Variable exponent diffusion for image detexturing

Pierre-Alain Fayolle, Alexander Belyaev

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We consider a variational approach to the problem of structure + texture decomposition (also known as cartoon + texture decomposition). As usual for many variational problems in image analysis and processing, the energy we minimize consists of two terms: a data-fitting term and a regularization term. The main feature of our approach consists of choosing parameters in the regularization term adaptively. Namely, the regularization term is given by a weighted p(·)-Dirichlet-based energy ∫a(x)|∇u|p(x), where the weight and exponent functions are determined from an analysis of the spectral content of the image curvature. Our numerical experiments, both qualitative and quantitative, suggest that the proposed approach delivers better results than state-of-the-art methods for extracting the structure from textured and mosaic images, as well as competitive results on image enhancement problems.
Original languageEnglish
Article number81
JournalMachine Vision and Applications
Issue number5
Early online date10 Aug 2023
Publication statusPublished - Sept 2023


  • Image decomposition
  • Structure extraction
  • Total variation
  • Variable exponent
  • Variational formulation


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