Kristin: For each segment, we have the initial depth computed using any standard correlation based dense stereo technique. The author has make a simplistic assumption that each segment has k-neighbors ( which maynot be true but here we are just interested to get a "feel" of complexity involved ). With the above assumption we say that a segment's depth is either equal to its initial depth or equal to the depth of one of its k neighbors. Hence for each segment, we have k+1 guesses of depth. Since we have s no. of segments, the depth map can have (k+1)^s different structures.

I am not sure about the term AAM but I know of algorithms that use projection of 3D back to 2D to test the validity of generated 3D model.