article

Periodic Plus Smooth Image Decomposition

Author:

Lionel MoisanAuthors Info & Claims

Journal of Mathematical Imaging and Vision, Volume 39, Issue 2

Pages 161 - 179

https://doi.org/10.1007/s10851-010-0227-1

Published: 01 February 2011 Publication History

Abstract

When the Discrete Fourier Transform of an image is computed, the image is implicitly assumed to be periodic. Since there is no reason for opposite borders to be alike, the "periodic" image generally presents strong discontinuities across the frame border. These edge effects cause several artifacts in the Fourier Transform, in particular a well-known "cross" structure made of high energy coefficients along the axes, which can have strong consequences on image processing or image analysis techniques based on the image spectrum (including interpolation, texture analysis, image quality assessment, etc.). In this paper, we show that an image can be decomposed into a sum of a "periodic component" and a "smooth component", which brings a simple and computationally efficient answer to this problem. We discuss the interest of such a decomposition on several applications.

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Cited By

Jacanamejoy Jamioy CMeneses-Casas NForero M(2019)Image Feature Detection Based on Phase Congruency by Monogenic Filters with New Noise EstimationPattern Recognition and Image Analysis10.1007/978-3-030-31332-6_50(577-588)Online publication date: 1-Jul-2019
https://dl.acm.org/doi/10.1007/978-3-030-31332-6_50
Mahmood FToots MÖfverstedt LSkoglund U(2018)Algorithm and Architecture Optimization for 2D Discrete Fourier Transforms with Simultaneous Edge Artifact RemovalInternational Journal of Reconfigurable Computing10.1155/2018/14031812018Online publication date: 1-Jan-2018
https://dl.acm.org/doi/10.1155/2018/1403181
Aherrahrou NTairi H(2018)A new image watermarking technique based on periodic plus smooth decomposition (PPSD)Soft Computing - A Fusion of Foundations, Methodologies and Applications10.1007/s00500-017-2501-222:7(2369-2379)Online publication date: 1-Apr-2018
https://dl.acm.org/doi/10.1007/s00500-017-2501-2
Show More Cited By

Periodic Plus Smooth Image Decomposition
1. Computing methodologies
  1. Artificial intelligence
  2. Computer graphics
2. Mathematics of computing
  1. Mathematical analysis
    1. Numerical analysis

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cover image Journal of Mathematical Imaging and Vision

Journal of Mathematical Imaging and Vision Volume 39, Issue 2

February 2011

106 pages

ISSN:0924-9907

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Copyright © Copyright © 2011 Springer Science+Business Media, LLC.

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Kluwer Academic Publishers

United States

Publication History

Published: 01 February 2011

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Cited By

Jacanamejoy Jamioy CMeneses-Casas NForero M(2019)Image Feature Detection Based on Phase Congruency by Monogenic Filters with New Noise EstimationPattern Recognition and Image Analysis10.1007/978-3-030-31332-6_50(577-588)Online publication date: 1-Jul-2019
https://dl.acm.org/doi/10.1007/978-3-030-31332-6_50
Mahmood FToots MÖfverstedt LSkoglund U(2018)Algorithm and Architecture Optimization for 2D Discrete Fourier Transforms with Simultaneous Edge Artifact RemovalInternational Journal of Reconfigurable Computing10.1155/2018/14031812018Online publication date: 1-Jan-2018
https://dl.acm.org/doi/10.1155/2018/1403181
Aherrahrou NTairi H(2018)A new image watermarking technique based on periodic plus smooth decomposition (PPSD)Soft Computing - A Fusion of Foundations, Methodologies and Applications10.1007/s00500-017-2501-222:7(2369-2379)Online publication date: 1-Apr-2018
https://dl.acm.org/doi/10.1007/s00500-017-2501-2
Bailey DMahmood FSkoglund U(2017)Reducing the Cost of Removing Border Artefacts in Fourier TransformsProceedings of the 8th International Symposium on Highly Efficient Accelerators and Reconfigurable Technologies10.1145/3120895.3120899(1-6)Online publication date: 7-Jun-2017
https://dl.acm.org/doi/10.1145/3120895.3120899
Abergel RMoisan L(2017)The Shannon Total VariationJournal of Mathematical Imaging and Vision10.1007/s10851-017-0733-559:2(341-370)Online publication date: 1-Oct-2017
https://dl.acm.org/doi/10.1007/s10851-017-0733-5
Tartavel GGousseau YPeyré G(2015)Variational Texture Synthesis with Sparsity and Spectrum ConstraintsJournal of Mathematical Imaging and Vision10.1007/s10851-014-0547-752:1(124-144)Online publication date: 1-May-2015
https://dl.acm.org/doi/10.1007/s10851-014-0547-7
Galerne BLagae ALefebvre SDrettakis G(2012)Gabor noise by exampleACM Transactions on Graphics10.1145/2185520.218556931:4(1-9)Online publication date: 1-Jul-2012
https://dl.acm.org/doi/10.1145/2185520.2185569

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