霍夫圆检测精度很低

Question

我试图从一个看起来非常清晰的图像中检测圆形。我确实意识到圆的一部分丢失了，但从我读到的关于霍夫变换的内容来看，这似乎不会导致我遇到的问题。

输入：

输出：

代码：

// Read the image
Mat src = Highgui.imread("input.png");

// Convert it to gray
Mat src_gray = new Mat();
Imgproc.cvtColor(src, src_gray, Imgproc.COLOR_BGR2GRAY);

// Reduce the noise so we avoid false circle detection
//Imgproc.GaussianBlur( src_gray, src_gray, new Size(9, 9), 2, 2 );

Mat circles = new Mat();

/// Apply the Hough Transform to find the circles
Imgproc.HoughCircles(src_gray, circles, Imgproc.CV_HOUGH_GRADIENT, 1, 1, 160, 25, 0, 0);

// Draw the circles detected
for( int i = 0; i < circles.cols(); i++ ) {
    double[] vCircle = circles.get(0, i);

    Point center = new Point(vCircle[0], vCircle[1]);
    int radius = (int) Math.round(vCircle[2]);

    // circle center
    Core.circle(src, center, 3, new Scalar(0, 255, 0), -1, 8, 0);
    // circle outline
    Core.circle(src, center, radius, new Scalar(0, 0, 255), 3, 8, 0);
}

// Save the visualized detection.
String filename = "output.png";
System.out.println(String.format("Writing %s", filename));
Highgui.imwrite(filename, src);

我将高斯模糊注释掉了，因为（直觉上相反）它大大增加了发现的同样不准确的圆圈的数量。

我的输入图像有什么问题会导致 Hough 不能像我预期的那样工作吗？我的参数偏离了吗？

编辑：第一个答案提出了关于 Hough 的最小/最大半径提示的好点。我拒绝添加这些参数，因为这篇文章中的示例图像只是数千张半径从 ~20 到几乎无穷大不等的图像之一。

Answer 1

我已经从这个答案中调整了我的 RANSAC 算法：Detect semi-circle in opencv

主意：

1. 从您的二值边缘图像中随机选择 3 个点
2. 从这 3 个点创建一个圆
3. 测试这个圈子有多“好”

4. 如果它比此图像中先前找到的最佳圆圈更好，请记住

5. 循环 1-4，直到达到一定的迭代次数。然后接受找到的最佳圆。

6. 从图像中删除已接受的圆圈

7. 重复 1-6 直到找到所有圆圈

问题：

1. 目前你必须知道你想在图像中找到多少个圆圈
2. 仅针对该图像进行了测试。
3. 代码

结果：

代码：

    inline void getCircle(cv::Point2f& p1,cv::Point2f& p2,cv::Point2f& p3, cv::Point2f& center, float& radius)
    {
      float x1 = p1.x;
      float x2 = p2.x;
      float x3 = p3.x;

      float y1 = p1.y;
      float y2 = p2.y;
      float y3 = p3.y;

      // PLEASE CHECK FOR TYPOS IN THE FORMULA :)
      center.x = (x1*x1+y1*y1)*(y2-y3) + (x2*x2+y2*y2)*(y3-y1) + (x3*x3+y3*y3)*(y1-y2);
      center.x /= ( 2*(x1*(y2-y3) - y1*(x2-x3) + x2*y3 - x3*y2) );

      center.y = (x1*x1 + y1*y1)*(x3-x2) + (x2*x2+y2*y2)*(x1-x3) + (x3*x3 + y3*y3)*(x2-x1);
      center.y /= ( 2*(x1*(y2-y3) - y1*(x2-x3) + x2*y3 - x3*y2) );

      radius = sqrt((center.x-x1)*(center.x-x1) + (center.y-y1)*(center.y-y1));
    }



    std::vector<cv::Point2f> getPointPositions(cv::Mat binaryImage)
    {
     std::vector<cv::Point2f> pointPositions;

     for(unsigned int y=0; y<binaryImage.rows; ++y)
     {
         //unsigned char* rowPtr = binaryImage.ptr<unsigned char>(y);
         for(unsigned int x=0; x<binaryImage.cols; ++x)
         {
             //if(rowPtr[x] > 0) pointPositions.push_back(cv::Point2i(x,y));
             if(binaryImage.at<unsigned char>(y,x) > 0) pointPositions.push_back(cv::Point2f(x,y));
         }
     }

     return pointPositions;
    }


    float verifyCircle(cv::Mat dt, cv::Point2f center, float radius, std::vector<cv::Point2f> & inlierSet)
    {
     unsigned int counter = 0;
     unsigned int inlier = 0;
     float minInlierDist = 2.0f;
     float maxInlierDistMax = 100.0f;
     float maxInlierDist = radius/25.0f;
     if(maxInlierDist<minInlierDist) maxInlierDist = minInlierDist;
     if(maxInlierDist>maxInlierDistMax) maxInlierDist = maxInlierDistMax;

