Dimensionality Reduction for Information Geometric Characterization of Surface Topographies

Dodson, CTJ and Mettanen, M and Sampson, WW (2017) Dimensionality Reduction for Information Geometric Characterization of Surface Topographies. In: Computational Information Geometry: For Image And Signal Processing. Signals and Communication Technology . Springer, Switzerland, pp. 133-147. ISBN 978-3-319-47058-0

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Abstract

Stochastic textures with features spanning many length scales arise in a range of contexts in physical and natural sciences, from nanostructures like synthetic bone to ocean wave height distributions and cosmic phenomena like inter-galactic cluster void distributions. Here we used a data set of 35 surface topographies, each of 2400x2400 pixels with spatial resolution between 4~\mum\ and 7~\mum\ per pixel, and fitted trivariate Gaussian distributions to represent their spatial structures. For these we computed pairwise information metric distances using the Fisher-Rao metric. Then dimensionality reduction was used to reveal the groupings among subsets of samples in an easily comprehended graphic in 3-space. The samples here came from the papermaking industry but such a reduction of large frequently noisy spatial data sets is useful in a range of materials and contexts at all scales.

Item Type: Book Section
Uncontrolled Keywords: Dimensionality reduction, information metric, surface topography, trivariate Gaussian
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 53 Differential geometry
MSC 2010, the AMS's Mathematics Subject Classification > 62 Statistics
Depositing User: Prof CTJ Dodson
Date Deposited: 12 Dec 2016
Last Modified: 20 Oct 2017 14:13
URI: http://eprints.maths.manchester.ac.uk/id/eprint/2518

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