An algebraic approach to surface reconstruction from gradient fields

TitleAn algebraic approach to surface reconstruction from gradient fields
Publication TypeConference Papers
Year of Publication2005
AuthorsAgrawal A, Chellappa R, Raskar R
Conference NameComputer Vision, 2005. ICCV 2005. Tenth IEEE International Conference on
Date Published2005/10//
Keywordsalgebra;, algebraic, approach;, Computer, confinement;, discrete, domain, error, field;, from, gradient, graph, image, integrability;, linear, local, methods;, photometric, reconstruction;, shading;, SHAPE, stereo;, surface, system;, theory;, vision;

Several important problems in computer vision such as shape from shading (SFS) and photometric stereo (PS) require reconstructing a surface from an estimated gradient field, which is usually non-integrable, i.e. have non-zero curl. We propose a purely algebraic approach to enforce integrability in discrete domain. We first show that enforcing integrability can be formulated as solving a single linear system Ax =b over the image. In general, this system is under-determined. We show conditions under which the system can be solved and a method to get to those conditions based on graph theory. The proposed approach is non-iterative, has the important property of local error confinement and can be applied to several problems. Results on SFS and PS demonstrate the applicability of our method.