Check if convexhull has parallel lines

edit

I have a simple program that finds convex hulls and draws them onto my frame.

For my application, I am interested in one convex hull in particular shown below inside the labels S and V.

One way I thought of narrowing it down is looking for convex hulls which consist of parallel lines by performing a theta test for parallelism.

The structure returned by convexHull is of vector<vector<Point>>. Below is a sample image showing the points of one convex inside the container

My questions are:

1. Is (634, 599)->(387, 599)->....->(634, 597)->(634, 599) the relation between the points? If no, what is then?
2. Along with parallelism, length is another factor I had in mind to filter out useless convexes. Any better suggestions to detect this structure?

Any recommendations/responses are highly appreciated it!

Edit 1

Sample Image

Minimal Code

int main(int argc, const char * argv[])
{
    Mat frame, grey, threshold, cannyEdge, gaussianBlur;
    vector<vector<Point>> contours;

    VideoCapture camera(0);

    if(!camera.isOpened())
    {
        cerr << "Error grabbing the camera\n";
        return -1;
    }

    while(true)
    {
        camera.read(frame);

        cvtColor(frame, grey, COLOR_BGR2GRAY);

        for(int mainIndex = 0; mainIndex <= 12; ++mainIndex)
        {
            int autoThreshold = 200 - 15 * mainIndex;

            // TODO: tweak these values around
            Canny(grey, cannyEdge, 25, 2*autoThreshold, 3, true);
            GaussianBlur(cannyEdge, gaussianBlur, Size(3,3), 0);
            findContours(gaussianBlur, contours, hierarchy, CV_RETR_LIST, CHAIN_APPROX_SIMPLE);

            Mat contoursFrame = Mat::zeros(frame.size(), CV_8UC3);
            Mat convexHullFrame = Mat::zeros(frame.size(), CV_8UC3);

            convexes.resize(contours.size());

            for(size_t index = 0; index < contours.size(); ++index)
            {
                convexHull(contours[index], convexes[index]);
            }

            cout << "Found " << thresholdCentres.size() << " circles at threshold " << autoThreshold << endl;

            for(size_t index = 0; index < contours.size(); ++index)
            {
                Scalar colour = Scalar(rng.uniform(0, 255), rng.uniform(0, 255), rng.uniform(0, 255));
                drawContours(contoursFrame, contours, int(index), colour, 2, LINE_8);
                drawContours(convexHullFrame, convexes, int(index), colour, 2, LINE_8);
            }

            imshow("Convex", convexHullFrame);
            imshow("Contours", contoursFrame);
        }

        char tappedKey = waitKey(1);

        if(tappedKey == 27)
        {
            break;
        }
    }

    destroyAllWindows();

    camera.release();

    return 0;
}