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Qualitative and Quantitative Behaviour of Geometrical PDEs in Image Processing

  • Arjan Kuijper
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4843)

Abstract

We analyse a series of approaches to evolve images. It is motivated by combining Gaussian blurring, the Mean Curvature Motion (used for denoising and edge-preserving), and maximal blurring (used for inpainting). We investigate the generalised method using the combination of second order derivatives in terms of gauge coordinates.

For the qualitative behaviour, we derive a solution of the PDE series and mention its properties briefly. Relations with general diffusion equations are discussed. Quantitative results are obtained by a novel implementation whose stability and convergence is analysed.

The practical results are visualised on a real-life image, showing the expected qualitative behaviour. When a constraint is added that penalises the distance of the results to the input image, one can vary the desired amount of blurring and denoising.

Keywords

Order Derivative Qualitative Behaviour Large Time Step Curvature Motion Geometrical Evolution 
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-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Arjan Kuijper
    • 1
  1. 1.Radon Institute for Computational and Applied Mathematics, LinzAustria

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