Computational Optimization and Applications

, Volume 54, Issue 2, pp 215–237 | Cite as

A full second order variational model for multiscale texture analysis

  • Maïtine BergouniouxEmail author
  • Loïc Piffet


We present a second order image decomposition model to perform denoising and texture extraction. We look for the decomposition f=u+v+w where u is a first order term, v a second order term and w the (0 order) remainder term. For highly textured images the model gives a two-scale texture decomposition: u can be viewed as a macro-texture (larger scale) whose oscillations are not too large and w is the micro-texture (very oscillating) that may contain noise. We perform mathematical analysis of the model and give numerical examples.


Second order total variation Image reconstruction Denoising Texture analysis Variational method 


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© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.UFR Sciences, Math., Labo. MAPMO, UMR 7349Université d’OrléansOrléans cedex 2France

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