On perpendicular texture or: Why do we see more flowers in the distance?

Almost all work on texture in the computer vision and graphics communities has modeled the texture as tangential, i.e. lying in the tangent plane to the surface. This is equivalent to thinking of the texture as a pattern painted on the surface. Three-dimensional textures, where the elements may point out of the surface, have largely been ignored. We study a special class of 3D textures, perpendicular textures where we can model the elements as being normal to the surface. The perspective projection of perpendicularly textured surfaces results in several interesting phenomena, which do not occur in the much-studied tangential texture case. These include occlusion, foreshortening and illumination. In this paper, we study the geometry of the problem, modeling the locations of the elements of the texture as being a realization of a spatial point process. Relations between slant and tilt of the surface, density and height of elements and occlusions are derived. Occlusions can now be used as a cue to infer shape, instead of being treated as a source of error.