A Discrete Cross-Diffusion Model for Image Restoration
In this paper a fully discrete cross-diffusion model for image restoration is introduced. The image is represented by a two-component vector field, and the restoration process is governed by a nonlinear cross-diffusion difference system. We explore numerically the potentialities of using the nonlinear cross-diffusion approach as an image filter, in particular as a preprocessing step for image segmentation.
This work was supported by Spanish Ministerio de Economía y Competitividad under the Research Grant MTM2014-54710-P. A. Araújo and S. Barbeiro were also supported by the Centre for Mathematics of the University of Coimbra—UID/MAT/00324/2013, funded by the Portuguese Government through FCT/MCTES and co-funded by the European Regional Development Fund through the Partnership Agreement PT2020.
- 1.Araújo, A., Barbeiro, S., Cuesta, E., Durán, A.: Cross-diffusion systems for image processing: I. The linear case. Preprint available at http://arxiv.org/abs/1605.02923
- 2.Araújo, A., Barbeiro, S., Cuesta, E., Durán, A.: Cross-diffusion systems for image processing: II. The nonlinear case. Preprint available at http://arxiv.org/abs/1605.03721
- 7.Crété-Roffet, F., Dolmiere, T., Ladret, P., Nicolas, M.: The blur effect: perception and estimation with a new no-reference perceptual blur metric. In: Proceedings of SPIE on Human Vision and Electronic Imaging XII, San Jose, California, USA. 11 pp. (2007)Google Scholar
- 11.Lorenz, D.A., Bredies, K., Zeevi, Y.Y.: Nonlinear complex and cross diffusion. Unpublished report, University of Bremen (2006)Google Scholar