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September 2012 Fibre-generated point processes and fields of orientations
Bryony J. Hill, Wilfrid S. Kendall, Elke Thönnes
Ann. Appl. Stat. 6(3): 994-1020 (September 2012). DOI: 10.1214/12-AOAS553

Abstract

This paper introduces a new approach to analyzing spatial point data clustered along or around a system of curves or “fibres.” Such data arise in catalogues of galaxy locations, recorded locations of earthquakes, aerial images of minefields and pore patterns on fingerprints. Finding the underlying curvilinear structure of these point-pattern data sets may not only facilitate a better understanding of how they arise but also aid reconstruction of missing data. We base the space of fibres on the set of integral lines of an orientation field. Using an empirical Bayes approach, we estimate the field of orientations from anisotropic features of the data. We then sample from the posterior distribution of fibres, exploring models with different numbers of clusters, fitting fibres to the clusters as we proceed. The Bayesian approach permits inference on various properties of the clusters and associated fibres, and the results perform well on a number of very different curvilinear structures.

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Bryony J. Hill. Wilfrid S. Kendall. Elke Thönnes. "Fibre-generated point processes and fields of orientations." Ann. Appl. Stat. 6 (3) 994 - 1020, September 2012. https://doi.org/10.1214/12-AOAS553

Information

Published: September 2012
First available in Project Euclid: 31 August 2012

zbMATH: 1254.62101
MathSciNet: MR3012518
Digital Object Identifier: 10.1214/12-AOAS553

Keywords: earthquakes , Empirical Bayes , fibre processes , field of orientations , fingerprints , Markov chain Monte Carlo , spatial birth–death process , spatial point processes , tensor fields

Rights: Copyright © 2012 Institute of Mathematical Statistics

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Vol.6 • No. 3 • September 2012
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