An Algebraic Approach to Surface Reconstruction from Gradient Fields
Abstract
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.
Cite
Text
Agrawal et al. "An Algebraic Approach to Surface Reconstruction from Gradient Fields." IEEE/CVF International Conference on Computer Vision, 2005. doi:10.1109/ICCV.2005.31Markdown
[Agrawal et al. "An Algebraic Approach to Surface Reconstruction from Gradient Fields." IEEE/CVF International Conference on Computer Vision, 2005.](https://mlanthology.org/iccv/2005/agrawal2005iccv-algebraic/) doi:10.1109/ICCV.2005.31BibTeX
@inproceedings{agrawal2005iccv-algebraic,
title = {{An Algebraic Approach to Surface Reconstruction from Gradient Fields}},
author = {Agrawal, Amit K. and Chellappa, Rama and Raskar, Ramesh},
booktitle = {IEEE/CVF International Conference on Computer Vision},
year = {2005},
pages = {174-181},
doi = {10.1109/ICCV.2005.31},
url = {https://mlanthology.org/iccv/2005/agrawal2005iccv-algebraic/}
}