line image and disparity map

I have two inputs, an image made of lines called I and its disparity map, called D. I first do some preprocessing on the image I to "clean up" the image (I skeletonize it) to make it continuous and easier to process. call the new image I'.

When I overlap I' with D, the new line is no longer alone the "edges" in D. Can I process D in a similar way to ensure that the new lines will line up with the disparity map again?