opencv c++ find inscribing circle of a contour

Question

I want to find the maximum inscribing circle of contour.

I have detected the contour with cv::findContours and it is there as a vector<Point>.

I know how to detect the minimum enclosing circle (cv::minEnclosingCircle), but not how to get the maximum inclosing circle. How to do this?

Question2: How do i get the inscribing and circumscribing circles centered on the center of mass?

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For clarification, i try to describe, what i mean with these circels:

1. min enclosing circle: touching object from outside, center position doesn't matter, minimum area.
2. circumscribing circle: touching object from outside, center position on the center of mass of the object, minimum area.
3. max inclosing circle: touching object from inside, center position doesn't matter, maximum area.
4. inscribing circle: touching object from inside, center position on the center of mass of the object, maximum area.

Answer 1

You can:

1) create a mask from your contour

2) Compute the distanceTransform on the mask

3) The highest value is the radius, its position is the center

Code:

#include <opencv2\opencv.hpp>

int main()
{
    // Load image
    cv::Mat1b img = cv::imread("path_to_img", cv::IMREAD_GRAYSCALE);

    // Correct image
    cv::Mat1b bin = img < 127;

    // Find contour
    std::vector<std::vector<cv::Point>> contours;
    cv::findContours(bin, contours, cv::RETR_EXTERNAL, cv::CHAIN_APPROX_SIMPLE);

    // Draw on mask
    cv::Mat1b mask(bin.rows, bin.cols, uchar(0));
    cv::drawContours(mask, contours, 0, cv::Scalar(255), cv::FILLED);

    // Distance Trasnsform
    cv::Mat1f dt;
    cv::distanceTransform(mask, dt, cv::DIST_L2, 5, cv::DIST_LABEL_PIXEL);

    // Find max value
    double max_val;
    cv::Point max_loc;
    cv::minMaxLoc(dt, nullptr, &max_val, nullptr, &max_loc);

    // Output image
    cv::Mat3b out;
    cv::cvtColor(img, out, cv::COLOR_GRAY2BGR);
    cv::circle(out, max_loc, max_val, cv::Scalar(0, 255, 0));

    return 0;
}

Answer 2

At least i solved the calculation of the two circles with the center on the center of mass (in a way similar to @Grillteller suggested):

Point2f p_Contour_first = vp_Contour[0];
double circumCirc_Radius  = norm(p_Centroid - p_Contour_first);
double inscriCirc_Radius  = norm(p_Centroid - p_Contour_first);
for(int p = 0; p < vp_Contour.size(); p++)
{
    Point2f p_Contour_current = vp_Contour[p];
    double r = norm(p_Centroid - p_Contour_current);
    if(r < inscriCirc_Radius) inscriCirc_Radius = r;
    if(r > circumCirc_Radius) circumCirc_Radius = r;
}

But the original question remeains (max area, center pos doesn't matter).