Deep structure from a geometric point of view

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Abstract

The geometry of "empty" scale space is investigated. Byvirtue of the proposed geometric axioms the generating PDE, the linearisotropic heat equation, can be presented in covariant, or geometricalform. The postulate of a metric for scale space cannot be upheld, asit is incompatible with the generating equation. Two familiar instancesof scale spaces consistent with the geometric axioms are considered byway of example, viz. classical, homogeneous scale space, and foveal scalespace.
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
Chapter12
Pages135-145
Number of pages11
ISBN (Electronic)978-3-540-32097-5
ISBN (Print)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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