Symmetric shape-from-shading using self-ratio image

In this paper, we present a symmetric shape-from-shading (SFS) approach to recover both shape and albedo for symmetric objects. Lambertian surfaces wi th unknown varying albedo and orthographic projections are assumed. In our formulation of symmetric SFS, we have two image irradiance equations. One i s the standard equation used in SFS, and the other is a self-ratio image ir radiance equation. This new image irradiance equation relates the self-rati o image which is defined as the ratio of two-halves of the input image to l ight source and surface shape. The introduction of the self-ratio image fac ilitates the direct use of symmetry cue. Based on the self-ratio image, a n ew model-based symmetric source-from-shading algorithm is also presented. W e then propose symmetric SFS algorithms to recover both shape and albedo fr om a single image and present experimental results. The new symmetric SFS scheme has one important property: the existence of a unique (global) solution which consists of unique (local) solutions at eac h point simultaneously obtained using the intensity information at that poi nt and the surrounding local region and the assumption of a C-2 surface. Pr oofs for the existence of a unique solution in the cases of unknown constan t and non-constant albedos are provided.