Efficient Computation of the Inverse Gradient on Irregular Domains
Abstract
The inverse gradient problem, finding a scalar field f with a gradient near a given vector field <b xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">g</b> on some bounded and connected domain Ω ϵ R <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">𝓃</sup> , can be solved by means of a Poisson equation with inhomogeneous Neumann boundary conditions. We present an elementary derivation of this partial differential equation and an efficient multigrid-based method to numerically compute the inverse gradient on non-rectangular domains. The utility of the method is demonstrated by a range of important medical applications such as phase unwrapping, pressure computation, inverse deformation fields, and fiber bundle tracking.
Cite
Text
Farnebäck et al. "Efficient Computation of the Inverse Gradient on Irregular Domains." IEEE/CVF International Conference on Computer Vision, 2007. doi:10.1109/ICCV.2007.4409176Markdown
[Farnebäck et al. "Efficient Computation of the Inverse Gradient on Irregular Domains." IEEE/CVF International Conference on Computer Vision, 2007.](https://mlanthology.org/iccv/2007/farneback2007iccv-efficient/) doi:10.1109/ICCV.2007.4409176BibTeX
@inproceedings{farneback2007iccv-efficient,
title = {{Efficient Computation of the Inverse Gradient on Irregular Domains}},
author = {Farnebäck, Gunnar and Rydell, Joakim and Ebbers, Tino and Andersson, Mats T. and Knutsson, Hans},
booktitle = {IEEE/CVF International Conference on Computer Vision},
year = {2007},
pages = {1-8},
doi = {10.1109/ICCV.2007.4409176},
url = {https://mlanthology.org/iccv/2007/farneback2007iccv-efficient/}
}