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An algebraic approach to surface reconstruction from gradient fields

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3 Author(s)
Agrawal, A. ; Center for Autom. Res., Maryland Univ., College Park, MD, USA ; Chellappa, R. ; Raskar, R.

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.

Published in:

Computer Vision, 2005. ICCV 2005. Tenth IEEE International Conference on  (Volume:1 )

Date of Conference:

17-21 Oct. 2005