Stereo Reconstruction of Reflecting Surfaces

摘要

Classical stereo reconstruction with two cameras is based on 3D points visible from both perspectives. With reflecting surfaces, however, this approach leads to 3D reconstruction of the virtual images of the light sources and is thus inadequate for the 3D measurement of the specular surface. A detailed analysis of the reflection phenomena shows that, given a pinhole camera and light sources, the visible image of the reflected lights leads to a differential equation of the surface. A numerical solution of this differential equation thus reconstructs the surface, provided that an initial value, i.e., the 3D coordinates of some point of the surface, is given. If an initial value is not available, the view of a second pinhole camera will generate a second differential equation. Looking for a simultaneous solution of both differential equations thus leads to a 3D reconstruction of the specular surface.