Fibre-generated point processes and fields of orientations

TL;DR

This paper presents a Bayesian method for analyzing spatial point data by estimating underlying fibre structures and orientations, aiding in understanding and reconstructing curvilinear patterns in various applications.

Contribution

It introduces a novel Bayesian framework that estimates orientation fields and samples fibre structures from point data, improving analysis of curvilinear spatial patterns.

Findings

Effective in identifying fibre structures in diverse datasets

Performs well in reconstructing missing data along curves

Provides a flexible Bayesian approach for cluster and fibre inference

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.