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An algebraic approach to surface reconstruction from gradient fields
Ist Teil von
Tenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1, 2005, Vol.1, p.174-181 Vol. 1
Ort / Verlag
IEEE
Erscheinungsjahr
2005
Quelle
IEEE/IET Electronic Library
Beschreibungen/Notizen
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.