Doxygen tutorials: basic structure
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Maksim Shabunin
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Histogram Equalization {#tutorial_histogram_equalization}
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======================
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Goal
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----
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In this tutorial you will learn:
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- What an image histogram is and why it is useful
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- To equalize histograms of images by using the OpenCV <function@ref> cv::equalizeHist
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Theory
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------
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### What is an Image Histogram?
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- It is a graphical representation of the intensity distribution of an image.
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- It quantifies the number of pixels for each intensity value considered.
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### What is Histogram Equalization?
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- It is a method that improves the contrast in an image, in order to stretch out the intensity
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range.
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- To make it clearer, from the image above, you can see that the pixels seem clustered around the
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middle of the available range of intensities. What Histogram Equalization does is to *stretch
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out* this range. Take a look at the figure below: The green circles indicate the
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*underpopulated* intensities. After applying the equalization, we get an histogram like the
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figure in the center. The resulting image is shown in the picture at right.
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### How does it work?
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- Equalization implies *mapping* one distribution (the given histogram) to another distribution (a
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wider and more uniform distribution of intensity values) so the intensity values are spreaded
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over the whole range.
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- To accomplish the equalization effect, the remapping should be the *cumulative distribution
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function (cdf)* (more details, refer to *Learning OpenCV*). For the histogram \f$H(i)\f$, its
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*cumulative distribution* \f$H^{'}(i)\f$ is:
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\f[H^{'}(i) = \sum_{0 \le j < i} H(j)\f]
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To use this as a remapping function, we have to normalize \f$H^{'}(i)\f$ such that the maximum value
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is 255 ( or the maximum value for the intensity of the image ). From the example above, the
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cumulative function is:
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- Finally, we use a simple remapping procedure to obtain the intensity values of the equalized
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image:
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\f[equalized( x, y ) = H^{'}( src(x,y) )\f]
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Code
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----
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- **What does this program do?**
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- Loads an image
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- Convert the original image to grayscale
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- Equalize the Histogram by using the OpenCV function @ref cv::EqualizeHist
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- Display the source and equalized images in a window.
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- **Downloadable code**: Click
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[here](https://github.com/Itseez/opencv/tree/master/samples/cpp/tutorial_code/Histograms_Matching/EqualizeHist_Demo.cpp)
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- **Code at glance:**
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@code{.cpp}
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#include "opencv2/highgui.hpp"
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#include "opencv2/imgproc.hpp"
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#include <iostream>
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#include <stdio.h>
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using namespace cv;
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using namespace std;
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/* @function main */
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int main( int argc, char** argv )
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{
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Mat src, dst;
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char* source_window = "Source image";
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char* equalized_window = "Equalized Image";
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/// Load image
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src = imread( argv[1], 1 );
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if( !src.data )
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{ cout<<"Usage: ./Histogram_Demo <path_to_image>"<<endl;
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return -1;}
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/// Convert to grayscale
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cvtColor( src, src, COLOR_BGR2GRAY );
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/// Apply Histogram Equalization
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equalizeHist( src, dst );
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/// Display results
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namedWindow( source_window, WINDOW_AUTOSIZE );
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namedWindow( equalized_window, WINDOW_AUTOSIZE );
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imshow( source_window, src );
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imshow( equalized_window, dst );
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/// Wait until user exits the program
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waitKey(0);
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return 0;
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}
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@endcode
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Explanation
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-----------
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1. Declare the source and destination images as well as the windows names:
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@code{.cpp}
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Mat src, dst;
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char* source_window = "Source image";
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char* equalized_window = "Equalized Image";
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@endcode
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2. Load the source image:
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@code{.cpp}
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src = imread( argv[1], 1 );
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if( !src.data )
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{ cout<<"Usage: ./Histogram_Demo <path_to_image>"<<endl;
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return -1;}
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@endcode
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3. Convert it to grayscale:
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@code{.cpp}
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cvtColor( src, src, COLOR_BGR2GRAY );
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@endcode
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4. Apply histogram equalization with the function @ref cv::equalizeHist :
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@code{.cpp}
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equalizeHist( src, dst );
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@endcode
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As it can be easily seen, the only arguments are the original image and the output (equalized)
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image.
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5. Display both images (original and equalized) :
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@code{.cpp}
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namedWindow( source_window, WINDOW_AUTOSIZE );
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namedWindow( equalized_window, WINDOW_AUTOSIZE );
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imshow( source_window, src );
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imshow( equalized_window, dst );
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@endcode
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6. Wait until user exists the program
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@code{.cpp}
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waitKey(0);
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return 0;
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@endcode
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Results
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-------
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1. To appreciate better the results of equalization, let's introduce an image with not much
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contrast, such as:
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which, by the way, has this histogram:
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notice that the pixels are clustered around the center of the histogram.
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2. After applying the equalization with our program, we get this result:
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this image has certainly more contrast. Check out its new histogram like this:
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Notice how the number of pixels is more distributed through the intensity range.
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**note**
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Are you wondering how did we draw the Histogram figures shown above? Check out the following
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tutorial!
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