Locally isometric and conformal parameterization of image manifold

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

5 Citations (Scopus)

Abstract

Images can be represented as vectors in a high-dimensional Image space with components specifying light intensities at image pixels. To avoid the â curse of dimensionality', the original high-dimensional image data are transformed into their lower-dimensional features preserving certain subject-driven data properties. These properties can include âinformation-preserving' when using the constructed low-dimensional features instead of original high-dimensional vectors, as well preserving the distances and angles between the original high-dimensional image vectors. Under the commonly used Manifold assumption that the high-dimensional image data lie on or near a certain unknown low-dimensional Image manifold embedded in an ambient high-dimensional âõbservation' space, a constructing of the lower-dimensional features consists in constructing an Embedding mapping from the Image manifold to Feature space, which, in turn, determines a low-dimensional parameterization of the Image manifold. We propose a new geometrically motivated Embedding method which constructs a low-dimensional parameterization of the Image manifold and provides the information-preserving property as well as the locally isometric and conformal properties.

Original languageEnglish
Title of host publicationEighth International Conference on Machine Vision, ICMV 2015
EditorsAntanas Verikas, Petia Radeva, Dmitry Nikolaev
PublisherSPIE
Volume9875
ISBN (Electronic)9781510601161
DOIs
Publication statusPublished - 2015
Externally publishedYes
Event8th International Conference on Machine Vision, ICMV 2015 - Barcelona, Spain
Duration: 19 Nov 201521 Nov 2015

Publication series

NameProceedings of SPIE - The International Society for Optical Engineering
Volume9875
ISSN (Print)0277-786X
ISSN (Electronic)1996-756X

Conference

Conference8th International Conference on Machine Vision, ICMV 2015
Country/TerritorySpain
CityBarcelona
Period19/11/1521/11/15

Keywords

  • conformal embedding
  • Image manifold
  • isometry embedding
  • low-dimensional parameterization
  • manifold learning
  • tangent spaces
  • tangent vector fields

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