What a coincidence! I have been looking at the edit distance problem, because it can be applied to computer vision. One of the uses is if you have a stereo image pair you can figure out the depth of the objects in the scene, by matching corresponding features. The edit distance problem helps with figuring out which pixels in one stereo image correspond to pixels in the other stereo image.

I am hoping with a bit more effort I can understand the dynamic programming side of it better.