The most important part of this, I think, is the simple idea that, in the situation assumed in the paper (a field of similar texture objects on a simple surface), for any region of the image:

Occlusion will cause the viewing geometry to dictate how much of the field of view is filled by the top of the texture-object, and how much is filled by the bottom.

This means that you can measure how much of each part of the texture-object you see (by color or some other feature) and determine what the viewing geometry/surface geometry is for that region of the image.

This paper interests me mostly in the possibility of using raw data to learn the features that indicate the top vs bottom of the texture object (rather than starting out knowing that the simple feature of color alone is a enough, and that yellow is the top, green the bottom.

You can skip section 5 if you'd like, it makes the generalization from planar surfaces to curved surfaces.