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Positive Signal Spaces and the Mehler-Fock Transform
Linköping University, Department of Science and Technology, Media and Information Technology. Linköping University, Faculty of Science & Engineering.ORCID iD: 0000-0001-7557-4904
2017 (English)In: GEOMETRIC SCIENCE OF INFORMATION, GSI 2017, SPRINGER INTERNATIONAL PUBLISHING AG , 2017, Vol. 10589, p. 745-753Conference paper, Published paper (Refereed)
Abstract [en]

Eigenvector expansions and perspective projections are used to decompose a space of positive functions into a product of a half-axis and a solid unit ball. This is then used to construct a conical coordinate system where one component measures the distance to the origin, a radial measure of the distance to the axis and a unit vector describing the position on the surface of the ball. A Lorentz group is selected as symmetry group of the unit ball which leads to the Mehler-Fock transform as the Fourier transform of functions depending an the radial coordinate only. The theoretical results are used to study statistical properties of edge magnitudes computed from databases of image patches. The constructed radial values are independent of the orientation of the incoming light distribution (since edge-magnitudes are used), they are independent of global intensity changes (because of the perspective projection) and they characterize the second order statistical moment properties of the image patches. Using a large database of images of natural scenes it is shown that the generalized extreme value distribution provides a good statistical model of the radial components. Finally, the visual properties of textures are characterized using the Mehler-Fock transform of the probability density function of the generalized extreme value distribution.

Place, publisher, year, edition, pages
SPRINGER INTERNATIONAL PUBLISHING AG , 2017. Vol. 10589, p. 745-753
Series
Lecture Notes in Computer Science, ISSN 0302-9743
National Category
Computer Vision and Robotics (Autonomous Systems)
Identifiers
URN: urn:nbn:se:liu:diva-150324DOI: 10.1007/978-3-319-68445-1_86ISI: 000440482500086ISBN: 978-3-319-68445-1 (print)ISBN: 978-3-319-68444-4 (print)OAI: oai:DiVA.org:liu-150324DiVA, id: diva2:1239429
Conference
3rd International SEE Conference on Geometric Science of Information (GSI)
Note

Funding Agencies|Swedish Research Council [2014-6227]

Available from: 2018-08-16 Created: 2018-08-16 Last updated: 2018-08-16

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CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • oxford
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf