count the number of distinct object in a video

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Hi, I have a video containig object moving with different speed. I would like to count how many object cross a line. For now I am able to track every object in a frame and I write the center of every object on the frame. My first attempt to count these objects was to compare the coordinate of every object with the coordinate of the line (for example my line is horizontal so I compare the Y coordinate). But some object are moving too fast and in the first frame their Y coordinate is less than the Y coordinate of the line and in the next frame it's more. So I decided to extend the counting area (20 pixels) but now I am counting some object twice...

Here is my code :

//update the background model
pMOG2->apply(frame, fgMaskMOG2);

    ///////////////////////////////////////////////////////////////////  
    //morphology element  
    Mat element = getStructuringElement(MORPH_RECT, Size(7, 7), Point(3, 3));
    //pre procesing  
    //1 point delete   
    morphologyEx(fgMaskMOG2, fgMaskMOG2, CV_MOP_CLOSE, element);

    //Find contour  
    ContourImg = fgMaskMOG2.clone();
    //less blob delete  
    vector< vector< Point> > contours;
    vector<Vec4i> hierarchy;
    findContours(ContourImg,
        contours, hierarchy, // a vector of contours  
        CV_RETR_EXTERNAL, // retrieve the external contours  
        CV_CHAIN_APPROX_NONE); // all pixels of each contours  

    /// Get the moments
    vector<Moments> mu(contours.size());
    vector<Point> mc(contours.size());
    vector<Rect> mr(contours.size());   
    /// Draw mass center and contours
    for (int i = 0; i< contours.size(); i++)
    {
        mu[i] = moments(contours[i], false);

        if (contourArea(contours[i], false) > 200){
            mc[i] = Point(mu[i].m10 / mu[i].m00, mu[i].m01 / mu[i].m00);
            mr[i] = boundingRect(contours[i]);
            drawContours(frame, contours, i, CV_RGB(255, 0, 0), 1, 8, hierarchy, 0, Point());
            rectangle(frame, mr[i], CV_RGB(255, 0, 0));
            circle(frame, mc[i], 4, CV_RGB(255, 0, 0), -1, 8, 0);
            if (mc[i].y > 190 && mc[i].y < 210){
                detectedObj = detectedObj + 1;
            }
        }
    }

Maybe the way I am trying to do it is not the best.

How can I manage to count the object crossing a line or an area without missing some or counting twice the same? Thx