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

Pascal Peter, Joachim Weickert, Axel Munk, Tatyana Krivobokova, Housen Li

Publications: Contribution to bookContribution to proceedingsPeer Reviewed

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.
Original languageEnglish
Title of host publicationEnergy Minimization Methods in Computer Vision and Pattern Recognition. EMMCVPR 2015
EditorsXue-Cheng Tai, Egil Bae, Tony F. Chan, Marius Lysaker
PublisherSpringer
Pages263-277
Number of pages15
VolumeVol. 8932
ISBN (Electronic)978-3-319-14612-6
ISBN (Print)978-3-319-14611-9
Publication statusPublished - 2015
Externally publishedYes

Publication series

SeriesLecture Notes in Computer Science
Volume8932
ISSN0302-9743

Austrian Fields of Science 2012

  • 101018 Statistics

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