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VARIATIONAL PRINCIPLES IN IMAGE PROCESSING AND THE REGULARIZATION OF ORIENTATION FIELDS.
- Source :
- International Journal of Bifurcation & Chaos in Applied Sciences & Engineering; Aug2009, Vol. 19 Issue 8, p2705-2716, 12p, 3 Color Photographs, 1 Black and White Photograph, 10 Diagrams
- Publication Year :
- 2009
-
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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 02181274
- Volume :
- 19
- Issue :
- 8
- Database :
- Complementary Index
- Journal :
- International Journal of Bifurcation & Chaos in Applied Sciences & Engineering
- Publication Type :
- Academic Journal
- Accession number :
- 44985632
- Full Text :
- https://doi.org/10.1142/S0218127409024426