collision detection - Are there well-known algorithms for fitting a polygon to an arbitrary shape?

I'm using the Chipmunk physics engine to make the levels for a 2D C game. I'd like to be able to fit a polygon to an arbitrary shape to serve as the collision mask. Given a black and white collision mask for an arbitrary level object like this:

Are there any well-known algorithms for getting this:

I could then use the red polygon to create a physics object to go with the image.

Answer

This is known as generating a concave hull, and is in the general case pretty complicated (much more so than the convex hull).

One commonly-recommended method is using alpha shapes.

There are more good resources on the problem here, here, and here.