SEGMENTATION OF SURFACE CURVATURE WITH A PHOTOMETRIC INVARIANT

Gaussian curvature is an intrinsic local shape characteristic of a smo oth object surface that is invariant to orientation of the object in t hree-dimensional space and viewpoint. Accurate determination of the si gn 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 object s in automated vision tasks and manipulation of objects by a robot. We present a multiple-illumination technique that directly identifies el liptical, hyperbolic, and parabolic points from diffuse reflection on a smooth object surface. This technique is based on a photometric inva riant that involves the behavior of the image intensity gradient under varying illumination under the assumption of the image irradiance equ ation. The nature of this photometric invariant permits direct segment ation of a smooth object surface according to the sign of Gaussian cur vature independent of knowledge of local surface orientation, independ ent of diffuse surface albedo, and with only approximate knowledge of the geometry of multiple incident illumination. In comparison with pho tometric stereo, this new technique determines the sign of Gaussian cu rvature directly from image features without having to derive local su rface orientation and does not require the calibration of the reflecta nce map from an object of known shape of similar material or precise k nowledge of all incident illuminations. We demonstrate how this segmen tation technique works under conditions of simulated image noise and p resent actual experimental imaging results.