A Curvature Based Descriptor Invariant to Pose and Albedo Derived from Photometric Data

Gaussian curvature is an invariant local descriptor of smooth surfaces. We present an object signature which is a condensed representation of the distribution of Gaussian curvature information at visible object points. An invariant related to Gaussian curvature at a point is derived from the covariance matrix of the photometric values in a neighborhood about that point. In addition, we introduce an albedo-normalization method that is capable of cancelling albedo on Lambertian surfaces. We use three illumination conditions, two of which are unknown. The three-tuple of intensity values at a point is related via a one-to-one mapping to the surface normal at that point. The determinant of the covariance matrix of the local three-tuples is invariant to albedo, rotation and translation. The collection of determinants over mutually illuminated object points is combined into a signature distribution which is albedo, rotation, translation, and scale invariant. An object recognition methodology using these signatures is proposed.