clearer, from the image above, you can see that the pixels seem clustered around the 27 middle of the available range of intensities. What Histogram Equalization does is to *stretch 28 out* this range. Take a look at the figure below: The green circles indicate the 29 *underpopulated* intensities. After applying the equalization, we get an histogram like the 30 figure in the center. The resulting image is shown in the picture at right. 31 32 33 34### How does it work? 35 36- Equalization implies *mapping* one distribution (the given histogram) to another distribution (a 37 wider and more uniform distribution of intensity values) so the intensity values are spreaded 38 over the whole range. 39- To accomplish the equalization effect, the remapping should be the *cumulative distribution 40 function (cdf)* (more details, refer to *Learning OpenCV*). For the histogram \f$H(i)\f$, its 41 *cumulative distribution* \f$H^{'}(i)\f$ is: 42 43 \f[H^{'}(i) = \sum_{0 \le j < i} H(j)\f] 44 45 To use this as a remapping function, we have to normalize \f$H^{'}(i)\f$ such that the maximum value 46 is 255 ( or the maximum value for the intensity of the image ). From the example above, the 47 cumulative function is: 48 49  50 51- Finally, we use a simple remapping procedure to obtain the intensity values of the equalized 52 image: 53 54 \f[equalized( x, y ) = H^{'}( src(x,y) )\f] 55 56Code 57---- 58 59- **What does this program do?** 60 - Loads an image 61 - Convert the original image to grayscale 62 - Equalize the Histogram by using the OpenCV function @ref cv::equalizeHist 63 - Display the source and equalized images in a window. 64- **Downloadable code**: Click 65 [here](https://github.com/Itseez/opencv/tree/master/samples/cpp/tutorial_code/Histograms_Matching/EqualizeHist_Demo.cpp) 66- **Code at glance:** 67 @include samples/cpp/tutorial_code/Histograms_Matching/EqualizeHist_Demo.cpp 68 69Explanation 70----------- 71 72-# Declare the source and destination images as well as the windows names: 73 @code{.cpp} 74 Mat src, dst; 75 76 char* source_window = "Source image"; 77 char* equalized_window = "Equalized Image"; 78 @endcode 79-# Load the source image: 80 @code{.cpp} 81 src = imread( argv[1], 1 ); 82 83 if( !src.data ) 84 { cout<<"Usage: ./Histogram_Demo <path_to_image>"<<endl; 85 return -1;} 86 @endcode 87-# Convert it to grayscale: 88 @code{.cpp} 89 cvtColor( src, src, COLOR_BGR2GRAY ); 90 @endcode 91-# Apply histogram equalization with the function @ref cv::equalizeHist : 92 @code{.cpp} 93 equalizeHist( src, dst ); 94 @endcode 95 As it can be easily seen, the only arguments are the original image and the output (equalized) 96 image. 97 98-# Display both images (original and equalized) : 99 @code{.cpp} 100 namedWindow( source_window, WINDOW_AUTOSIZE ); 101 namedWindow( equalized_window, WINDOW_AUTOSIZE ); 102 103 imshow( source_window, src ); 104 imshow( equalized_window, dst ); 105 @endcode 106-# Wait until user exists the program 107 @code{.cpp} 108 waitKey(0); 109 return 0; 110 @endcode 111 112Results 113------- 114 115-# To appreciate better the results of equalization, let's introduce an image with not much 116 contrast, such as: 117 118  119 120 which, by the way, has this histogram: 121 122  123 124 notice that the pixels are clustered around the center of the histogram. 125 126-# After applying the equalization with our program, we get this result: 127 128  129 130 this image has certainly more contrast. Check out its new histogram like this: 131 132  133 134 Notice how the number of pixels is more distributed through the intensity range. 135 136@note 137Are you wondering how did we draw the Histogram figures shown above? Check out the following 138tutorial! 139
