Variational principles in image processing and the regularization of orientation fields

Jaime Cisternas, Marcelo GÁlvez, Bram Stieltjes, Frederik B. Laun

Research output: Contribution to conferencePaper

1 Scopus citations

Abstract

Variational principles and partial differential equations have proved to be fundamental elements in the mathematical modeling of extended systems in physics and engineering. Of particular interest are the equations that arise from a free energy functional. Recently variational principles have begun to be used in Image Processing to perform basic tasks such as denoising, debluring, etc. Great improvements can be achieved by selecting the most appropriate form for the functional. In this article we show how these ideas can be applied not just to scalar fields (i.e. grayscale images) but also to curved manifolds such as the space of orientations. This work is motivated by the denoising of images acquired with Magnetic Resonance scanners using diffusion-sensitized magnetic gradients.
Original languageAmerican English
Pages2705-2716
Number of pages12
DOIs
StatePublished - 1 Jan 2009
EventInternational Journal of Bifurcation and Chaos -
Duration: 1 Jan 2010 → …

Conference

ConferenceInternational Journal of Bifurcation and Chaos
Period1/01/10 → …

Keywords

  • Anisotropic diffusion
  • Image processing
  • Magnetic resonance imaging
  • Orientation field
  • Variational principles

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