Constrained Flows of Matrix-Valued Functions: Application to Diffusion Tensor Regularization
Abstract
Nonlinear partial differential equations (PDE) are now widely used to regularize images. They allow to eliminate noise and artifacts while preserving large global features, such as object contours. In this context, we propose a geometric framework to design PDE flows acting on constrained datasets. We focus our interest on flows of matrix-valued functions undergoing orthogonal and spectral constraints. The corresponding evolution PDE’s are found by minimization of cost functionals, and depend on the natural metrics of the underlying constrained manifolds (viewed as Lie groups or homogeneous spaces). Suitable numerical schemes that fit the constraints are also presented. We illustrate this theoretical framework through a recent and challenging problem in medical imaging: the regularization of diffusion tensor volumes (DTMRI).
Cite
Text
Chefd'Hotel et al. "Constrained Flows of Matrix-Valued Functions: Application to Diffusion Tensor Regularization." European Conference on Computer Vision, 2002. doi:10.1007/3-540-47969-4_17Markdown
[Chefd'Hotel et al. "Constrained Flows of Matrix-Valued Functions: Application to Diffusion Tensor Regularization." European Conference on Computer Vision, 2002.](https://mlanthology.org/eccv/2002/chefdaposhotel2002eccv-constrained/) doi:10.1007/3-540-47969-4_17BibTeX
@inproceedings{chefdaposhotel2002eccv-constrained,
title = {{Constrained Flows of Matrix-Valued Functions: Application to Diffusion Tensor Regularization}},
author = {Chefd'Hotel, Christophe and Tschumperlé, David and Deriche, Rachid and Faugeras, Olivier D.},
booktitle = {European Conference on Computer Vision},
year = {2002},
pages = {251-265},
doi = {10.1007/3-540-47969-4_17},
url = {https://mlanthology.org/eccv/2002/chefdaposhotel2002eccv-constrained/}
}