Detection of contours intersections

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To apply the "geometric solution", you need to know the points to write the equation of the line, this is not so easy.

You could use the hit-and-miss morphology to find a particular pattern...in this case the 3-point junctions.

Below is my implementation to achieve the following result (Src, Junctions and Final):

See http://homepages.inf.ed.ac.uk/rbf/HIP... for more details about hit-and-miss

In short, you have to define the right kernel for each pattern you want to detect. In OpenCV hit-and-miss (is available thanks to @LorenaGdL ) you have to use:

• 1 => white is required here
• -1 => black is required here
• 0 => doesn't matter

Than, catch all directions/orientation rotating the kernel

Here is the code:

    // This is your sample image (objects are black)
    cv::Mat src = (cv::Mat_<UINT8>(7, 8) <<
        0, 1, 1, 1, 1, 1, 0, 0,
        1, 0, 1, 1, 1, 0, 1, 1,
        1, 1, 0, 0, 0, 1, 1, 1,
        1, 1, 1, 0, 0, 0, 1, 1,
        1, 0, 0, 1, 1, 1, 0, 1,
        0, 1, 1, 1, 1, 1, 0, 0,
        0, 1, 1, 1, 1, 1, 1, 1);
void GetJunctions(const Mat &src, Mat &dst)
{
    // the hit-and-miss kernels to locate 3-points junctions
    // to be used in each directions
    // NOTE: float type is needed due to limitation/bug in warpAffine with signed char
    cv::Mat k1 = (cv::Mat_<float>(3, 3) <<
        0,  1,  0,
        0,  1,  0,
        1,  0,  1);
    cv::Mat k2 = (cv::Mat_<float>(3, 3) <<
        1,  0,  0,
        0,  1,  0,
        1,  0,  1);
    cv::Mat k3 = (cv::Mat_<float>(3, 3) <<
        0, -1,  1,
        1,  1, -1,
        0,  1, 0);
    // Some useful declarations
    Mat tmp, rotMat;
    Size ksize = k1.size();
    Point center = Point(ksize.width / 2, ksize.height / 2);
    // 90 degrees rotation matrix
    rotMat = getRotationMatrix2D(center, 90, 1);
    // dst accumulates all matches
    dst = Mat::zeros(src.size(), CV_16UC1);
    // Do hit & miss for all possible directions (0,90,180,270)
    int op = MORPH_HITMISS;
    for (int i = 0; i < 3; i++)
    {
        morphologyEx(src, tmp, op, Mat_<INT8>(k1), Point(-1, -1), 1, BORDER_CONSTANT, 0);
        add(dst, tmp, dst, noArray(), dst.type());
        morphologyEx(src, tmp, op, Mat_<INT8>(k2), Point(-1, -1), 1, BORDER_CONSTANT, 0);
        add(dst, tmp, dst, noArray(), dst.type());
        morphologyEx(src, tmp, op, Mat_<INT8>(k3), Point(-1, -1), 1, BORDER_CONSTANT, 0);
        add(dst, tmp, dst, noArray(), dst.type());
        // Rotate the kernels (90deg)
        warpAffine(k1, k1, rotMat, ksize);
        warpAffine(k2, k2, rotMat, ksize);
        warpAffine(k3, k3, rotMat, ksize);
    }
    // normalize the accumulator to 0..255
    cv::normalize(dst, tmp, 0, 255, cv::NORM_MINMAX);
    tmp.convertTo(dst, src.type());
}
int main()
{
    src *= 255;
    // Morphology logic is: white objects on black foreground
    src = ~src;
    // Get junctions
    Mat junctionsScore, dst;
    vector<Point> junctionsPoint;Point pt;
    GetJunctions(src, junctionsScore);
    // Draw markers where junction score is non zero
    cvtColor(src, dst, CV_GRAY2BGR);
    findNonZero(junctionsScore, junctionsPoint);
    for (size_t i = 0; i < junctionsPoint.size(); i++)
    {
        pt = junctionsPoint[i];
        char score = junctionsScore.at<uchar>(pt);
        dst.at<Vec3b>(pt) = Vec3b(0 ...