Gaussian curvature is an intrinsic local shape characteristic of a smooth object surface that is invariant to orientation of the object in three-dimensional 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 on a smooth object surface. This technique is based on a photometric invariant that involves the behavior of the image intensity gradient under varying illumination under the assumption of the image irradiance equation. The nature of this photometric invariant permits 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 the 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 present actual experimental imaging results.
© 1994 Optical Society of AmericaFull Article | PDF Article
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