Surface Orientation From Two Camera Stereo With Polarizers

We present a simple method for determining the 3-D orientation of a flat surface from the specular reflection of light, exploiting the polarizing properties of materials. Existing methods which compute surface orientation from specular reflection are purely intensity based and need to rely upon precise knowledge of how specularly reflecting light rays are initially incident upon the material surface. These methods require elaborate structured lighting environments which involve much preliminary calibration. The method presented here computes surface orientation independent of any a priori knowledge of the geometry of specular reflection, as long as specular reflection occurs into the camera sensor from points of interest at which orientation is to be constrained. This obviates the need for any structured lighting. By observing how the transmitted intensity of specularly reflected light through a polarizing filter is varied by rotating the filter, one can determine the specular plane of incidence in which the path of specular reflection must lie. Under the assumption that the surface normal is contained in the specular plane of incidence, a determination of two nonparallel specular planes of incidence from a stereo pair of cameras yields a computation of the surface normal from their planar intersection. For flat surfaces the correspondence of points between the stereo pair of cameras need not be precise, only that the intersecting specular planes of incidence correspond to two points that lie on the same flat surface, or on two flat surfaces with equivalent orientation. This is a much weaker correspondence requirement than for conventional parallax stereo.