Locally Analytic Schemes for Diffusion Filtering of Images

author: Martin Welk, Saarland University
published: Dec. 17, 2007,   recorded: September 2007,   views: 4420


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Nonlinear diffusion filtering has proven its value as a versatile tool for structure-preserving image denoising. Among the most interesting methods of this class are tensor-driven anisotropic diffusion as well as singular isotropic diffusion filters like total variation flow. For different reasons, devising good numerical algorithms for these filters is challenging.

A spatial discretisation transforms nonlinear diffusion partial differential equations into systems of ordinary differential equations. Their investigation yields insights into the properties of diffusion-based algorithms but leads also to the design of new algorithms with favourable stability properties which are at the same time simple to implement. Moreover, interesting links to wavelet-based denoising methods are established in this way.

The talk focusses on the construction and properties of locally (semi-)analytic schemes for nonlinear isotropic and anisotropic diffusion on 2D images, with extensions to the 3D case.

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