## Local geometry of surfaces from shading analysis

JOSA A, Vol. 11, Issue 5, pp. 1575-1579 (1994)

http://dx.doi.org/10.1364/JOSAA.11.001575

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### Abstract

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

**History**

Original Manuscript: February 26, 1993

Revised Manuscript: December 3, 1993

Manuscript Accepted: December 3, 1993

Published: May 1, 1994

**Citation**

Mario Ferraro, "Local geometry of surfaces from shading analysis," J. Opt. Soc. Am. A **11**, 1575-1579 (1994)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-11-5-1575

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