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Fibre-generated point processes and fields of orientations. (English) Zbl 1254.62101

Summary: 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.

MSC:

62M30 Inference from spatial processes
60G55 Point processes (e.g., Poisson, Cox, Hawkes processes)
62C12 Empirical decision procedures; empirical Bayes procedures
86A17 Global dynamics, earthquake problems (MSC2010)
65C40 Numerical analysis or methods applied to Markov chains
86A32 Geostatistics
65C60 Computational problems in statistics (MSC2010)

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