Detect quasi-parallel lines with spurs in a binary image
I would start with a pruning algorithm (see skeleton pruning) in order to erase small segments, then use:


the Hough transform, but segments are not really straights.
if the pruning was a success, then you separate each segment and use the first and last point to compute the orientation, which will define when line are parallel. You will have to introduce a tolerance because you want quasi-parallel lines.