# American Institute of Mathematical Sciences

November  2007, 1(4): 593-608. doi: 10.3934/ipi.2007.1.593

## Conditional image diffusion

 1 Universitat de les Illes Balears, Ctra Valldemossa km 7.5, Palma de Mallorca, 07122, Spain, Spain, Spain 2 Universitat de les Illes Balears, Crta. de Valldemossa, km 7.5, 07122 Palma de Mallorca

Received  May 2007 Published  October 2007

In this paper, a theoretical framework for the conditional diffusion of digital images is presented. Different approaches have been proposed to solve this problem by extrapolating the idea of the anisotropic diffusion for a grey level images to vector-valued images. Then, the diffusion of each channel is conditioned to a direction which normally takes into account information from all channels. In our approach, the diffusion model assumes the a priori knowledge of the diffusion direction during all the process.
The consistency of the model is shown by proving the existence and uniqueness of solution for the proposed equation from the viscosity solutions theory. Also a numerical scheme adapted to this equation based on the neighborhood filter is proposed. Finally, we discuss several applications and we compare the corresponding numerical schemes for the proposed model.
Citation: Antoni Buades, Bartomeu Coll, Jose-Luis Lisani, Catalina Sbert. Conditional image diffusion. Inverse Problems and Imaging, 2007, 1 (4) : 593-608. doi: 10.3934/ipi.2007.1.593
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