Image Texture and the "Flow of Light"
March 8, 2006
The "Shading Cue" is conventionally framed in the context of perfectly smooth surfaces. "Shading" has ancient roots in the visual arts, and became canonized in the late 20thc. as the "Shape From Shading (SFS) Problem". I reconsider the problem as conventionally posed, presenting a novel analysis of its "observational basis''. When rough surfaces are considered the image structure is augmented (from mere contrast gradient in the former case) with the image illuminance flow structure revealed by texture. The direction and two differential invariants of this flow can be estimated robustly via the structure tensor. This changes the nature of the "shading cue" qualitatively. Shading alone does not specify surface curvature orthogonal to the illumination direction, a lack of data that has to be made up for by the surface integrability conditions. Hence conventional SFS algorithms are based on partial differential equations with global boundary conditions. Allowing illuminance flow as an additional observable alleviates this problem and purely local, algebraic approaches to SFS become feasible. Algorithms can be shown to exist that derive surface curvature from shading and flow observations through a linear operator applied to the observables, the operator being a function of surface attitude and beam direction. Such an approach neatly reveals the remaining group of ambiguity transformations in an intuitive way. I propose novel ways to deal with the intrinsic ambiguities of photomorphometrics. Instead of attempting to find the full class of equivalent solutions I look for specific solutions given certain a priori guesses. Such methods are much more similar to likely mechanisms of human psychogenesis, in particular visual perception, than the conventional "Marrian" approach. I present methods that boil down to linear, local computation, thus very robust and possibly implementable in neural wetware.