The relations between parabolic and planar points of a Lambertian surface M and critical points of the corresponding image irradiance E are studied. It is proved that critical points of E, with the exception of nondegenerate global maxima, occur at points on M with zero Gaussian curvature and that critical points of E that are stable with respect to changes of the position of the light source occur at planar points of M. Furthermore, it is shown that at global maxima of E there exists a simple relation between the principal curvatures of M and L, the graph of E. The relations between planar (parabolic) points of L and planar (parabolic) points of M are also analyzed. Finally, some relationships between isophotes of E and lines of curvature of M are investigated.
© 1994 Optical Society of America
Original Manuscript: February 26, 1993
Revised Manuscript: December 3, 1993
Manuscript Accepted: December 3, 1993
Published: May 1, 1994
Mario Ferraro, "Local geometry of surfaces from shading analysis," J. Opt. Soc. Am. A 11, 1575-1579 (1994)