How Shading Constrains Surface Patches without Knowledge of Light Sources
Benjamin Kunsberg, Steven W. Zucker · SIAM Journal on Imaging Sciences · 2014
Shape-from-shading (SFS) is a classical inverse problem in computer and human vision. This shape reconstruction problem is inherently ill-posed. We show that the isophotes on smooth surfaces with Lambertian reflectance can be directly related to surface properties without consideration of the light source. Using techniques from modern differential geometry, we derive relationships between the curvature of the isophotes and the shape operator for the surface. Neurobiology motivates the geometric approach, and our calculations allow us to characterize the matching local family of surfaces that can result from any given shading patch. We illustrate the local ambiguity in several examples.