Fibre-generated point processes and fields of orientations
Hill, Bryony J., Kendall, Wilfrid S. and Thönnes, Elke. (2012) Fibre-generated point processes and fields of orientations. Annals of Applied Statistics, Vol.6 (No.3). pp. 994-1020. ISSN 1941-7330
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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.
|Item Type:||Journal Article|
|Subjects:||Q Science > QA Mathematics|
|Divisions:||Faculty of Science > Statistics|
|Library of Congress Subject Headings (LCSH):||Point processes, Bayesian statistical decision theory|
|Journal or Publication Title:||Annals of Applied Statistics|
|Publisher:||Institute of Mathematical Statistics|
|Page Range:||pp. 994-1020|
|Access rights to Published version:||Restricted or Subscription Access|
ADLER, R. J. and TAYLOR, J. E. (2007). Random Fields and Geometry. Springer, New York.
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