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The classical approach to shape from shading problems is to find a numerical solution of the image irradiance partial differential equation. It is always assumed that the parameters of this equation (the light source direction and surface albedo) can be estimated in advance. For images which contain shadows and occluding contours, this decoupling of problems is artificial. We develop a new approach to solving these equations. It is based on modern differential geometry, and solves for light source, surface shape, and material changes concurrently. Local scene elements (scenels) are estimated from the shading flow field, and smoothness, material, and light source compatibility conditions resolve them into consistent scene descriptions. Shadows and related difficulties for the classical approach are discussed.

Shading flows and scenel bundles: A new approach to shape from shading