imgproc模塊--輪廓矩

1.目的
（1）使用openCV函數moments計算圖像所有的矩
（2）使用openCV函數contoursArea計算輪廓面積
（3）使用openCV函數arcLength計算曲線或者輪廓長度

2.原理
[1]空間矩的計算

[2]中心矩的計算

其中：

[3]歸一化的中心矩的計算

在openCV中
// 空間矩 double m00, m10, m01, m20, m11, m02, m30, m21, m12, m03;
// 中心矩 double mu20, mu11, mu02, mu30, mu21, mu12, mu03;
// 中心歸一化矩 double nu20, nu11, nu02, nu30, nu21, nu12, nu03;

3.完整代碼
（1）CommonInclude.h

#ifndef COMMON_INCLUDE
#define COMMON_INCLUDE
#include<iostream>
#include<opencv2/core/core.hpp>
#include<opencv2/highgui/highgui.hpp>
#include<opencv2/imgproc/imgproc.hpp>
using namespace std;
using namespace cv;
#endif

（2）ContoursMoment.cpp

#include "CommonInclude.h"

Mat src; Mat src_gray;
int thresh = 100;
int max_thresh = 255;
RNG rng(12345);

/** @thresh_callback 函數 */
void thresh_callback(int, void* )
{
    Mat canny_output;
    vector<vector<Point> > contours;
    vector<Vec4i> hierarchy;

    /// 使用Canndy檢測邊緣
    Canny( src_gray, canny_output, thresh, thresh*2, 3 );
    /// 找到輪廓
    findContours( canny_output, contours, hierarchy, CV_RETR_TREE, CV_CHAIN_APPROX_SIMPLE, Point(0, 0) );

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

    ///  計算質心:
    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 );
    }

    /// 繪製輪廓
    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 );
    }

    /// 顯示到窗口中
    namedWindow( "Contours", CV_WINDOW_AUTOSIZE );
    imshow( "Contours", drawing );

    /// 通過m00計算輪廓面積並且和OpenCV函數比較
    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 ) );
    }
}

/** @主函數 */
int main( int argc, char** argv )
{
    /// 讀入原圖像, 返回3通道圖像數據
    src = imread( argv[1], 1 );

    /// 把原圖像轉化成灰度圖像並進行平滑
    cvtColor( src, src_gray, CV_BGR2GRAY );
    blur( src_gray, src_gray, Size(3,3) );

    /// 創建新窗口
    char* source_window = "Source";
    namedWindow( source_window, CV_WINDOW_AUTOSIZE );
    imshow( source_window, src );

    createTrackbar( " Canny thresh:", "Source", &thresh, max_thresh, thresh_callback );
    thresh_callback( 0, 0 );

    waitKey(0);
    return(0);
}

參考文獻
1.http://www.opencv.org.cn/opencvdoc/2.3.2/html/doc/tutorials/imgproc/shapedescriptors/moments/moments.html