We present a multiple illumination technique that directly recovers the viewer-centered curvature matrix, up to a scalar factor, at each mutually illuminated point on a smooth object surface. This technique is completely independent of knowledge of incident illumination orientation, local surface orientation, or diffuse surface albedo. The cornerstore of this technique is the use of theintegrability constraintwhich is a fundamental mathematical property of smooth surfaces. The integrability constraint allows the derivation of an equation at each object point, which is linear in terms of quantities involving the initially unknown parameters of incident illumination orientation. These quantities, which we call thegradient ratio constants, can be simultaneously solved for five or more equations arising from the same number of object points. We show that deriving these gradient ratio constants provides just enough calibration information about incident illumination geometry to compute the viewer-centered curvature matrix at each object point, up to a scalar multiple. We demonstrate three important applications of this technique: (i) segmentation of the object surface by sign of Gaussian curvature, (ii) further segmentation of nonnegative Gaussian curvature into convexity and concavity, and (iii) reconstruction of the surface height, independent of knowledge of incident illumination orientation and diffuse surface albedo.

We present a multiple illumination technique that directly recovers the viewer-centered curvature matrix up to a scalar factor, at each mutually illuminated point on a smooth object surface. This technique is completely independent of knowledge of incident illumination orientation, local surface orientation, or diffuse surface albedo. The cornerstone of this technique is the use of the integrability constraint which is a fundamental mathematical property of smooth surfaces. The integrability constraint allows the derivation of an equation at each object point, which is linear in terms of quantities involving the initially unknown parameters of incident illumination orientation. These quantities, which we call the gradient ratio constants, can be simultaneously solved for from five or more equations arising from the same number of object points. We show that deriving these gradient ratio constants provides just enough calibration information about incident illumination geometry to compute the viewer-centered curvature matrix at each object point, up to a scalar multiple. We demonstrate two important applications of this technique: segmentation of the object surface by sign of Gaussian curvature, and further segmentation of non-negative Gaussian curvature into convexity and concavity.>

Gaussian curvature is an intrinsic local shape characteristic of a smooth object surface that is invariant to orientation of the object in 3-D 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. The nature of this photometric invariant allows 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, is invariant to incident orientation errors of two of three light sources, and is invariant to the relative strength of incident radiance with respect to each of these light sources. We demonstrate how this segmentation technique works under conditions of simulated image noise, and actual experimental imaging results.>