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A full second order variational model for multiscale texture analysis

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Abstract

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.

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Notes

  1. We are very grateful to Pierre Weiss who provided the codes to compute the G-norm efficiently.

  2. Many others examples can be found at http://web.me.com/maitine.bergounioux/PagePro/Publications.html.

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  1. UFR Sciences, Math., Labo. MAPMO, UMR 7349, Université d’Orléans, Route de Chartres, BP 6759, 45067, Orléans cedex 2, France

    Maïtine Bergounioux & Loïc Piffet

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  1. Maïtine Bergounioux
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  2. Loïc Piffet
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Correspondence to Maïtine Bergounioux.

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Bergounioux, M., Piffet, L. A full second order variational model for multiscale texture analysis. Comput Optim Appl 54, 215–237 (2013). https://doi.org/10.1007/s10589-012-9484-9

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