ML Anthology

Riemannian Analysis of Probability Density Functions with Applications in Vision

Anuj Srivastava, Ian Jermyn, Shantanu H. Joshi
CVPR 2007
doi:10.1109/CVPR.2007.383188 /cvpr/2007/srivastava2007cvpr-riemannian/

Abstract

Applications in computer vision involve statistically analyzing an important class of constrained, nonnegative functions, including probability density functions (in texture analysis), dynamic time-warping functions (in activity analysis), and re-parametrization or non-rigid registration functions (in shape analysis of curves). For this one needs to impose a Riemannian structure on the spaces formed by these functions. We propose a "spherical" version of the Fisher-Rao metric that provides closed-form expressions for geodesics and distances, and allows fast computation of sample statistics. To demonstrate this approach, we present an application in planar shape classification.

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Text

Srivastava et al. "Riemannian Analysis of Probability Density Functions with Applications in Vision." IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2007. doi:10.1109/CVPR.2007.383188

Markdown

[Srivastava et al. "Riemannian Analysis of Probability Density Functions with Applications in Vision." IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2007.](https://mlanthology.org/cvpr/2007/srivastava2007cvpr-riemannian/) doi:10.1109/CVPR.2007.383188

BibTeX

@inproceedings{srivastava2007cvpr-riemannian,
  title     = {{Riemannian Analysis of Probability Density Functions with Applications in Vision}},
  author    = {Srivastava, Anuj and Jermyn, Ian and Joshi, Shantanu H.},
  booktitle = {IEEE/CVF Conference on Computer Vision and Pattern Recognition},
  year      = {2007},
  doi       = {10.1109/CVPR.2007.383188},
  url       = {https://mlanthology.org/cvpr/2007/srivastava2007cvpr-riemannian/}
}