A photometric invariant and shape constraints at parabolic points

Using rigorous methods the authors have shown that the invariant direction of isophotes at parabolic points is the projection of the principal direction of zero curvature onto the image plane. They have gone beyond considering the limited case of pure orthographic projection and have shown under what conditions this photometric invariance property breaks down and is best approximated in perspective images, and for a nondistant light source. In addition to giving experimental evidence supporting their claim about how isophotes are parallel to the direction of zero curvature at parabolic points, the authors suggest possible applications of this geometric cue to determination of orientation and curvature at parabolic points. The best advantage taken from this geometric cue is when constraint information can be obtained, knowing absolutely nothing about the reflectance map. The true power of a physical invariant is the information it gives under the most generic conditions possible, in this case any type of smooth reflectance map