Geometry from specularities

Abstract

An algorithm is described for accurate computation of horizontal and vertical stereoscopic disparities of specular points, relative to nearby surface points. Knowledge of such disparities is shown to restrict principal curvatures (with known light-source position) to lie on a hyperbolic constraint-curve. Monocular appearance of specularities is known also to constrain surface shape. It is shown that, at best, there remains a fourfold ambiguity of local surface curvature. In the case of a light source that is of unknown shape but known to be compace (in a precise sense), elongated specularities have geometrical significance. The axis of such a specularity, backprojected onto the surface tangent plane, approximates to a line of curvature. The approximation improves as the specularity becomes more elongated and the source more compact. These ideas have been incorporated into an existing stereo vision system, and shown to work well with real and simulated images.