Characterizing Ambiguity in Light Source Invariant Shape from Shading
This work addresses ambiguity in shape reconstruction for computer vision, offering a novel approach to a classical inverse problem.
The paper tackles the ill-defined shape from shading problem by introducing a mathematical formulation using covariant derivatives of the shading flow field to characterize local surface ambiguities, showing that second derivatives of brightness are light source invariant and can be used to define families of possible surfaces.
Shape from shading is a classical inverse problem in computer vision. This shape reconstruction problem is inherently ill-defined; it depends on the assumed light source direction. We introduce a novel mathematical formulation for calculating local surface shape based on covariant derivatives of the shading flow field, rather than the customary integral minimization or P.D.E approaches. On smooth surfaces, we show second derivatives of brightness are independent of the light sources and can be directly related to surface properties. We use these measurements to define the matching local family of surfaces that can result from any given shading patch, changing the emphasis to characterizing ambiguity in the problem. We give an example of how these local surface ambiguities collapse along certain image contours and how this can be used for the reconstruction problem.