Don't you hate it when people write code with no comments? I'm sure you won't do that now that you see how hard it is to understand someone else's code.
It looks like they're flattening the image by doing a local histogram equalization to undue local brightness variation. Then they blur it and subtract it from the original to get vessels that are brighter than the local background. Not sure you need to do that since the adapthisteq() image is already pretty much background corrected. I suggest you display each image after it's computed to understand what it does, then put that in a comment so you'll know later what it does.
