The Annals of Applied Statistics

Fibre-generated point processes and fields of orientations

Bryony J. Hill, Wilfrid S. Kendall, and Elke Thönnes

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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.

Article information

Source
Ann. Appl. Stat., Volume 6, Number 3 (2012), 994-1020.

Dates
First available in Project Euclid: 31 August 2012

Permanent link to this document
https://projecteuclid.org/euclid.aoas/1346418571

Digital Object Identifier
doi:10.1214/12-AOAS553

Mathematical Reviews number (MathSciNet)
MR3012518

Zentralblatt MATH identifier
1254.62101

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

Citation

Hill, Bryony J.; Kendall, Wilfrid S.; Thönnes, Elke. Fibre-generated point processes and fields of orientations. Ann. Appl. Stat. 6 (2012), no. 3, 994--1020. doi:10.1214/12-AOAS553. https://projecteuclid.org/euclid.aoas/1346418571


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