Blurring-Invariant Riemannian Metrics for Comparing Signals and Images
Abstract
We propose a novel Riemannian framework for comparing signals and images in a manner that is invariant to their levels of blur. This framework uses a log-Fourier representation of signals/images in which the set of all possible Gaussian blurs of a signal, i.e. its orbits under semigroup action of Gaussian blur functions, is a straight line. Using a set of Riemannian metrics under which the group actions are by isometries, the orbits are compared via distances between orbits. We demonstrate this framework using a number of experimental results involving 1D signals and 2D images.
Cite
Text
Zhang et al. "Blurring-Invariant Riemannian Metrics for Comparing Signals and Images." IEEE/CVF International Conference on Computer Vision, 2011. doi:10.1109/ICCV.2011.6126442Markdown
[Zhang et al. "Blurring-Invariant Riemannian Metrics for Comparing Signals and Images." IEEE/CVF International Conference on Computer Vision, 2011.](https://mlanthology.org/iccv/2011/zhang2011iccv-blurring/) doi:10.1109/ICCV.2011.6126442BibTeX
@inproceedings{zhang2011iccv-blurring,
title = {{Blurring-Invariant Riemannian Metrics for Comparing Signals and Images}},
author = {Zhang, Zhengwu and Klassen, Eric and Srivastava, Anuj and Turaga, Pavan K. and Chellappa, Rama},
booktitle = {IEEE/CVF International Conference on Computer Vision},
year = {2011},
pages = {1770-1775},
doi = {10.1109/ICCV.2011.6126442},
url = {https://mlanthology.org/iccv/2011/zhang2011iccv-blurring/}
}