On Depth Recovery from Gradient Vector Fields

Abstract

Depth recovery from gradient vector fields is required when reconstructing a surface (in three-dimensional space) from its gradients. Such a reconstruction task results, for example, for techniques in computer vision aiming at calculating surface normals (such as shape from shading, photometric stereo, shape from texture, shape from contours and so on). Surprisingly, discrete integration has not been studied very intensively so far. This chapter presents three classes of methods for solving problems of depth recovery from gradient vector fields: a two-scan method, a Fourier-transform based method, and a wavelet-transform based method. These methods extend previously known techniques, and related proofs are given in a short but concise form. The two-scan method consists of two different scans through a given gradient vector field. The final surface height values can be determined by averaging these two scans. Fourier-transform based methods are noniterative so that boundary conditions are not needed, and their robustness to noisy gradient estimates can be improved by choosing associated weighting parameters. The wavelet-transform based method overcomes the disadvantage of the Fourier-transform based method, which implicitly require that a surface height function is periodic. Experimental results using synthetic and real images are also presented.