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Image Compression with Anisotropic Diffusion

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  • Published: 29 April 2008
  • Volume 31, pages 255–269, (2008)
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Image Compression with Anisotropic Diffusion
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  • Irena Galić1,2,
  • Joachim Weickert1,
  • Martin Welk1,
  • Andrés Bruhn1,
  • Alexander Belyaev3 &
  • …
  • Hans-Peter Seidel2 

  • 2666 Accesses

  • 113 Citations

  • 1 Altmetric

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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.

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Authors and Affiliations

  1. Mathematical Image Analysis Group, Faculty of Mathematics and Computer Science, Saarland University, Building E1.1, 66041, Saarbrücken, Germany

    Irena Galić, Joachim Weickert, Martin Welk & Andrés Bruhn

  2. Max-Planck Institute for Informatics, Stuhlsatzenhausweg 85, 66123, Saarbrücken, Germany

    Irena Galić & Hans-Peter Seidel

  3. EECE, School of Engineering and Physical Sciences, Earl Mountbatten Building, Heriot-Watt University, Riccarton, Edinburgh, EH14 4AS, UK

    Alexander Belyaev

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  1. Irena Galić
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Galić, I., Weickert, J., Welk, M. et al. Image Compression with Anisotropic Diffusion. J Math Imaging Vis 31, 255–269 (2008). https://doi.org/10.1007/s10851-008-0087-0

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  • Received: 12 November 2007

  • Accepted: 27 March 2008

  • Published: 29 April 2008

  • Issue Date: July 2008

  • DOI: https://doi.org/10.1007/s10851-008-0087-0

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Keywords

  • Partial differential equations
  • Nonlinear diffusion
  • Image compression
  • Image inpainting
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