Shading, a View from the Inside

Shape from shading arose from artistic practice, and later experimental psychology, but its formal structure has only been established recently by computer vision. Some of its algorithms have led to useful applications. Psychology has reversely borrowed these formalisms in attempts to come to grips with shading as a depth cue. Results have been less than spectacular. The reason might well be that these formalisms are all based on Euclidean geometry and physics (radiometry), which, are the right tools in third person accounts, but have little relevance to first person accounts, and thus are biologically (and consequently psychologically) of minor interest. We propose a formal theory of the shading cue in the first person account, 'a view from the inside'. Such a perspective is also required for autonomous robots in AI. This formalism cannot be based on Euclidean geometry, nor on radiometry, but on the structure of pictorial space, and the structure of brightness space. The formalism, though different in kind, has a simple relation to the computer vision accounts. It has great robustness, is free from calibration issues, and allows purely local shape inferences. It is especially suited to biological (and thus AI) implementation. We consider a number of predictions and confront them with available empirical evidence.