recover the shape from edge-only picture?

edit

hi, I have some edge-only picture, and I want to do something to recover it to a image with area.

for example: I have this picture:

and I want the image becomes this

(what should I call this? a picture with area?)

I think numbers of dilation and erosin would work, but actually the fingers may tend to stick together. Some active contour algorithm may find the contour of overall picture, but it is really slow. What other algorithm I can use? thanks for any advice!