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.
|Number of pages||12|
|Journal||International Journal of Bifurcation and Chaos in Applied Sciences and Engineering|
|State||Published - Aug 2009|
Bibliographical noteFunding Information:
The authors would like to acknowledge funding from Fondecyt Grant 1070098 (JC), Universidad de los Andes Grant ICIV-003-08 (JC), Fondecyt Grant 1070550 (MG), and Fondecyt Grant 7070081 (BS). The authors thank Takeshi Asahi and Gonzalo Rojas for providing the images of diffusion weighted MRI.
- Anisotropic diffusion
- Image processing
- Magnetic resonance imaging
- Orientation field
- Variational principles