On tensor-based PDEs and their corresponding variational formulations with application to color image denoising

Authors:
Freddie Åström;George Baravdish;Michael Felsberg
Affiliations:
Computer Vision Laboratory, Department of E.E., Linköping University, Sweden, Center for Medical Image Science and Visualization (CMIV), Linköping University, Sweden;Department of Science and Technology, Linköping University, Sweden;Computer Vision Laboratory, Department of E.E., Linköping University, Sweden, Center for Medical Image Science and Visualization (CMIV), Linköping University, Sweden
Venue:
ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part III
Year:
2012

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Abstract

The case when a partial differential equation (PDE) can be considered as an Euler-Lagrange (E-L) equation of an energy functional, consisting of a data term and a smoothness term is investigated. We show the necessary conditions for a PDE to be the E-L equation for a corresponding functional. This energy functional is applied to a color image denoising problem and it is shown that the method compares favorably to current state-of-the-art color image denoising techniques.