Isometrically invariant description of deformable objects based on the fractional heat equation

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DOIResolve DOI: http://doi.org/10.1007/978-3-642-40246-3_17
AuthorSearch for: ; Search for:
TypeBook Chapter
Proceedings titleComputer Analysis of Images and Patterns : 15th International Conference, CAIP 2013, York, UK, August 27-29, 2013, Proceedings, Part II
Series titleLecture Notes In Computer Science; Volume 8048
Conference15th International Conference on Computer Analysis of Images and Patterns (CAIP 2013), August 27-29, 2013, York, United Kingdom
ISSN0302-9743
0302-9743
ISBN978-3-642-40245-6
978-3-642-40246-3
Pages135143; # of pages: 9
SubjectFractional; Heat equation; Isometry; Kernel; Path integral; Geometry; Heat transfer; Image analysis; Random processes; Partial differential equations
AbstractRecently, a number of researchers have turned their attention to the creation of isometrically invariant shape descriptors based on the heat equation. The reason for this surge in interest is that the Laplace-Beltrami operator, associated with the heat equation, is highly dependent on the topology of the underlying manifold, which may lead to the creation of highly accurate descriptors. In this paper, we propose a generalisation based on the fractional heat equation. While the heat equation enables one to explore the shape with a Markovian Gaussian random walk, the fractional heat equation explores the manifold with a non-Markovian Lévy random walk. This generalisation provides two advantages. These are, first, that the process has a memory of the previously explored geometry and, second, that it is possible to correlate points or vertices which are not part of the same neighbourhood. Consequently, a highly accurate, contextual shape descriptor may be obtained. © 2013 Springer-Verlag.
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PublisherSpringer Berlin Heidelberg
LanguageEnglish
AffiliationInformation and Communication Technologies; National Research Council Canada
Peer reviewedYes
NPARC number21270709
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Record identifier1d17627a-da37-4b8b-a51e-c4498afb89bf
Record created2014-02-17
Record modified2016-06-27
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