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A gradient field approach to modelling fibre-generated spatial point processes

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Hill, Bryony, Kendall, Wilfrid S. and Thönnes, Elke (2011) A gradient field approach to modelling fibre-generated spatial point processes. Working Paper. Coventry: University of Warwick. Centre for Research in Statistical Methodology. Working papers, Vol.2011 (No.18).

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Official URL: http://www2.warwick.ac.uk/fac/sci/statistics/crism...

Abstract

A new non-parametric model is introduced for point processes that are clustered along curves
or fibres, with additional background noise. The model identifies random curves as integral lines of a
gradient field. In principle this enables the inclusion of all possible non-self-intersecting curves with
one underlying smoothness constraint. Markov chain Monte Carlo is combined with Empirical Bayes
to provide a practical estimation procedure for properties of the underlying fibre distribution, based
on the observed point pattern data. Comparisons are made with other techniques in the literature.
Illustrations of the methodology include applications to fingerprints, earthquakes and galaxies.

Item Type:

Working or Discussion Paper (Working Paper)

Subjects:

Q Science > QA Mathematics

Divisions:

Faculty of Science > Statistics

Library of Congress Subject Headings (LCSH):

Point processes -- Mathematical models

Series Name:

Working papers

Publisher:

University of Warwick. Centre for Research in Statistical Methodology

Place of Publication:

Coventry

Official Date:

2011

Dates:

Date	Event
2011	Published

Volume:

Vol.2011

Number:

No.18

Status:

Not Peer Reviewed

Access rights to Published version:

Open Access

References:

Dryden IL, Koloydenko A, Zhou D (2009), \Non-Euclidean statistics for covariance matrices, with applications
to diffusion tensor imaging". Annals of Applied Statistics;3(3):1102{1123.
Hastie T, Stuetzle W (1989), \Principal curves". Journal of the American Statistical Association;84(406):502{
516.
Stanford DC, Raftery AE (2000), \Finding curvilinear features in spatial point patterns: principal curve clustering
with noise". IEEE Transactions on Pattern Analysis and Machine Intelligence;22(6):601{609.
Stoica RS, Martinez VJ, Saar E (2007), \A three-dimensional object point process for detection of cosmic
filaments". Journal of the Royal Statistical Society: Series C (Applied Statistics);56(4):459{477.
Su J (2009), A Tensor Approach to Fingerprint Analysis, PhD Thesis, University of Warwick.
Su J, Hill B, Kendall WS, Thonnes E (2008), \Inference for point processes with unobserved, one-dimensional
reference structure". University of Warwick Department of Statistics CRiSM Working Paper No.8{10.
Watson, C (2001), NIST Special Database 30: Dual Resolution Images from Paired Fingerprint Cards. National
Institute of Standards and Technology, Gaithersburg, Md, USA. 2001.

URI:

http://wrap.warwick.ac.uk/id/eprint/35064

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