Statistical analysis on stiefel and grassmann manifolds with applications in computer vision

Pavan Turaga, Ashok Veeraraghavan, Rama Chellappa

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

129 Citations (Scopus)

Abstract

Many applications in computer vision and pattern recognition involve drawing inferences on certain manifold-valued parameters. In order to develop accurate inference algorithms on these manifolds we need to a) understand the geometric structure of these manifolds b) derive appropriate distance measures and c) develop probability distribution functions (pdf) and estimation techniques that are consistent with the geometric structure of these manifolds. In this paper, we consider two related manifolds - the Stiefel manifold and the Grassmann manifold, which arise naturally in several vision applications such as spatio-temporal modeling, affine invariant shape analysis, image matching and learning theory. We show how accurate statistical characterization that reflects the geometry of these manifolds allows us to design efficient algorithms that compare favorably to the state of the art in these very different applications. In particular, we describe appropriate distance measures and parametric and non-parametric density estimators on these manifolds. These methods are then used to learn class conditional densities for applications such as activity recognition, video based face recognition and shape classification.

Original languageEnglish (US)
Title of host publication26th IEEE Conference on Computer Vision and Pattern Recognition, CVPR
DOIs
StatePublished - 2008
Externally publishedYes
Event26th IEEE Conference on Computer Vision and Pattern Recognition, CVPR - Anchorage, AK, United States
Duration: Jun 23 2008Jun 28 2008

Other

Other26th IEEE Conference on Computer Vision and Pattern Recognition, CVPR
CountryUnited States
CityAnchorage, AK
Period6/23/086/28/08

Fingerprint

Computer vision
Statistical methods
Image matching
Face recognition
Probability distributions
Pattern recognition
Distribution functions
Geometry

ASJC Scopus subject areas

  • Computer Vision and Pattern Recognition
  • Control and Systems Engineering

Cite this

Turaga, P., Veeraraghavan, A., & Chellappa, R. (2008). Statistical analysis on stiefel and grassmann manifolds with applications in computer vision. In 26th IEEE Conference on Computer Vision and Pattern Recognition, CVPR [4587733] https://doi.org/10.1109/CVPR.2008.4587733

Statistical analysis on stiefel and grassmann manifolds with applications in computer vision. / Turaga, Pavan; Veeraraghavan, Ashok; Chellappa, Rama.

26th IEEE Conference on Computer Vision and Pattern Recognition, CVPR. 2008. 4587733.

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

Turaga, P, Veeraraghavan, A & Chellappa, R 2008, Statistical analysis on stiefel and grassmann manifolds with applications in computer vision. in 26th IEEE Conference on Computer Vision and Pattern Recognition, CVPR., 4587733, 26th IEEE Conference on Computer Vision and Pattern Recognition, CVPR, Anchorage, AK, United States, 6/23/08. https://doi.org/10.1109/CVPR.2008.4587733
Turaga P, Veeraraghavan A, Chellappa R. Statistical analysis on stiefel and grassmann manifolds with applications in computer vision. In 26th IEEE Conference on Computer Vision and Pattern Recognition, CVPR. 2008. 4587733 https://doi.org/10.1109/CVPR.2008.4587733
Turaga, Pavan ; Veeraraghavan, Ashok ; Chellappa, Rama. / Statistical analysis on stiefel and grassmann manifolds with applications in computer vision. 26th IEEE Conference on Computer Vision and Pattern Recognition, CVPR. 2008.
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