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Histogram Equalization {#tutorial_histogram_equalization}
======================
Goal
----
In this tutorial you will learn:
- What an image histogram is and why it is useful
- To equalize histograms of images by using the OpenCV function @ref cv::equalizeHist
Theory
------
### What is an Image Histogram?
- It is a graphical representation of the intensity distribution of an image.
- It quantifies the number of pixels for each intensity value considered.
### What is Histogram Equalization?
- 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.
### How does it work?
- 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 \f$H(i)\f$, its
*cumulative distribution* \f$H^{'}(i)\f$ is:
\f[H^{'}(i) = \sum_{0 \le j < i} H(j)\f]
To use this as a remapping function, we have to normalize \f$H^{'}(i)\f$ 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:
- Finally, we use a simple remapping procedure to obtain the intensity values of the equalized
image:
\f[equalized( x, y ) = H^{'}( src(x,y) )\f]
Code
----
- **What does this program do?**
- Loads an image
- Convert the original image to grayscale
- Equalize the Histogram by using the OpenCV function @ref cv::equalizeHist
- Display the source and equalized images in a window.
- **Downloadable code**: Click
[here](https://github.com/opencv/opencv/tree/master/samples/cpp/tutorial_code/Histograms_Matching/EqualizeHist_Demo.cpp)
- **Code at glance:**
@include samples/cpp/tutorial_code/Histograms_Matching/EqualizeHist_Demo.cpp
Explanation
-----------
-# Declare the source and destination images as well as the windows names:
@code{.cpp}
Mat src, dst;
char* source_window = "Source image";
char* equalized_window = "Equalized Image";
@endcode
-# Load the source image:
@code{.cpp}
src = imread( argv[1], 1 );
if( !src.data )
{ cout<<"Usage: ./Histogram_Demo <path_to_image>"<<endl;
return -1;}
@endcode
-# Convert it to grayscale:
@code{.cpp}
cvtColor( src, src, COLOR_BGR2GRAY );
@endcode
-# Apply histogram equalization with the function @ref cv::equalizeHist :
@code{.cpp}
equalizeHist( src, dst );
@endcode
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{.cpp}
namedWindow( source_window, WINDOW_AUTOSIZE );
namedWindow( equalized_window, WINDOW_AUTOSIZE );
imshow( source_window, src );
imshow( equalized_window, dst );
@endcode
-# Wait until user exists the program
@code{.cpp}
waitKey(0);
return 0;
@endcode
Results
-------
-# To appreciate better the results of equalization, let's introduce an image with not much
contrast, such as:
which, by the way, has this histogram:
notice that the pixels are clustered around the center of the histogram.
-# After applying the equalization with our program, we get this result:
this image has certainly more contrast. Check out its new histogram like this:
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!
|
