Are natural images of bounded variation?

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review

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Author(s)

Detail(s)

Original languageEnglish
Pages (from-to)634-648
Journal / PublicationSIAM Journal on Mathematical Analysis
Volume33
Issue number3
Publication statusPublished - 2001
Externally publishedYes

Abstract

The bounded variation assumption is the starting point of many methods in image analysis and processing. However, one common drawback of these methods is their inability to handle textures and small structures properly. Here we precisely show why natural images are incompletely represented by BV functions. Through an experimental study of the distribution of bilevels of natural images, we show that their total variation blows up to infinity with the increasing of resolution. To reach these conclusions, we compute bounds on the total variation, and we model convolution and sampling under quite general assumptions. © 2001 Society for Industrial and Applied Mathematics.

Research Area(s)

  • Bilevels, Bounded variation, Natural images, Power laws, Size distribution, Total variation, Wavelets

Bibliographic Note

Publication details (e.g. title, author(s), publication statuses and dates) are captured on an “AS IS” and “AS AVAILABLE” basis at the time of record harvesting from the data source. Suggestions for further amendments or supplementary information can be sent to lbscholars@cityu.edu.hk.

Citation Format(s)

Are natural images of bounded variation? / Gousseau, Yann; Morel, Jean-Michel.
In: SIAM Journal on Mathematical Analysis, Vol. 33, No. 3, 2001, p. 634-648.

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review