Segmentation of surface curvature using a photometric invariant

Gaussian curvature is an intrinsic local shape characteristic of a smooth object surface that is invariant to orientation of the object in 3D space and viewpoint. Accurate determination of the sign of Gaussian curvature at each point on a smooth object surface (i.e., the identification of hyperbolic, elliptical and parabolic points) can provide very important information for both recognition of objects in automated vision tasks and manipulation of objects by a robot. We present a multiple illumination technique that directly identifies elliptical, hyperbolic, and parabolic points from diffuse reflection from a smooth object surface. This technique is based upon a photometric invariant involving the behavior of the image intensity gradient under varying illumination under the assumption of the image irradiance equation. The nature of this photometric invariant allowed direct segmentation of a smooth object surface according to the sign of Gaussian curvature independent of knowledge of local surface orientation, independent of diffuse surface albedo, and with only approximate knowledge of the geometry of multiple incident illumination. In comparison with photometric stereo, this new technique determines the sign of Gaussian curvature directly from image features without having to derive local surface orientation, and, does not require calibration of the reflectance map from an object of known shape of similar material or precise knowledge of all incident illuminations. We demonstrate how this segmentation technique works under conditions of simulated image noise, and actual experimental imaging results.