Edge-based compression of cartoon-like images with homogeneous diffusion

  • Authors:

  • Markus Mainberger;Andrés Bruhn;Joachim Weickert;Søren Forchhammer

  • Affiliations:

  • Mathematical Image Analysis Group, Faculty of Mathematics and Computer Science, Campus E1.1, Saarland University, 66041 Saarbrücken, Germany;Mathematical Image Analysis Group, Faculty of Mathematics and Computer Science, Campus E1.1, Saarland University, 66041 Saarbrücken, Germany;Mathematical Image Analysis Group, Faculty of Mathematics and Computer Science, Campus E1.1, Saarland University, 66041 Saarbrücken, Germany;DTU Fotonik, Department of Photonics Engineering Coding and Visual Communication, Ørsteds Plads, Building 343, Technical University of Denmark, 2800 Kgs. Lyngby, Denmark

  • Venue:
  • Pattern Recognition
  • Year:
  • 2011

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Abstract

Edges provide semantically important image features. In this paper a lossy compression method for cartoon-like images is presented, which is based on edge information. Edges together with some adjacent grey/colour values are extracted and encoded using a classical edge detector, binary compression standards such as JBIG and state-of-the-art encoders such as PAQ. When decoding, information outside these encoded data is recovered by solving the Laplace equation, i.e. we inpaint with the steady state of a homogeneous diffusion process. For the discrete reconstruction problem, we prove existence and uniqueness and establish a maximum-minimum principle. Furthermore, we describe an efficient multigrid algorithm. The result is a simple codec that is able to encode and decode in real time. We show that for cartoon-like images this codec can outperform the JPEG standard and even its more advanced successor JPEG2000.