A spectral approach to total variation

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Abstract

The total variation (TV) functional is explored from a spectral perspective. We formulate a TV transform based on the second time derivative of the total variation flow, scaled by time. In the transformation domain disks yield impulse responses. This transformation can be viewed as a spectral domain, with somewhat similar intuition of classical Fourier analysis. A simple reconstruction formula from the TV spectral domain to the spatial domain is given. We can then design low-pass, high-pass and band-pass TV filters and obtain a TV spectrum of signals and images.

Original languageEnglish
Title of host publicationScale Space and Variational Methods in Computer Vision - 4th International Conference, SSVM 2013, Proceedings
Pages36-47
Number of pages12
DOIs
StatePublished - 2013
Event4th International Conference on Scale Space and Variational Methods in Computer Vision, SSVM 2013 - Leibnitz, Austria
Duration: 2 Jun 20136 Jun 2013

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume7893 LNCS

Conference

Conference4th International Conference on Scale Space and Variational Methods in Computer Vision, SSVM 2013
Country/TerritoryAustria
CityLeibnitz
Period2/06/136/06/13

Keywords

  • Scale Space
  • image analysis
  • total variation

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • General Computer Science

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