Relating image warping to 3D geometrical deformations

Abstract

We demonstrate that, for a large class of reflectance functions, there is a direct relationship between image warps and the corresponding geometric deformations of the underlying three-dimensional objects. This helps explain the hidden geometrical assumptions in object recognition schemes which involve two-dimensional image warping computed by matching image intensity. In addition, it allows us to propose a novel 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. 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 of faces.