如何寻找已知轮廓的最大内接圆
本博客相关代码已经被OpenCV收录:/samples/cpp/tutorial_code/ShapeDescriptors/pointPolygonTest_demo.cpp
一、问题的提出:
所谓内切圆,是指“与多边形各边都相切的圆“。我们这里需要找的是所谓”内接圆“,可以简单认为是”圆点在轮廓中,到轮廓中所有点的距离一样的图像“。在这所有的”内接圆“中,寻找半径最大的哪一个。
这个问题已经广泛讨论了,比如
![](https://img2023.cnblogs.com/blog/2917779/202212/2917779-20221223082434705-1709458423.png)
这样的图像,寻找轮廓的最大内接圆。
二、解决方法:
利用计算机图像学技术中轮廓的相关思路,可以直接从圆的定义解决此问题。基于OpenCV的代码和注释如下:
#include "stdafx.h" #include <iostream> using namespace std; using namespace cv; VP FindBigestContour(Mat src){ int imax = 0; //代表最大轮廓的序号 int imaxcontour = -1; //代表最大轮廓的大小 std::vector<std::vector<cv::Point>>contours; findContours(src,contours,CV_RETR_LIST,CV_CHAIN_APPROX_SIMPLE); for (int i=0;i<contours.size();i++){ int itmp = contourArea(contours[i]);//这里采用的是轮廓大小 if (imaxcontour < itmp ){ imax = i; imaxcontour = itmp; } } return contours[imax]; } int main(int argc, char* argv[]) { Mat src = imread("e:/template/cloud.png"); Mat temp; cvtColor(src,temp,COLOR_BGR2GRAY); threshold(temp,temp,100,255,THRESH_OTSU); imshow("src",temp); //寻找最大轮廓 VP VPResult = FindBigestContour(temp); //寻找最大内切圆 int dist = 0; int maxdist = 0; Point center; for(int i=0;i<src.cols;i++) { for(int j=0;j<src.rows;j++) { dist = pointPolygonTest(VPResult,cv::Point(i,j),true); if(dist>maxdist) { maxdist=dist; center=cv::Point(i,j); } } } //绘制结果 circle(src,center,maxdist,Scalar(0,0,255)); imshow("dst",src); waitKey(); }
其中
PointPolygonTest
测试点是否在多边形中
contour 输入轮廓.
pt 针对轮廓需要测试的点。
measure_dist 如果非0,函数将估算点到轮廓最近边的距离。
函数cvPointPolygonTest 决定测试点是否在轮廓内,轮廓外,还是轮廓的边上(或者共边的交点上),它的返回值是正负零,相对应的,当measure_dist=0时,返回值是1, -1,0, 同样当 measure_dist≠0 ,它是返回一个从点到最近的边的带符号距离。
测试点是否在多边形中
double cvPointPolygonTest( const CvArr* contour, CvPoint2D32f pt, int measure_dist );
pt 针对轮廓需要测试的点。
measure_dist 如果非0,函数将估算点到轮廓最近边的距离。
函数cvPointPolygonTest 决定测试点是否在轮廓内,轮廓外,还是轮廓的边上(或者共边的交点上),它的返回值是正负零,相对应的,当measure_dist=0时,返回值是1, -1,0, 同样当 measure_dist≠0 ,它是返回一个从点到最近的边的带符号距离。
结果:
![](https://img2023.cnblogs.com/blog/2917779/202212/2917779-20221223082536100-472237389.png)
三、优化的思路:
这里对圆心的遍历,是遍历了所有的图像上面的点。然而根据”内接圆心一定在轮廓内部“这个先验知识,可以缩小循环范围,提高算法效率。
2018年7月27日22:01:01 对opencv的官方例子进行修改,并提交github
![](https://img2023.cnblogs.com/blog/2917779/202212/2917779-20221223082559389-1394404813.png)
/** * @function pointPolygonTest_demo.cpp * @brief Demo code to use the pointPolygonTest function...fairly easy * @author OpenCV team */ #include "opencv2/highgui.hpp" #include "opencv2/imgproc.hpp" #include <iostream> using namespace cv; using namespace std; //return the biggest contour by size vector<Point> FindBiggestContour(Mat src){ int icount = 0; int imaxcontour = -1; std::vector<std::vector<cv::Point>>contours; findContours(src,contours,CV_RETR_LIST,CV_CHAIN_APPROX_SIMPLE); for (int i=0;i<contours.size();i++){ int itmp = contourArea(contours[i]); if (imaxcontour < itmp ){ icount = i; imaxcontour = itmp; } } return contours[icount]; } /** * @function main */ int main( void ) { /// Create an image const int r = 100; Mat src = Mat::zeros( Size( 4*r, 4*r ), CV_8U ); /// Create a sequence of points to make a contour vector<Point2f> vert(6); vert[0] = Point( 3*r/2, static_cast<int>(1.34*r) ); vert[1] = Point( 1*r, 2*r ); vert[2] = Point( 3*r/2, static_cast<int>(2.866*r) ); vert[3] = Point( 5*r/2, static_cast<int>(2.866*r) ); vert[4] = Point( 3*r, 2*r ); vert[5] = Point( 5*r/2, static_cast<int>(1.34*r) ); /// Draw it in src for( int i = 0; i < 6; i++ ) { line( src, vert[i], vert[(i+1)%6], Scalar( 255 ), 3 ); } /// Get the contours vector<vector<Point> > contours; findContours( src, contours, RETR_TREE, CHAIN_APPROX_SIMPLE); /// Calculate the distances to the contour Mat raw_dist( src.size(), CV_32F ); for( int i = 0; i < src.rows; i++ ) { for( int j = 0; j < src.cols; j++ ) { raw_dist.at<float>(i,j) = (float)pointPolygonTest( contours[0], Point2f((float)j, (float)i), true ); } } double minVal, maxVal; minMaxLoc( raw_dist, &minVal, &maxVal ); minVal = abs(minVal); maxVal = abs(maxVal); /// Depicting the distances graphically Mat drawing = Mat::zeros( src.size(), CV_8UC3 ); for( int i = 0; i < src.rows; i++ ) { for( int j = 0; j < src.cols; j++ ) { if( raw_dist.at<float>(i,j) < 0 ) { drawing.at<Vec3b>(i,j)[0] = (uchar)(255 - abs(raw_dist.at<float>(i,j)) * 255 / minVal); } else if( raw_dist.at<float>(i,j) > 0 ) { drawing.at<Vec3b>(i,j)[2] = (uchar)(255 - raw_dist.at<float>(i,j) * 255 / maxVal); } else { drawing.at<Vec3b>(i,j)[0] = 255; drawing.at<Vec3b>(i,j)[1] = 255; drawing.at<Vec3b>(i,j)[2] = 255; } } } //get the biggest Contour vector<Point> biggestContour = FindBiggestContour(src); //find the maximum enclosed circle int dist = 0; int maxdist = 0; Point center; for(int i=0;i<src.cols;i++) { for(int j=0;j<src.rows;j++) { dist = pointPolygonTest(biggestContour,cv::Point(i,j),true); if(dist>maxdist) { maxdist=dist; center=cv::Point(i,j); } } } circle(drawing,center,maxdist,Scalar(255,255,255)); /// Show your results imshow( "Source", src ); imshow( "Distance and maximum enclosed circle", drawing ); waitKey(); return 0; }
![](https://img2023.cnblogs.com/blog/2917779/202212/2917779-20221223082632322-669531263.png)
我的最终解: /** * @function pointPolygonTest_demo.cpp * @brief Demo code to use the pointPolygonTest function...fairly easy * @author OpenCV team * jsxyhelu(jsxyhelu@foxmail.com) */ #include "opencv2/highgui.hpp" #include "opencv2/imgproc.hpp" #include <iostream> using namespace cv; using namespace std; //get the biggest contour by size static vector<Point> FindBiggestContour(Mat src){ int max_area_contour_idx = 0; double max_area = -1; vector<vector<Point> >contours; findContours(src,contours,RETR_LIST,CHAIN_APPROX_SIMPLE); //handle case if no contours are detected CV_Assert(0 != contours.size()); for (uint i=0;i<contours.size();i++){ double temp_area = contourArea(contours[i]); if (max_area < temp_area ){ max_area_contour_idx = i; max_area = temp_area; } } return contours[max_area_contour_idx]; } /** * @function main */ int main( void ) { /// Create an image const int r = 100; Mat src = Mat::zeros( Size( 4*r, 4*r ), CV_8U ); /// Create a sequence of points to make a contour vector<Point2f> vert(6); vert[0] = Point( 3*r/2, static_cast<int>(1.34*r) ); vert[1] = Point( 1*r, 2*r ); vert[2] = Point( 3*r/2, static_cast<int>(2.866*r) ); vert[3] = Point( 5*r/2, static_cast<int>(2.866*r) ); vert[4] = Point( 3*r, 2*r ); vert[5] = Point( 5*r/2, static_cast<int>(1.34*r) ); /// Draw it in src for( int i = 0; i < 6; i++ ) { line( src, vert[i], vert[(i+1)%6], Scalar( 255 ), 3 ); } /// Get the contours vector<vector<Point> > contours; findContours( src, contours, RETR_TREE, CHAIN_APPROX_SIMPLE); /// Calculate the distances to the contour Mat raw_dist( src.size(), CV_32F ); for( int i = 0; i < src.rows; i++ ) { for( int j = 0; j < src.cols; j++ ) { raw_dist.at<float>(i,j) = (float)pointPolygonTest( contours[0], Point2f((float)j, (float)i), true ); } } double minVal, maxVal; minMaxLoc( raw_dist, &minVal, &maxVal ); minVal = abs(minVal); maxVal = abs(maxVal); /// Depicting the distances graphically Mat drawing = Mat::zeros( src.size(), CV_8UC3 ); for( int i = 0; i < src.rows; i++ ) { for( int j = 0; j < src.cols; j++ ) { if( raw_dist.at<float>(i,j) < 0 ) { drawing.at<Vec3b>(i,j)[0] = (uchar)(255 - abs(raw_dist.at<float>(i,j)) * 255 / minVal); } else if( raw_dist.at<float>(i,j) > 0 ) { drawing.at<Vec3b>(i,j)[2] = (uchar)(255 - raw_dist.at<float>(i,j) * 255 / maxVal); } else { drawing.at<Vec3b>(i,j)[0] = 255; drawing.at<Vec3b>(i,j)[1] = 255; drawing.at<Vec3b>(i,j)[2] = 255; } } } //get the biggest Contour vector<Point> biggestContour = FindBiggestContour(src); //handle case if biggestContour is empty CV_Assert(0 != biggestContour.size()); //find the maximum enclosed circle double maxdist = 0; Point center; //get the rect bounding the BiggestContour Rect rectBoundingBiggestContour = boundingRect(Mat(biggestContour)); for(int i=0;i<rectBoundingBiggestContour.width;i++) { for(int j=0;j<rectBoundingBiggestContour.height;j++) { Point tmpPoint = Point(rectBoundingBiggestContour.x + i,rectBoundingBiggestContour.y + j); double dist = pointPolygonTest(biggestContour,tmpPoint,true); if(dist>maxdist) { maxdist=dist; center= tmpPoint; } } } circle(drawing,center,(int)maxdist,Scalar(255,255,255)); /// Show your results imshow( "Source", src ); imshow( "Distance and maximum enclosed circle", drawing ); waitKey(); return 0; }