A comparison of the deep structure of alpha-scale spaces

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Abstract

We compare the topology and deep structure of alternative scale space representations, so called α-scale spaces, 1/2 ≤ α ≤ 1, which are subject to a first order pseudo partial differential equation on the upper half plane {(x,s) ∈ ℝ d ×ℝ|s > 0}. In particular, the cases α = 1 and α = 1/2, which correspond to respectively Poisson scale space and Gaussian scale space, are considered. Poisson scale space is equivalent to harmonic extension to the upper half plane, inducing potential physics, whereas Gaussian scale space is generated by the diffusion equation on the upper half plane, inducing heat physics. Despite the continuous connection (by parameter 1/2 ≤ α ≤ 1) between these scale spaces and the similarity between their convolution convolution kernels, we show both theoretically and experimentally that there is a strong difference between the topology in the deep structure of these scale spaces.
Original languageEnglish
Title of host publicationDeep Structure, Singularities, and Computer Vision
Subtitle of host publicationFirst International Workshop, DSSCV 2005, Maastricht, The Netherlands, June 9-10, 2005, Revised Selected Papers
EditorsO.F. Olsen, L.M.J. Florack, A. Kuijper
Place of PublicationBerlin
PublisherSpringer
Chapter21
Pages234-248
Number of pages15
ISBN (Electronic)978-3-540-32097-5
ISBN (Print)3-540-29836-3, 978-3-540-29836-6
DOIs
Publication statusPublished - 2005

Publication series

NameLecture Notes in Computer Science (LNCS)
Volume3753
ISSN (Print)0302-9743

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