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SCALESPACE
2007
Springer

A Generic Approach to the Filtering of Matrix Fields with Singular PDEs

13 years 9 months ago
A Generic Approach to the Filtering of Matrix Fields with Singular PDEs
Abstract. There is an increasing demand to develop image processing tools for the filtering and analysis of matrix-valued data, so-called matrix fields. In the case of scalar-valued images parabolic partial differential equations (PDEs) are widely used to perform filtering and denoising processes. Especially interesting from a theoretical as well as from a practical point of view are PDEs with singular diffusivities describing processes like total variation (TV-)diffusion, mean curvature motion and its generalisation, the so-called self-snakes. In this contribution we propose a generic framework that allows us to find the matrix-valued counterparts of the equations mentioned above. In order to solve these novel matrix-valued PDEs successfully we develop truly matrix-valued analogs to numerical solution schemes of the scalar setting. Numerical experiments performed on both synthetic and real world data substantiate the effectiveness of our matrix-valued, singular diffusion fil...
Bernhard Burgeth, Stephan Didas, Luc Florack, Joac
Added 09 Jun 2010
Updated 09 Jun 2010
Type Conference
Year 2007
Where SCALESPACE
Authors Bernhard Burgeth, Stephan Didas, Luc Florack, Joachim Weickert
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