How can I classify and store locations of lines from a line detector algorithm?

I used an Ellipse and line segment detector (http://ubee.enseeiht.fr/vision/ELSD/) to extract these geometric lines from an image. Now I want to obtain the x, y data for each line individually so that I can measure colour intensity either side of these lines in the original image

Is there any way I can classify these lines similar to how BWlabel function does?

I've tried using BWlabel and other functions for objects of connected pixels and points but these are generally for objects of 4 or 8 connected pixels and the lines in this image are only 1 pixel thick.

I am trying to recreate the work of the following paper as part of a project on schlieren imaging; (http://people.csail.mit.edu/talidekel/papers/DeviationMagnificationSIGA15.pdf)

Lines from ELSD;

Original Image;