.. _histogram_equalization: Histogram Equalization ********************** Goal ==== In this tutorial you will learn: .. container:: enumeratevisibleitemswithsquare * What an image histogram is and why it is useful * To equalize histograms of images by using the OpenCV function:equalize_hist:equalizeHist <> Theory ====== What is an Image Histogram? --------------------------- .. container:: enumeratevisibleitemswithsquare * It is a graphical representation of the intensity distribution of an image. * It quantifies the number of pixels for each intensity value considered. .. image:: images/Histogram_Equalization_Theory_0.jpg :align: center What is Histogram Equalization? ------------------------------- .. container:: enumeratevisibleitemswithsquare * It is a method that improves the contrast in an image, in order to stretch out the intensity range. * To make it clearer, from the image above, you can see that the pixels seem clustered around the middle of the available range of intensities. What Histogram Equalization does is to *stretch out* this range. Take a look at the figure below: The green circles indicate the *underpopulated* intensities. After applying the equalization, we get an histogram like the figure in the center. The resulting image is shown in the picture at right. .. image:: images/Histogram_Equalization_Theory_1.jpg :align: center How does it work? ----------------- .. container:: enumeratevisibleitemswithsquare * Equalization implies *mapping* one distribution (the given histogram) to another distribution (a wider and more uniform distribution of intensity values) so the intensity values are spreaded over the whole range. * To accomplish the equalization effect, the remapping should be the *cumulative distribution function (cdf)* (more details, refer to *Learning OpenCV*). For the histogram :math:H(i), its *cumulative distribution* :math:H^{'}(i) is: .. math:: H^{'}(i) = \sum_{0 \le j < i} H(j) To use this as a remapping function, we have to normalize :math:H^{'}(i) such that the maximum value is 255 ( or the maximum value for the intensity of the image ). From the example above, the cumulative function is: .. image:: images/Histogram_Equalization_Theory_2.jpg :align: center * Finally, we use a simple remapping procedure to obtain the intensity values of the equalized image: .. math:: equalized( x, y ) = H^{'}( src(x,y) ) Code ==== .. container:: enumeratevisibleitemswithsquare * **What does this program do?** .. container:: enumeratevisibleitemswithsquare * Loads an image * Convert the original image to grayscale * Equalize the Histogram by using the OpenCV function :equalize_hist:EqualizeHist <> * Display the source and equalized images in a window. * **Downloadable code**: Click here _ * **Code at glance:** .. code-block:: cpp #include "opencv2/highgui/highgui.hpp" #include "opencv2/imgproc/imgproc.hpp" #include #include using namespace cv; using namespace std; /** @function main */ int main( int argc, char** argv ) { Mat src, dst; char* source_window = "Source image"; char* equalized_window = "Equalized Image"; /// Load image src = imread( argv[1], 1 ); if( !src.data ) { cout<<"Usage: ./Histogram_Demo "<"<` : .. code-block:: cpp equalizeHist( src, dst ); As it can be easily seen, the only arguments are the original image and the output (equalized) image. #. Display both images (original and equalized) : .. code-block:: cpp namedWindow( source_window, CV_WINDOW_AUTOSIZE ); namedWindow( equalized_window, CV_WINDOW_AUTOSIZE ); imshow( source_window, src ); imshow( equalized_window, dst ); #. Wait until user exists the program .. code-block:: cpp waitKey(0); return 0; Results ======= #. To appreciate better the results of equalization, let's introduce an image with not much contrast, such as: .. image:: images/Histogram_Equalization_Original_Image.jpg :align: center which, by the way, has this histogram: .. image:: images/Histogram_Equalization_Original_Histogram.jpg :align: center notice that the pixels are clustered around the center of the histogram. #. After applying the equalization with our program, we get this result: .. image:: images/Histogram_Equalization_Equalized_Image.jpg :align: center this image has certainly more contrast. Check out its new histogram like this: .. image:: images/Histogram_Equalization_Equalized_Histogram.jpg :align: center Notice how the number of pixels is more distributed through the intensity range. .. note:: Are you wondering how did we draw the Histogram figures shown above? Check out the following tutorial!