Surface Shape from Warping

Abstract

We propose a variant of shape from shading which we call shape from image warping. The idea is that the three-dimensional shape of an object is estimated by determining how much the image of the object is warped with respect to the image of a known prototype shape. We demonstrate that, for a class of reflectance functions, there is a direct relationship between these image warps and geometric warps of the underlying three-dimensional shapes. Therefore detecting the image warp relative to a prototype of known shape allows us to reconstruct the shape of the imaged object. We derive properties of these shape warps and illustrate the results by recovering the shapes effaces. This relationship between image and shape warps helps us understand the relationship between image based models of object recognition and approaches based on three-dimensional object models.