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Justifying Tensor-Driven Diffusion from Structure-Adaptive Statistics of Natural Images

  • Pascal Peter
  • Joachim Weickert
  • Axel Munk
  • Tatyana Krivobokova
  • Housen Li
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8932)

Abstract

Tensor-driven anisotropic diffusion and regularisation have been successfully applied to a wide range of image processing and computer vision tasks such as denoising, inpainting, and optical flow. Empirically it has been shown that anisotropic models with a diffusion tensor perform better than their isotropic counterparts with a scalar-valued diffusivity function. However, the reason for this superior performance is not well understood so far. Moreover, the specific modelling of the anisotropy has been carried out in a purely heuristic way. The goal of our paper is to address these problems. To this end, we use the statistics of natural images to derive a unifying framework for eight isotropic and anisotropic diffusion filters that have a corresponding variational formulation. In contrast to previous statistical models, we systematically investigate structure-adaptive statistics by analysing the eigenvalues of the structure tensor. With our findings, we justify existing successful models and assess the relationship between accurate statistical modelling and performance in the context of image denoising.

Keywords

diffusion regularisation anisotropy diffusion tensor statistics of natural images image priors 

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Pascal Peter
    • 1
  • Joachim Weickert
    • 1
  • Axel Munk
    • 2
  • Tatyana Krivobokova
    • 3
  • Housen Li
    • 2
  1. 1.Mathematical Image Analysis Group, Faculty of Mathematics and Computer ScienceSaarland UniversitySaarbrückenGermany
  2. 2.Felix-Bernstein-Chair for Mathematical StatisticsInstitute of Mathematical StochasticsGöttingenGermany
  3. 3.Statistical Methods Group, Courant Research Centre “Poverty, Equity and Growth”GöttingenGermany

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