Hill, Bryony J. (2011) An orientation field approach to modelling fibre-generated spatial point processes. PhD thesis, University of Warwick.

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Abstract

This thesis introduces a new approach to analysing spatial point data clustered along
or around a system of curves or fibres with additional background noise. 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. The orientation field estimation draws on ideas from tensor
field theory (an area recently motivated by the study of magnetic resonance imaging
scans), using symmetric positive-definite matrices to estimate local anisotropies in
the point pattern through the tensor method. We also propose a new measure of
anisotropy, the modified square Fractional Anisotropy, whose statistical properties
are estimated for tensors calculated via the tensor method.
A continuous-time Markov chain Monte Carlo algorithm is used to draw samples
from the posterior distribution of fibres, exploring models with different numbers
of clusters, and fitting fibres to the clusters as it proceeds. The Bayesian approach
permits inference on various properties of the clusters and associated fibres, and the
resulting algorithm performs well on a number of very different curvilinear structures.

Item Type:	Thesis or Dissertation (PhD)
Subjects:	Q Science > QA Mathematics
Library of Congress Subject Headings (LCSH):	Point processes, Curves
Official Date:	September 2011
Dates:	Date Event September 2011 Submitted
Institution:	University of Warwick
Theses Department:	Department of Statistics
Thesis Type:	PhD
Publication Status:	Unpublished
Supervisor(s)/Advisor:	Thönnes, Elke ; Kendall, W. S.
Sponsors:	Aarhus universitet. Matematisk institut
Description:	This is an abridged version for electronic use; please see the official URL for details on how to access the full version.
Extent:	xi, 188 leaves : ill., charts
Language:	eng

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