Enforcing Integrability by Error Correction using L1-minimization

Surface reconstruction from gradient fields is an important final step in several applications involving gradient manipulations and estimation. Typically, the resulting gradient field is non-integrable due to linear/non-linear gradient manipulations, or due to presence of noise/outliers in gradient estimation. In this paper, we analyze integrability as error correction, inspired from recent work in compressed sensing, particulary L0-L1 equivalence. We propose to obtain the surface by finding the gradient field which best fits the corrupted gradient field in L1 sense. We present an exhaustive analysis of the properties of L1 solution for gradient field integration using linear algebra and graph analogy. We consider three cases: (a) noise, but no outliers (b) no-noise but outliers and (c) presence of both noise and outliers in the given gradient field. We show that L1 solution performs as well as least squares in the absence of outliers. While previous L0-L1 equivalence w...

• Type: Conference
• Year: CVPR
• Where: 2009
• Authors: Dikpal Reddy, Amit K. Agrawal, Rama Chellappa
• Keywords: Error Correction, Integrability, L1 Minimization, Sparsity, Surface Reconstruction