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Well, from your description I think that the HoughTransform algorithm for lines is what you are looking for. Using the latter algorithm it is really easy to retrieve the starting and the ending point/s of the line/s, which are stored in a vector. Moreover, you can get more information related to the found line/s, like angle, etc...
If you search in the net you will find several examples, on how to use the embedded function of the OpenCV library related to HoughTranform algorithm, both in C++ and in Python. Furthermore, here you can find a function about how you can obtain the intersection point of the lines. It is in C++, but I think that it is not gonna be a big deal to port it to Python.
Chears, tt :-)
