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Towards PDE-Based Image Compression

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Book cover Variational, Geometric, and Level Set Methods in Computer Vision (VLSM 2005)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 3752))

Abstract

While methods based on partial differential equations (PDEs) and variational techniques are powerful tools for denoising and inpainting digital images, their use for image compression was mainly focussing on pre- or postprocessing so far. In our paper we investigate their potential within the decoding step. We start with the observation that edge-enhancing diffusion (EED), an anisotropic nonlinear diffusion filter with a diffusion tensor, is well-suited for scattered data interpolation: Even when the interpolation data are very sparse, good results are obtained that respect discontinuities and satisfy a maximum–minimum principle. This property is exploited in our studies on PDE-based image compression. We use an adaptive triangulation method based on B-tree coding for removing less significant pixels from the image. The remaining points serve as scattered interpolation data for the EED process. They can be coded in a compact and elegant way that reflects the B-tree structure. Our experiments illustrate that for high compression rates and non-textured images, this PDE-based approach gives visually better results than the widely-used JPEG coding.

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Author information

Authors and Affiliations

  1. Mathematical Image Analysis Group, Faculty of Math. and Computer Science, Saarland University, Building 27, 66041, Saarbrücken, Germany

    Irena Galić, Joachim Weickert, Martin Welk & Andrés Bruhn

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

    Irena Galić, Alexander Belyaev & Hans-Peter Seidel

Authors
  1. Irena Galić
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  2. Joachim Weickert
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  3. Martin Welk
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  4. Andrés Bruhn
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  5. Alexander Belyaev
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  6. Hans-Peter Seidel
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Editor information

Editors and Affiliations

  1. MAS - Ecole Centrale Paris, Grande Voie des Vignes, 92295, Chatenay-Malabry, France

    Nikos Paragios

  2. I.N.R.I.A, 2004 route des lucioles,, 06902, Sophia-Antipolis, France

    Olivier Faugeras

  3. Department of Mathematics, UCLA,  

    Tony Chan

  4. Image and Pattern Analysis Group, Heidelberg Collaboratory for Image Processing, University of Heidelberg, Germany

    Christoph Schnörr

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© 2005 Springer-Verlag Berlin Heidelberg

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Galić, I., Weickert, J., Welk, M., Bruhn, A., Belyaev, A., Seidel, HP. (2005). Towards PDE-Based Image Compression. In: Paragios, N., Faugeras, O., Chan, T., Schnörr, C. (eds) Variational, Geometric, and Level Set Methods in Computer Vision. VLSM 2005. Lecture Notes in Computer Science, vol 3752. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11567646_4

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  • DOI: https://doi.org/10.1007/11567646_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-29348-4

  • Online ISBN: 978-3-540-32109-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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