Regularization Method for Depth from Noisy Gradient Vector Fields

Abstract

This paper presents a regularization method for surface reconstruction from noisy gradient vector fields. The algorithm takes as its input a discrete gradient vector field, obtained by applying a Shape from Shading or Photometric Stereo method. To derive this algorithm, we combine the integrability constraint and the surface curvature and area constraints into a single functional, which is then minimized. Therefore, value changes in the height or depth map will be more regular. To solve the minimization problem, we employ the Fourier transform theory rather than the Variational Principle. The Fourier transform of the (unknown) surface is expressed as a function of the (given) gradient's Fourier transforms. The relative depth values can be obtained by an inverse Fourier Transform and by choosing associated weighting parameters. The method is evaluated on gradient data delivered by a Photometric Stereo algorithm.