Integration of graph algorithms Opencv

Reference article: https://blog.csdn.net/PecoHe/article/details/89927842

                  https://blog.csdn.net/weixin_41695564/article/details/80056430

• Foreword

Integral graph algorithm first proposed by Crow in 1984, in order to improve rendering speed in multi-scale perspective projection. FIG integral algorithm is a fast algorithm for computing the image area and image area and the sum of squares. Its core idea is to find a table for each image to establish its own integral image, in the image processing stage you can find in order to achieve a direct calculation of the mean time linear convolution integral image according to pre-established look-up table. Did time convolution performed regardless of the window size . Such an algorithm is applied to the NCC based on fast matching, object detection and SURF conversion, edge detection, based on statistics and so on fast filter.

• Establish integral image

FIG integral calculated from the original image, the original image is assumed that the size of W * H, the integral image size (W + 1) * (H + 1). In the integral image (integral image) at any point in the upper left corner coordinates (x, y) at a value representing the original coordinates (x, y) of all pixels and the pixel values ​​(square sum is squared tables with). And tables and square tables and establish the following equation:

And tables:

Sum of squares table:

As shown below, assume the input image size is 2x2, 3x3 size of the integral FIG.

• Find integral image

As shown above, if you want to find pixel values ​​in the input image and a blue area (2 + 3 + 4 + 5 = 14), and in accordance with the table as long as the integration is performed twice FIG subtraction and one subtraction to: 46+ 10-22-20 = 14. That is bottom right corner of the upper left corner + - the top right - bottom left corner.

• Opencv examples

In calculating the integral of FIG opencv API Introduction:

//API一
void integral( InputArray src,     //输入图像
	       OutputArray sum,    //和表
               int sdepth = -1,);  //和表深度
 
//API二
void integral( InputArray src,     //输入图像
	       OutputArray sum,    //和表
               OutputArray sqsum,  //平方和表
               int sdepth = -1,    //和表深度,一般为CV_32S
               int sqdepth = -1 ); //平方和表深度，一般为CV_32F

FIG integral calculation and display:

                              

//////////////////////////////////
//opencv4.1.0
//////////////////////////////////

#include <opencv2/opencv.hpp>

using namespace std;
using namespace cv;

int main() {
	Mat src, sum, sqrsum;
	src = imread("1.png", 0);

	integral(src, sum, sqrsum, CV_32S, CV_32F);

	normalize(sum, sum, 0, 255, NORM_MINMAX, CV_8UC1, Mat());
	normalize(sqrsum, sqrsum, 0, 255, NORM_MINMAX, CV_8UC1, Mat());

        imshow("原图", src);
	imshow("和表积分图", sum);
	imshow("平方和表积分图", sqrsum);

	waitKey(0);
	return 0;
}

• Get the pixel values ​​within the specified area and

//////////////////////////////////
//opencv4.1.0
//////////////////////////////////

#include <opencv2/opencv.hpp>

using namespace std;
using namespace cv;

int get_block_sum(Mat &sum, int x1, int y1, int x2, int y2);

int main() {
	Mat src, sum, sqrsum;
	src = imread("1.png", 0);

	//获取ROI，便于观察（使用ImageWatch插件）
	int LR = 4;
	int LC = 4;
	int width = 6;
	int height = 6;
	Mat roi = src(Rect(LR, LC, width, height)).clone();   

	//计算积分图
	integral(src, sum, sqrsum, CV_32S, CV_32F);

	//利用积分图计算ROI内的像素值总和
	int value = get_block_sum(sum, LR, LC, LR + height, LC + width);
	cout << value << endl;

	imshow("原图", src);        
	waitKey(0);
	return 0;
}

int get_block_sum(Mat &sum, int x1, int y1, int x2, int y2) {
	int BottomRight = sum.at<int>(x2, y2);
	int TopLeft     = sum.at<int>(x1, y1);
	int TopRight    = sum.at<int>(x1, x2);
	int BottomLeft  = sum.at<int>(x2, y1);
	int sum_value = (BottomRight + TopLeft - TopRight - BottomLeft);
	return sum_value;
}