A note on local Morse theory in scale space and Gaussian deformations

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Abstract

In this note we study the local behavior of singularities occurring in scale space under Gaussian blurring. Based on ideas from singularity theory for vector fields this is done by considering deformations or unfoldings. To deal with the special nature of the problem the concept of Gaussian deformation is introduced. Using singularity theory the stability of these deformations is considered. New concepts of one-sided stability and one-sided equivalence are introduced. This way a classification of stable singularities is obtained which agrees with those known in literature.
Original languageEnglish
Title of host publicationDeep Structure, Singularities, and Computer Vision (First 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
Pages249-258
ISBN (Print)3-540-29836-3
DOIs
Publication statusPublished - 2005

Publication series

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

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