Curvature-based signatures for object description and recognition

An invariant related to Gaussian curvature at an object point is developed based upon the covariance matrix of photometric values within a local neighborhood about the point. We employ three illumination conditions, two of which are completely unknown. We never need to explicitly know the surface normal at a point. The determinant of the covariance matrix of the intensity three-tuples in the local neighborhood of an object point is shown to be invariant with respect to rotation and translation. A way of combining these determinants to form a signature distribution is formulated that is rotation, translation, and scale invariant. This signature is shown to be invariant over large ranges of poses of the same objects, while being significantly different between distinctly shaped objects. A new object recognition methodology is proposed by compiling signatures for only a few viewpoints of a given object.