TY  - GEN
T1  - A generic approach to diffusion filtering of matrix-fields
A1  - Burgeth,Bernhard
A1  - Didas,Stephan
A1  - Florack,Luc
A1  - Weickert,Joachim
Y1  - 2012/03/15
N2  - Diffusion tensor magnetic resonance imaging (DT-MRI), is a image acquisition method, that provides matrix-valued data, so-called matrix fields. Hence image processing tools for the filtering and analysis of these data types are in demand. In this artricle we propose a generic framework that allows us to find the matrix-valued counterparts of the Perona-Malik PDEs with various diffusivity functions. To this end we extend the notion of derivatives and associated differential operators to matrix fields of symmetric matrices by adopting an operator-algebraic point of view. 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 novel matrix-valued Perona-Malik diffusion filters.
CY  - Saarbrücken
PB  - Universitäts- und Landesbibliothek
AD  - Postfach 151141, 66041 Saarbrücken
UR  - http://scidok.sulb.uni-saarland.de/volltexte/2012/4722
ER  -