Gaussian curvature from photometric scatter plots

Abstract

Local surface curvature is an important shape descriptor, especially for smooth featureless objects. For this family of objects, if their surface is matte, there is a one-to-one mapping between their surface normal map and the photometric data collected from a scene under three different illumination conditions. This mapping allows for the extraction of the sign and the magnitude of Gaussian curvature (to within a constant multiple) directly from intensity values. Because all the computations are performed in photometric space, the normal map is never recovered. This implies that the precise location of the light sources is not needed for any of the computations. Experiments show that a simple setup with minimal illumination planning and calibration is sufficient for the extraction of Gaussian curvature for smooth diffuse surfaces.