https://stackoverflow.com/questions/26222525/opencv-detect-partial-circle-with-noise
using this as input (your own median filtered image (I've just cropped it):
First I "normalize" the image. I just stretch values, that smallest val is 0 and biggest val is 255, leading to this result: (maybe some real contrast enhancement is better)
after that I compute the threshold of that image with some fixed threshold (you might need to edit that and find a way to choose the threshold dynamically! a better contrast enhancement might help there)
from this image, I use some simple RANSAC circle detection(very similar to my answer in the linked semi-circle detection question), giving you this result as a best semi-sircle:
int main()
{
//cv::Mat color = cv::imread("../inputData/semi_circle_contrast.png");
cv::Mat color = cv::imread("../inputData/semi_circle_median.png");
cv::Mat gray;
// convert to grayscale
cv::cvtColor(color, gray, CV_BGR2GRAY);
// now map brightest pixel to 255 and smalles pixel val to 0. this is for easier finding of threshold
double min, max;
cv::minMaxLoc(gray,&min,&max);
float sub = min;
float mult = 255.0f/(float)(max-sub);
cv::Mat normalized = gray - sub;
normalized = mult * normalized;
cv::imshow("normalized" , normalized);
//--------------------------------
// now compute threshold
// TODO: this might ne a tricky task if noise differs...
cv::Mat mask;
//cv::threshold(input, mask, 0, 255, CV_THRESH_BINARY | CV_THRESH_OTSU);
cv::threshold(normalized, mask, 100, 255, CV_THRESH_BINARY);
std::vector<cv::Point2f> edgePositions;
edgePositions = getPointPositions(mask);
// create distance transform to efficiently evaluate distance to nearest edge
cv::Mat dt;
cv::distanceTransform(255-mask, dt,CV_DIST_L1, 3);
//TODO: maybe seed random variable for real random numbers.
unsigned int nIterations = 0;
cv::Point2f bestCircleCenter;
float bestCircleRadius;
float bestCirclePercentage = 0;
float minRadius = 50; // TODO: ADJUST THIS PARAMETER TO YOUR NEEDS, otherwise smaller circles wont be detected or "small noise circles" will have a high percentage of completion
//float minCirclePercentage = 0.2f;
float minCirclePercentage = 0.05f; // at least 5% of a circle must be present? maybe more...
int maxNrOfIterations = edgePositions.size(); // TODO: adjust this parameter or include some real ransac criteria with inlier/outlier percentages to decide when to stop
for(unsigned int its=0; its< maxNrOfIterations; ++its)
{
//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);
// inlier set unused at the moment but could be used to approximate a (more robust) circle from alle inlier
std::vector<cv::Point2f> inlierSet;
//verify or falsify the circle by inlier counting:
float cPerc = verifyCircle(dt,center,radius, inlierSet);
// update best circle information if necessary
if(cPerc >= bestCirclePercentage)
if(radius >= minRadius)
{
bestCirclePercentage = cPerc;
bestCircleRadius = radius;
bestCircleCenter = center;
}
}
// draw if good circle was found
if(bestCirclePercentage >= minCirclePercentage)
if(bestCircleRadius >= minRadius);
cv::circle(color, bestCircleCenter,bestCircleRadius, cv::Scalar(255,255,0),1);
cv::imshow("output",color);
cv::imshow("mask",mask);
cv::waitKey(0);
return 0;
}
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);
}
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;
}