Abstract

We analyze the problem of recovering the shape of a mirror surface. We generalize the results of [1], where the special case of planar and spherical mirror surfaces was considered, extending that analysis to any smooth surface. A calibrated scene composed of lines passing through a point is assumed. The lines are refiected by the mirror surface onto the image plane of a calibrated camera, where the intersection and orientation of such refiections are measured. The relationship between the local geometry of the surface around the point of refiection and the measurements is analyzed. We give necessary and suffcient conditions, as well as a practical algorithm, for recovering first order local information (positions and normals) when three intersecting lines are visible. A small number of ‘ghost solutions’ may arise. Second order surface geometry may also be obtained up to one unknown parameter. Experimental results with real mirror surfaces are presented. Keywords: Shape recovery, geometry, mirror surfaces.