Calculating moments of an image

Moments moments(InputArray array, bool binaryImage=false )

Parameters:	array – Raster image (single-channel, 8-bit or floating-point 2D array) or an array ( 1xN or Nx1 ) of 2D points (Point or Point2f ). binaryImage – If it is true, all non-zero image pixels are treated as 1’s. The parameter is used for images only. moments – Output moments.

The function computes moments, up to the 3rd order, of a vector shape or a rasterized shape. The results are returned in the structure Moments defined as:

class Moments
{
public:
    Moments();
    Moments(double m00, double m10, double m01, double m20, double m11,
            double m02, double m30, double m21, double m12, double m03 );
    Moments( const CvMoments& moments );
    operator CvMoments() const;

    // spatial moments
    double  m00, m10, m01, m20, m11, m02, m30, m21, m12, m03;
    // central moments
    double  mu20, mu11, mu02, mu30, mu21, mu12, mu03;
    // central normalized moments
    double  nu20, nu11, nu02, nu30, nu21, nu12, nu03;
}

In case of a raster image, the spatial moments Moments:: mji are computed as:

The central moments are computed as:

where is the mass center:

The normalized central moments Moments:: nuji are computed as:

The code provided below is slight modification of code given in OpenCV documentation.

Steps:

1. Load image
2. Convert to gray-scale.
3. Remove noise by blurring with a Gaussian filter
4. Detect edges using canny
5. Find contours (findContours)
6. Get the moments(Moments)
7. Draw contours 
8. Calculate the area with the moments 00 and compare with the result of the OpenCV function

Functions:

findContours, Moments, Canny, blur, cvtColor, imshow, imread, waitKey.

 

Example:

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#include "opencv2/highgui/highgui.hpp"
#include "opencv2/imgproc/imgproc.hpp"
#include <iostream>
#include <stdio.h>
#include <stdlib.h>

using namespace cv;
using namespace std;


RNG rng(12345);

void find_moments( Mat src );

int main( )
{
    /// Load source image, convert it to gray and blur it
    Mat src, gray;;
    src = imread("shapes.jpg", 1 );
    cvtColor( src, gray, CV_BGR2GRAY );
    blur( gray, gray, Size(3,3) );

    namedWindow( "Source", CV_WINDOW_AUTOSIZE );
    imshow( "Source", src );

    find_moments( gray );

    waitKey(0);
    return(0);
}

void find_moments( Mat gray )
{
    Mat canny_output;
    vector<vector<Point> > contours;
    vector<Vec4i> hierarchy;

    /// Detect edges using canny
    Canny( gray, canny_output, 50, 150, 3 );
    /// Find contours
    findContours( canny_output, contours, hierarchy, CV_RETR_TREE, CV_CHAIN_APPROX_SIMPLE, Point(0, 0) );

    /// Get the moments
    vector<Moments> mu(contours.size() );
    for( int i = 0; i < contours.size(); i++ )
    { mu[i] = moments( contours[i], false ); }

    ///  Get the mass centers:
    vector<Point2f> mc( contours.size() );
    for( int i = 0; i < contours.size(); i++ )
    { mc[i] = Point2f( mu[i].m10/mu[i].m00 , mu[i].m01/mu[i].m00 ); }

    /// Draw contours
    Mat drawing = Mat::zeros( canny_output.size(), CV_8UC3 );
    for( int i = 0; i< contours.size(); i++ )
    {
        Scalar color = Scalar( rng.uniform(0, 255), rng.uniform(0,255), rng.uniform(0,255) );
        drawContours( drawing, contours, i, color, 2, 8, hierarchy, 0, Point() );
        circle( drawing, mc[i], 4, color, -1, 8, 0 );
    }

    /// Show in a window
    namedWindow( "Contours", CV_WINDOW_AUTOSIZE );
    imshow( "Contours", drawing );

    /// Calculate the area with the moments 00 and compare with the result of the OpenCV function
    printf("\t Info: Area and Contour Length \n");
    for( int i = 0; i< contours.size(); i++ )
        printf(" * Contour[%d] - Area (M_00) = %.2f - Area OpenCV: %.2f - Length: %.2f \n", i, mu[i].m00, contourArea(contours[i]), arcLength( contours[i], true ) );

}

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