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Histogram Calculation

Prev Tutorial: Histogram Equalization
Next Tutorial: Histogram Comparison

Original author Ana Huamán
Compatibility OpenCV >= 3.0

Goal

In this tutorial you will learn how to:

  • Use the OpenCV function cv::split to divide an image into its correspondent planes.
  • To calculate histograms of arrays of images by using the OpenCV function cv::calcHist
  • To normalize an array by using the function cv::normalize
Note
In the last tutorial (Histogram Equalization) we talked about a particular kind of histogram called Image histogram. Now we will considerate it in its more general concept. Read on!

What are histograms?

  • Histograms are collected counts of data organized into a set of predefined bins
  • When we say data we are not restricting it to be intensity values (as we saw in the previous Tutorial Histogram Equalization). The data collected can be whatever feature you find useful to describe your image.
  • Let's see an example. Imagine that a Matrix contains information of an image (i.e. intensity in the range 0255):
  • What happens if we want to count this data in an organized way? Since we know that the range of information value for this case is 256 values, we can segment our range in subparts (called bins) like:

    [0,255]=[0,15][16,31]....[240,255]range=bin1bin2....binn=15

    and we can keep count of the number of pixels that fall in the range of each bini. Applying this to the example above we get the image below ( axis x represents the bins and axis y the number of pixels in each of them).

  • This was just a simple example of how an histogram works and why it is useful. An histogram can keep count not only of color intensities, but of whatever image features that we want to measure (i.e. gradients, directions, etc).
  • Let's identify some parts of the histogram:
    1. dims: The number of parameters you want to collect data of. In our example, dims = 1 because we are only counting the intensity values of each pixel (in a greyscale image).
    2. bins: It is the number of subdivisions in each dim. In our example, bins = 16
    3. range: The limits for the values to be measured. In this case: range = [0,255]
  • What if you want to count two features? In this case your resulting histogram would be a 3D plot (in which x and y would be binx and biny for each feature and z would be the number of counts for each combination of (binx,biny). The same would apply for more features (of course it gets trickier).

What OpenCV offers you

For simple purposes, OpenCV implements the function cv::calcHist , which calculates the histogram of a set of arrays (usually images or image planes). It can operate with up to 32 dimensions. We will see it in the code below!

Code

  • What does this program do?
    • Loads an image
    • Splits the image into its R, G and B planes using the function cv::split
    • Calculate the Histogram of each 1-channel plane by calling the function cv::calcHist
    • Plot the three histograms in a window
  • Downloadable code: Click here
  • Code at glance:
    #include <iostream>
    using namespace std;
    using namespace cv;
    int main(int argc, char** argv)
    {
    CommandLineParser parser( argc, argv, "{@input | lena.jpg | input image}" );
    Mat src = imread( samples::findFile( parser.get<String>( "@input" ) ), IMREAD_COLOR );
    if( src.empty() )
    {
    return EXIT_FAILURE;
    }
    vector<Mat> bgr_planes;
    split( src, bgr_planes );
    int histSize = 256;
    float range[] = { 0, 256 }; //the upper boundary is exclusive
    const float* histRange[] = { range };
    bool uniform = true, accumulate = false;
    Mat b_hist, g_hist, r_hist;
    calcHist( &bgr_planes[0], 1, 0, Mat(), b_hist, 1, &histSize, histRange, uniform, accumulate );
    calcHist( &bgr_planes[1], 1, 0, Mat(), g_hist, 1, &histSize, histRange, uniform, accumulate );
    calcHist( &bgr_planes[2], 1, 0, Mat(), r_hist, 1, &histSize, histRange, uniform, accumulate );
    int hist_w = 512, hist_h = 400;
    int bin_w = cvRound( (double) hist_w/histSize );
    Mat histImage( hist_h, hist_w, CV_8UC3, Scalar( 0,0,0) );
    normalize(b_hist, b_hist, 0, histImage.rows, NORM_MINMAX, -1, Mat() );
    normalize(g_hist, g_hist, 0, histImage.rows, NORM_MINMAX, -1, Mat() );
    normalize(r_hist, r_hist, 0, histImage.rows, NORM_MINMAX, -1, Mat() );
    for( int i = 1; i < histSize; i++ )
    {
    line( histImage, Point( bin_w*(i-1), hist_h - cvRound(b_hist.at<float>(i-1)) ),
    Point( bin_w*(i), hist_h - cvRound(b_hist.at<float>(i)) ),
    Scalar( 255, 0, 0), 2, 8, 0 );
    line( histImage, Point( bin_w*(i-1), hist_h - cvRound(g_hist.at<float>(i-1)) ),
    Point( bin_w*(i), hist_h - cvRound(g_hist.at<float>(i)) ),
    Scalar( 0, 255, 0), 2, 8, 0 );
    line( histImage, Point( bin_w*(i-1), hist_h - cvRound(r_hist.at<float>(i-1)) ),
    Point( bin_w*(i), hist_h - cvRound(r_hist.at<float>(i)) ),
    Scalar( 0, 0, 255), 2, 8, 0 );
    }
    imshow("Source image", src );
    imshow("calcHist Demo", histImage );
    return EXIT_SUCCESS;
    }
    Designed for command line parsing.
    Definition utility.hpp:890
    n-dimensional dense array class
    Definition mat.hpp:829
    _Tp & at(int i0=0)
    Returns a reference to the specified array element.
    bool empty() const
    Returns true if the array has no elements.
    std::string String
    Definition cvstd.hpp:151
    #define CV_8UC3
    Definition interface.h:90
    int cvRound(double value)
    Rounds floating-point number to the nearest integer.
    Definition fast_math.hpp:200
    void imshow(const String &winname, InputArray mat)
    Displays an image in the specified window.
    int waitKey(int delay=0)
    Waits for a pressed key.
    int main(int argc, char *argv[])
    Definition highgui_qt.cpp:3
    Definition core.hpp:107
    STL namespace.

