Image Compression with Anisotropic Diffusion

  • Irena Galić
  • Joachim Weickert
  • Martin Welk
  • Andrés Bruhn
  • Alexander Belyaev
  • Hans-Peter Seidel
Open Access
Article

Abstract

Compression is an important field of digital image processing where well-engineered methods with high performance exist. Partial differential equations (PDEs), however, have not much been explored in this context so far. In our paper we introduce a novel framework for image compression that makes use of the interpolation qualities of edge-enhancing diffusion. Although this anisotropic diffusion equation with a diffusion tensor was originally proposed for image denoising, we show that it outperforms many other PDEs when sparse scattered data must be interpolated. To exploit this property for image compression, we consider an adaptive triangulation method for removing less significant pixels from the image. The remaining points serve as scattered interpolation data for the diffusion process. They can be coded in a compact way that reflects the B-tree structure of the triangulation. We supplement the coding step with a number of amendments such as error threshold adaptation, diffusion-based point selection, and specific quantisation strategies. Our experiments illustrate the usefulness of each of these modifications. They demonstrate that for high compression rates, our PDE-based approach does not only give far better results than the widely-used JPEG standard, but can even come close to the quality of the highly optimised JPEG2000 codec.

Keywords

Partial differential equations Nonlinear diffusion Image compression Image inpainting 

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Copyright information

© The Author(s) 2008

Authors and Affiliations

  • Irena Galić
    • 1
    • 2
  • Joachim Weickert
    • 1
  • Martin Welk
    • 1
  • Andrés Bruhn
    • 1
  • Alexander Belyaev
    • 3
  • Hans-Peter Seidel
    • 2
  1. 1.Mathematical Image Analysis Group, Faculty of Mathematics and Computer ScienceSaarland UniversitySaarbrückenGermany
  2. 2.Max-Planck Institute for InformaticsSaarbrückenGermany
  3. 3.EECE, School of Engineering and Physical Sciences, Earl Mountbatten BuildingHeriot-Watt UniversityEdinburghUK

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