Riemannian Analysis of Probability Density Functions with Applications in Vision
- 1 June 2007
- conference paper
- Published by Institute of Electrical and Electronics Engineers (IEEE)
- No. 10636919,p. 1-8
- https://doi.org/10.1109/cvpr.2007.383188
Abstract
Applications in computer vision involve statistically analyzing an important class of constrained, non-negative 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 geodesies and distances, and allows fast computation of sample statistics. To demonstrate this approach, we present an application in planar shape classification.Keywords
This publication has 7 references indexed in Scilit:
- The Function Space of an ActivityPublished by Institute of Electrical and Electronics Engineers (IEEE) ,2006
- Riemannian geometries on spaces of plane curvesJournal of the European Mathematical Society, 2006
- Using the KL-Center for Efficient and Accurate Retrieval of Distributions Arising from Texture ImagesPublished by Institute of Electrical and Electronics Engineers (IEEE) ,2005
- Detection of image structures using the Fisher information and the Rao metricPublished by Institute of Electrical and Electronics Engineers (IEEE) ,2004
- Invariance in motion analysis of videosPublished by Association for Computing Machinery (ACM) ,2003
- Minimax Entropy Principle and Its Application to Texture ModelingNeural Computation, 1997
- Riemannian center of mass and mollifier smoothingCommunications on Pure and Applied Mathematics, 1977