Explanation

  • Load the source image

    CommandLineParser parser( argc, argv, "{@input | lena.jpg | input image}" );
    Mat src = imread( samples::findFile( parser.get<String>( "@input" ) ), IMREAD_COLOR );
    if( src.empty() )
    {
    return EXIT_FAILURE;
    }
  • Separate the source image in its three R,G and B planes. For this we use the OpenCV function cv::split :

    vector<Mat> bgr_planes;
    split( src, bgr_planes );

    our input is the image to be divided (this case with three channels) and the output is a vector of Mat )

  • Now we are ready to start configuring the histograms for each plane. Since we are working with the B, G and R planes, we know that our values will range in the interval [0,255]
  • Establish the number of bins (5, 10...):

    int histSize = 256;
  • Set the range of values (as we said, between 0 and 255 )

    float range[] = { 0, 256 }; //the upper boundary is exclusive
    const float* histRange[] = { range };
  • We want our bins to have the same size (uniform) and to clear the histograms in the beginning, so:

    bool uniform = true, accumulate = false;
  • We proceed to calculate the histograms by using the OpenCV function cv::calcHist :

    Mat b_hist, g_hist, r_hist;
    calcHist( &bgr_planes[0], 1, 0, Mat(), b_hist, 1, &histSize, histRange, uniform, accumulate );
    calcHist( &bgr_planes[1], 1, 0, Mat(), g_hist, 1, &histSize, histRange, uniform, accumulate );
    calcHist( &bgr_planes[2], 1, 0, Mat(), r_hist, 1, &histSize, histRange, uniform, accumulate );
  • where the arguments are (C++ code):
    • &bgr_planes[0]: The source array(s)
    • 1: The number of source arrays (in this case we are using 1. We can enter here also a list of arrays )
    • 0: The channel (dim) to be measured. In this case it is just the intensity (each array is single-channel) so we just write 0.
    • Mat(): A mask to be used on the source array ( zeros indicating pixels to be ignored ). If not defined it is not used
    • b_hist: The Mat object where the histogram will be stored
    • 1: The histogram dimensionality.
    • histSize: The number of bins per each used dimension
    • histRange: The range of values to be measured per each dimension
    • uniform and accumulate: The bin sizes are the same and the histogram is cleared at the beginning.
  • Create an image to display the histograms:

    int hist_w = 512, hist_h = 400;
    int bin_w = cvRound( (double) hist_w/histSize );
    Mat histImage( hist_h, hist_w, CV_8UC3, Scalar( 0,0,0) );
  • Notice that before drawing, we first cv::normalize the histogram so its values fall in the range indicated by the parameters entered:

    normalize(b_hist, b_hist, 0, histImage.rows, NORM_MINMAX, -1, Mat() );
    normalize(g_hist, g_hist, 0, histImage.rows, NORM_MINMAX, -1, Mat() );
    normalize(r_hist, r_hist, 0, histImage.rows, NORM_MINMAX, -1, Mat() );
  • this function receives these arguments (C++ code):
    • b_hist: Input array
    • b_hist: Output normalized array (can be the same)
    • 0 and histImage.rows: For this example, they are the lower and upper limits to normalize the values of r_hist
    • NORM_MINMAX: Argument that indicates the type of normalization (as described above, it adjusts the values between the two limits set before)
    • -1: Implies that the output normalized array will be the same type as the input
    • Mat(): Optional mask
  • Observe that to access the bin (in this case in this 1D-Histogram):

    for( int i = 1; i < histSize; i++ )
    {
    line( histImage, Point( bin_w*(i-1), hist_h - cvRound(b_hist.at<float>(i-1)) ),
    Point( bin_w*(i), hist_h - cvRound(b_hist.at<float>(i)) ),
    Scalar( 255, 0, 0), 2, 8, 0 );
    line( histImage, Point( bin_w*(i-1), hist_h - cvRound(g_hist.at<float>(i-1)) ),
    Point( bin_w*(i), hist_h - cvRound(g_hist.at<float>(i)) ),
    Scalar( 0, 255, 0), 2, 8, 0 );
    line( histImage, Point( bin_w*(i-1), hist_h - cvRound(r_hist.at<float>(i-1)) ),
    Point( bin_w*(i), hist_h - cvRound(r_hist.at<float>(i)) ),
    Scalar( 0, 0, 255), 2, 8, 0 );
    }

    we use the expression (C++ code):

    b_hist.at<float>(i)

    where i indicates the dimension. If it were a 2D-histogram we would use something like:

    b_hist.at<float>( i, j )
  • Finally we display our histograms and wait for the user to exit:

    imshow("Source image", src );
    imshow("calcHist Demo", histImage );

Result

  1. Using as input argument an image like the one shown below:
  1. Produces the following histogram: