How do I follow the detected line and find more points connected to it?

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So I have create a code to find the edge of a wall, through finding the intersect of the lines from the edges detected within a ROI. I have the coordinates of the lines in (x1,y1,x2,y2) form, for this case, I would have 3 lines from that point.

[https://i.imgur.com/Vm0JWE4.png]

What I would like to do, is follow the lines along the edges and find another intersection. How do I go about doing this search? I would like to do this with limited regions of interest, whereby I perform canny only on the initial ROI, and also run canny on a certain ROI around the line.