Image compression with anisotropic diffusion

Irena Galić, Joachim Weickert, Martin Welk, Andrés Bruhn, Alexander Belyaev, Hans Peter Seidel

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120 Citations (Scopus)
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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.

Original languageEnglish
Pages (from-to)255-269
Number of pages15
JournalJournal of Mathematical Imaging and Vision
Issue number2-3
Publication statusPublished - Jul 2008


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


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