Paper Info
Title
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 filters.
Year
Venue
Keywords
2007
SSVM
singular pdes,generic approach,numerical experiment,matrix-valued analog,matrix-valued data,so-called matrix field,real world data,novel matrix-valued pdes,singular diffusivities,singular diffusion filter,matrix-valued counterpart,numerical solution scheme,image processing,total variation
Field
DocType
Volume
Matrix (mathematics),Mathematical analysis,Generalization,Scalar (physics),Mean curvature,Image processing,Filter (signal processing),Partial differential equation,Mathematics,Parabola
Conference
4485
ISSN
Citations 
PageRank 
0302-9743
6
0.47
References 
Authors
8
4
Name
Order
Citations
PageRank
Bernhard Burgeth135826.09
Stephan Didas228117.12
L. M. J. Florack31212210.47
Joachim Weickert45489391.03