232 research outputs found
Classification of lung disease in HRCT scans using integral geometry measures and functional data analysis
A framework for classification of chronic lung disease from high-resolution CT scans is presented. We use a set of features which measure the local morphology and topology of the 3D voxels within the lung parenchyma and apply functional data classification to the extracted features. We introduce the measures, Minkowski functionals, which derive from integral geometry and show results of classification on lungs containing various stages of chronic lung disease: emphysema, fibrosis and honey-combing. Once trained, the presented method is shown to be efficient and specific at characterising the distribution of disease in HRCT slices
Minkowski Tensors of Anisotropic Spatial Structure
This article describes the theoretical foundation of and explicit algorithms
for a novel approach to morphology and anisotropy analysis of complex spatial
structure using tensor-valued Minkowski functionals, the so-called Minkowski
tensors. Minkowski tensors are generalisations of the well-known scalar
Minkowski functionals and are explicitly sensitive to anisotropic aspects of
morphology, relevant for example for elastic moduli or permeability of
microstructured materials. Here we derive explicit linear-time algorithms to
compute these tensorial measures for three-dimensional shapes. These apply to
representations of any object that can be represented by a triangulation of its
bounding surface; their application is illustrated for the polyhedral Voronoi
cellular complexes of jammed sphere configurations, and for triangulations of a
biopolymer fibre network obtained by confocal microscopy. The article further
bridges the substantial notational and conceptual gap between the different but
equivalent approaches to scalar or tensorial Minkowski functionals in
mathematics and in physics, hence making the mathematical measure theoretic
method more readily accessible for future application in the physical sciences
Evidence for Filamentarity in the Las Campanas Redshift Survey
We apply Shapefinders, statistical measures of `shape' constructed from two
dimensional partial Minkowski functionals, to study the degree of filamentarity
in the Las Campanas Redshift Survey (LCRS). In two dimensions, three Minkowski
functionals characterise the morphology of an object, they are: its perimeter
(L), area (S), and genus. Out of L and S a single dimensionless Shapefinder
Statistic, F can be constructed (0 <=F <=1). F acquires extreme values on a
circle (F = 0) and a filament (F = 1). Using F, we quantify the extent of
filamentarity in the LCRS by comparing our results with a Poisson distribution
with similar geometrical properties and having the same selection function as
the survey. Our results unambiguously demonstrate that the LCRS displays a high
degree of filamentarity both in the Northern and Southern galactic sections a
result that is in general agreement with the visual appearance of the
catalogue. It is well known that gravitational clustering from Gaussian initial
conditions gives rise to the development of non-Gaussianity reflected in the
formation of a network-like filamentary structure on supercluster scales.
Consequently the fact that the smoothed LCRS catalogue shows properties
consistent with those of a Gaussian random field (Colley 1997) whereas the
unsmoothed catalogue demonstrates the presence of filamentarity lends strong
support to the conjecture that the large scale clustering of galaxies is driven
by gravitational instability.Comment: Accepted for publication in Ap
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