Depth Recovery from Noisy Gradient Vector Fields Using Regularization

Abstract

This paper presents a regularization based 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 variational approach to avoid using the initial and boundary conditions. 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 shape-from-shading algorithm. Experimental results using both synthetic and real images show that the new algorithm is more robust against noise than existing methods.