     // choose samples along the circle and count inlier percentage
     for(float t =0; t<2*3.14159265359f; t+= 0.05f)
     {
         counter++;
         float cX = radius*cos(t) + center.x;
         float cY = radius*sin(t) + center.y;

         if(cX < dt.cols)
         if(cX >= 0)
         if(cY < dt.rows)
         if(cY >= 0)
         if(dt.at<float>(cY,cX) < maxInlierDist)
         {
            inlier++;
            inlierSet.push_back(cv::Point2f(cX,cY));
         }
     }

     return (float)inlier/float(counter);
    }

    float evaluateCircle(cv::Mat dt, cv::Point2f center, float radius)
    {

        float completeDistance = 0.0f;
        int counter = 0;

        float maxDist = 1.0f;   //TODO: this might depend on the size of the circle!

        float minStep = 0.001f;
        // choose samples along the circle and count inlier percentage

        //HERE IS THE TRICK that no minimum/maximum circle is used, the number of generated points along the circle depends on the radius.
        // if this is too slow for you (e.g. too many points created for each circle), increase the step parameter, but only by factor so that it still depends on the radius

        // the parameter step depends on the circle size, otherwise small circles will create more inlier on the circle
        float step = 2*3.14159265359f / (6.0f * radius);
        if(step < minStep) step = minStep; // TODO: find a good value here.

        //for(float t =0; t<2*3.14159265359f; t+= 0.05f) // this one which doesnt depend on the radius, is much worse!
        for(float t =0; t<2*3.14159265359f; t+= step)
        {
            float cX = radius*cos(t) + center.x;
            float cY = radius*sin(t) + center.y;

            if(cX < dt.cols)
                if(cX >= 0)
                    if(cY < dt.rows)
                        if(cY >= 0)
                            if(dt.at<float>(cY,cX) <= maxDist)
                            {
                                completeDistance += dt.at<float>(cY,cX);
                                counter++;
                            }

        }

        return counter;
    }


    int main()
    {
    //RANSAC

    cv::Mat color = cv::imread("HoughCirclesAccuracy.png");

    // convert to grayscale
    cv::Mat gray;
    cv::cvtColor(color, gray, CV_RGB2GRAY);

    // get binary image
    cv::Mat mask = gray > 0;

    unsigned int numberOfCirclesToDetect = 2;   // TODO: if unknown, you'll have to find some nice criteria to stop finding more (semi-) circles

    for(unsigned int j=0; j<numberOfCirclesToDetect; ++j)
    {
        std::vector<cv::Point2f> edgePositions;
        edgePositions = getPointPositions(mask);

        std::cout << "number of edge positions: " << edgePositions.size() << std::endl;

        // create distance transform to efficiently evaluate distance to nearest edge
        cv::Mat dt;
        cv::distanceTransform(255-mask, dt,CV_DIST_L1, 3);



        unsigned int nIterations = 0;

        cv::Point2f bestCircleCenter;
        float bestCircleRadius;
        //float bestCVal = FLT_MAX;
        float bestCVal = -1;

        //float minCircleRadius = 20.0f; // TODO: if you have some knowledge about your image you might be able to adjust the minimum circle radius parameter.
        float minCircleRadius = 0.0f;

        //TODO: implement some more intelligent ransac without fixed number of iterations
        for(unsigned int i=0; i<2000; ++i)
        {
            //RANSAC: randomly choose 3 point and create a circle:
            //TODO: choose randomly but more intelligent,
            //so that it is more likely to choose three points of a circle.
            //For example if there are many small circles, it is unlikely to randomly choose 3 points of the same circle.
            unsigned int idx1 = rand()%edgePositions.size();
            unsigned int idx2 = rand()%edgePositions.size();
            unsigned int idx3 = rand()%edgePositions.size();

            // we need 3 different samples:
            if(idx1 == idx2) continue;
            if(idx1 == idx3) continue;
            if(idx3 == idx2) continue;

            // create circle from 3 points:
            cv::Point2f center; float radius;
            getCircle(edgePositions[idx1],edgePositions[idx2],edgePositions[idx3],center,radius);

            if(radius < minCircleRadius)continue;


            //verify or falsify the circle by inlier counting:
            //float cPerc = verifyCircle(dt,center,radius, inlierSet);
            float cVal = evaluateCircle(dt,center,radius);

            if(cVal > bestCVal)
            {
                bestCVal = cVal;
                bestCircleRadius = radius;
                bestCircleCenter = center;
            }

            ++nIterations;
        }
        std::cout << "current best circle: " << bestCircleCenter << " with radius: " << bestCircleRadius << " and nInlier " << bestCVal << std::endl;
        cv::circle(color,bestCircleCenter,bestCircleRadius,cv::Scalar(0,0,255));

        //TODO: hold and save the detected circle.

        //TODO: instead of overwriting the mask with a drawn circle it might be better to hold and ignore detected circles and dont count new circles which are too close to the old one.
        // in this current version the chosen radius to overwrite the mask is fixed and might remove parts of other circles too!

        // update mask: remove the detected circle!
        cv::circle(mask,bestCircleCenter, bestCircleRadius, 0, 10); // here the radius is fixed which isnt so nice.
    }

    cv::namedWindow("edges"); cv::imshow("edges", mask);
    cv::namedWindow("color"); cv::imshow("color", color);

    cv::imwrite("detectedCircles.png", color);
    cv::waitKey(-1);
    return 0;
    }