Computation of the Sign of the Gaussian Curvature of a Surface from Multiple Unknown Illumination Images without Knowledge of the Reflectance Property

摘要

This paper presents a new method for determining the sign of the Gaussian curvature at points on an object surface from image shading observed under three lighting directions. The method does not require either knowledge of properties of surface reflectance or knowledge of lighting directions. It is based on the novel notion of the pseudo-Gaussian image (PGI) that we introduce in this paper. The PGI is similar to the Gaussian image of a surface, but is constructed by image intensities. The Gaussian image has structures that are closely related to the sign of the Gaussian curvature on the surface. We show that the PGI also has the same structures, and therefore the sign of the Gaussian curvature can be obtained by examining the structures of the PGI. A smooth surface is segmented into regions of positive and negative signs of the Gaussian curvature. Since the curvature is intrinsic to the surface shape, the segmentation results can be applied to several vision tasks such as pose estimation and object identification. In comparison with a similar method of Wolff and Fan, the present method has advantages such that it can deal with non-Lambertian surfaces and that lighting directions may be arbitrary as long as they are linearly independent.