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Proceedings Paper

Probability distributions from Riemannian geometry, generalized hybrid Monte Carlo sampling, and path integrals
Author(s): E. Paquet; H. L. Viktor
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Paper Abstract

When considering probabilistic pattern recognition methods, especially methods based on Bayesian analysis, the probabilistic distribution is of the utmost importance. However, despite the fact that the geometry associated with the probability distribution constitutes essential background information, it is often not ascertained. This paper discusses how the standard Euclidian geometry should be generalized to the Riemannian geometry when a curvature is observed in the distribution. To this end, the probability distribution is defined for curved geometry. In order to calculate the probability distribution, a Lagrangian and a Hamiltonian constructed from curvature invariants are associated with the Riemannian geometry and a generalized hybrid Monte Carlo sampling is introduced. Finally, we consider the calculation of the probability distribution and the expectation in Riemannian space with path integrals, which allows a direct extension of the concept of probability to curved space.

Paper Details

Date Published: 27 January 2011
PDF: 8 pages
Proc. SPIE 7864, Three-Dimensional Imaging, Interaction, and Measurement, 78640X (27 January 2011); doi: 10.1117/12.872862
Show Author Affiliations
E. Paquet, National Research Council Canada (Canada)
Univ. of Ottawa (Canada)
H. L. Viktor, Univ. of Ottawa (Canada)


Published in SPIE Proceedings Vol. 7864:
Three-Dimensional Imaging, Interaction, and Measurement
J. Angelo Beraldin; Ian E. McDowall; Atilla M. Baskurt; Margaret Dolinsky; Geraldine S. Cheok; Michael B. McCarthy; Ulrich Neuschaefer-Rube, Editor(s)

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