A fundamental relationship between bilateral filtering, adaptive smoothing, and the nonlinear diffusion equation

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452 Scopus citations

Abstract

In this paper, the relationship between bilateral filtering and anisotropic diffusion is examined. The bilateral filtering approach represents a large class of nonlinear digital image filters. We first explore the connection between anisotropic diffusion and adaptive smoothing, and then the connection between adaptive smoothing and bilateral filtering. Previously, adaptive smoothing was considered an inconsistent approximation to the nonlinear diffusion equation. We extend adaptive smoothing to make it consistent, thus enabling a unified viewpoint that relates between nonlinear digital image filters and the nonlinear diffusion equation.

Original languageEnglish
Pages (from-to)844-847
Number of pages4
JournalIEEE Transactions on Pattern Analysis and Machine Intelligence
Volume24
Issue number6
DOIs
StatePublished - 1 Jun 2002
Externally publishedYes

Keywords

  • Adaptive smoothing
  • Anisotropic diffusion
  • Bilateral filtering
  • Denoising

ASJC Scopus subject areas

  • Software
  • Computer Vision and Pattern Recognition
  • Computational Theory and Mathematics
  • Artificial Intelligence
  • Applied Mathematics

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