Towards PDE-Based image compression

  • Authors:

  • Irena Galić;Joachim Weickert;Martin Welk;Andrés Bruhn;Alexander Belyaev;Hans-Peter Seidel

  • Affiliations:

  • Mathematical Image Analysis Group, Faculty of Math. and Computer Science, Saarland University, Saarbrücken, Germany;Mathematical Image Analysis Group, Faculty of Math. and Computer Science, Saarland University, Saarbrücken, Germany;Mathematical Image Analysis Group, Faculty of Math. and Computer Science, Saarland University, Saarbrücken, Germany;Mathematical Image Analysis Group, Faculty of Math. and Computer Science, Saarland University, Saarbrücken, Germany;Max-Planck Institute for Informatics, Saarbrücken, Germany;Max-Planck Institute for Informatics, Saarbrücken, Germany

  • Venue:
  • VLSM'05 Proceedings of the Third international conference on Variational, Geometric, and Level Set Methods in Computer Vision
  • Year:
  • 2005

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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.