Abstract

A special case of the shape from shading problem, applicable to surfaces with unusual reflecting properties, was solved by Rindfleisch (1966). For the special reflectance properties he considered, a profile of the solution surface can be obtained by integrating along predetermined straight lines in the image plane. The general problem was formulated and solved later (Horn, 1970 and 1975). The method of characteristic strip expansion was used originally to solve the nonlinear first-order partial differential image irradiance equation. The reflectance map makes the analysis of the shape from shading algorithm much easier, provided that both light sources and viewer are far away from the scene being viewed (Horn, 1977; Horn and Sjoberg, 1979). Several iterative schemes, mostly based on minimization of some function containing an integral of the brightness error, arose later (Woodham, 1977; Strat, 1979; Ikeuchi and Horn, 1981; Kirk, 1984; Brooks and Horn, 1985; Horn and Brooks, 1986; Kirk, 1987; Frankot and Chellappa, 1988). For a collection of papers on shape from shading, as well as a review of the subject and an extensive bibliography, see “Shape from Shading" (Horn and Brooks, 1989).

© 1989 Optical Society of America