How can I find an approximate intersection of two lines in a binary image?

I guess I'd try thresholding

binaryImage = grayImage < 128

Then call bwmorph to skeletonize

skelImage = bwmorph(binaryImage, 'skel', inf);

Then call bwmorph again to find crossing points.

crossings = bwmorph(skelImage, 'branchpoints');

This is untested, so give it a shot and let me know how it goes. There is a possibility you could get spurious branchpoints depending on how ragged your thick lines are.