Blurring-invariant Riemannian metrics for comparing signals and images

Zhengwu Zhang, Eric Klassen, Anuj Srivastava, Pavan Turaga, Rama Chellappa

Research output: Chapter in Book/Report/Conference proceedingConference contribution

10 Citations (Scopus)

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.

Original languageEnglish (US)
Title of host publicationProceedings of the IEEE International Conference on Computer Vision
Pages1770-1775
Number of pages6
DOIs
StatePublished - 2011
Externally publishedYes
Event2011 IEEE International Conference on Computer Vision, ICCV 2011 - Barcelona, Spain
Duration: Nov 6 2011Nov 13 2011

Other

Other2011 IEEE International Conference on Computer Vision, ICCV 2011
CountrySpain
CityBarcelona
Period11/6/1111/13/11

Fingerprint

Orbits

ASJC Scopus subject areas

  • Software
  • Computer Vision and Pattern Recognition

Cite this

Zhang, Z., Klassen, E., Srivastava, A., Turaga, P., & Chellappa, R. (2011). Blurring-invariant Riemannian metrics for comparing signals and images. In Proceedings of the IEEE International Conference on Computer Vision (pp. 1770-1775). [6126442] https://doi.org/10.1109/ICCV.2011.6126442

Blurring-invariant Riemannian metrics for comparing signals and images. / Zhang, Zhengwu; Klassen, Eric; Srivastava, Anuj; Turaga, Pavan; Chellappa, Rama.

Proceedings of the IEEE International Conference on Computer Vision. 2011. p. 1770-1775 6126442.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Zhang, Z, Klassen, E, Srivastava, A, Turaga, P & Chellappa, R 2011, Blurring-invariant Riemannian metrics for comparing signals and images. in Proceedings of the IEEE International Conference on Computer Vision., 6126442, pp. 1770-1775, 2011 IEEE International Conference on Computer Vision, ICCV 2011, Barcelona, Spain, 11/6/11. https://doi.org/10.1109/ICCV.2011.6126442
Zhang Z, Klassen E, Srivastava A, Turaga P, Chellappa R. Blurring-invariant Riemannian metrics for comparing signals and images. In Proceedings of the IEEE International Conference on Computer Vision. 2011. p. 1770-1775. 6126442 https://doi.org/10.1109/ICCV.2011.6126442
Zhang, Zhengwu ; Klassen, Eric ; Srivastava, Anuj ; Turaga, Pavan ; Chellappa, Rama. / Blurring-invariant Riemannian metrics for comparing signals and images. Proceedings of the IEEE International Conference on Computer Vision. 2011. pp. 1770-1775
@inproceedings{22bab1260a4e46ff84f768659cf545dd,
title = "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.",
author = "Zhengwu Zhang and Eric Klassen and Anuj Srivastava and Pavan Turaga and Rama Chellappa",
year = "2011",
doi = "10.1109/ICCV.2011.6126442",
language = "English (US)",
isbn = "9781457711015",
pages = "1770--1775",
booktitle = "Proceedings of the IEEE International Conference on Computer Vision",

}

TY - GEN

T1 - Blurring-invariant Riemannian metrics for comparing signals and images

AU - Zhang, Zhengwu

AU - Klassen, Eric

AU - Srivastava, Anuj

AU - Turaga, Pavan

AU - Chellappa, Rama

PY - 2011

Y1 - 2011

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84863042732&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84863042732&partnerID=8YFLogxK

U2 - 10.1109/ICCV.2011.6126442

DO - 10.1109/ICCV.2011.6126442

M3 - Conference contribution

SN - 9781457711015

SP - 1770

EP - 1775

BT - Proceedings of the IEEE International Conference on Computer Vision

ER -