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Combining Curvature Motion and Edge-Preserving Denoising

  • Stephan Didas
  • Joachim Weickert
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4485)

Abstract

In this paper we investigate a family of partial differential equations (PDEs) for image processing which can be regarded as isotropic nonlinear diffusion with an additional factor on the right-hand side. The one-dimensional analogues to this filter class have been motivated as scaling limits of one-dimensional adaptive averaging schemes. In 2-D, mean curvature motion is one of the most prominent examples of this family of PDEs. Other representatives of the filter class combine properties of curvature motion with the enhanced edge preservation of Perona-Malik diffusion. It becomes appearent that these PDEs require a careful discretisation. Numerical experiments display the differences between Perona-Malik diffusion, classical mean curvature motion and the proposed extensions. We consider, for example, enhanced edge sharpness, the question of morphological invariance, and the behaviour with respect to noise.

Keywords

Curvature Motion Morphological Invariance Small Time Step Size Shrinkage Time Convex Plane Curf 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Stephan Didas
    • 1
  • Joachim Weickert
    • 1
  1. 1.Mathematical Image Analysis Group, Department of Mathematics and Computer Science, Saarland University, Building E1 1, 66041 Saarbrücken 

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