Shape from Texture Through Deformations

Abstract

This paper is a contribution to the recovery of shape from texture under perspective projection. We regard shape from texture as a statistical estimation problem, the texture being the realization of a stochastic process. There are two minimal conditions in order for the problem to be solvable: the first is a stationarity condition on the texture with respect to the surface; the second is the regularity of the surface. Information about the surface is obtained by estimating a deformation map. We prove that at a fine scale, the wavelet decomposition of the image obeys a transport PDE, the coefficients of which can be estimated, and related to the deformation map. We show how the global surface shape can then be integrated.