Local Surface Curvature Analysis based on Reflection Estimation

In this paper, we propose a novel reflection based method to estimate the profile of specular surface. For a calibrated scene with a fixed straight line light source, the line is reflected by the surface to image plane of a camera. Then the local geometry between the surface and reflected line is estimated. Firstly, in order to find relationship among the object position, object surface curvature and line reflection curvature, we study the fundamental theory of the geometry between a hemisphere and a line source. Then we extend our approach to the surface with arbitrary curvature. Experiments are conducted with spherical surface and paraboloid surface. Results show that our method is able to obtain surface curvature and reflection position on the surface merely by measuring the curvature of the reflected line.