Removing parallel edges from binary image
Just a suggestion:


perform binary skeletonization
detect lines as connected sets of pixels
for every line, find distance to nearest pixel on some other line
compute average distance between inspected line and the nearest line
if the computed distance lays within some predefined interval (say, 3-8 pixels), consider it a double-line and remove both lines


The interval can be determined statistically because double lines have distances forming a distribution, which can be separated well from other line distances in the image.