Riemannian Analysis of Probability Density Functions with Applications in Vision

Joshi, S.; Srivastava, A.; Jermyn, I.H.

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.

Citation

Joshi, S., Srivastava, A., & Jermyn, I. (2007, June). Riemannian Analysis of Probability Density Functions with Applications in Vision. Presented at IEEE Conference on Computer Vision and Pattern Recognition 2007, Minneapolis

• Presentation Conference Type: Conference Paper (published)
• Conference Name: IEEE Conference on Computer Vision and Pattern Recognition 2007
• Publication Date: Jun 1, 2007
• Deposit Date: Aug 12, 2011
• Publicly Available Date: Apr 20, 2016
• Pages: 1664-1671
• Series ISSN: 1063-6919
• Book Title: 2007 IEEE Conference on Computer Vision and Pattern Recognition ; proceedings
• DOI: https://doi.org/10.1109/cvpr.2007.383188
• Public URL: https://durham-repository.worktribe.com/output/1159057