%0 Conference Paper
%B Computer Vision, 2005. ICCV 2005. Tenth IEEE International Conference on
%D 2005
%T An algebraic approach to surface reconstruction from gradient fields
%A Agrawal,A.
%A Chellapa, Rama
%A Raskar, R.
%K algebra;
%K algebraic
%K approach;
%K Computer
%K confinement;
%K discrete
%K domain
%K error
%K field;
%K from
%K gradient
%K graph
%K image
%K integrability;
%K linear
%K local
%K methods;
%K photometric
%K reconstruction;
%K shading;
%K SHAPE
%K stereo;
%K surface
%K system;
%K theory;
%K vision;
%X 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.
%B Computer Vision, 2005. ICCV 2005. Tenth IEEE International Conference on
%V 1
%P 174 - 181 Vol. 1 - 174 - 181 Vol. 1
%8 2005/10//
%G eng
%R 10.1109/ICCV.2005.31