Workshop on Bioimaging II / PDEs, Thu, 22 Nov, 2007
Speaker: Bernhard Burgeth
Abstract
Since the advent of diffusion tensor magnetic resonance imaging (DT-MRI) the processing of matrix-valued data, so-called matrix fields, became an important task in medical imaging.
In the case of scalar-valued images nonlinear parabolic partial differential equations (PDEs) are used to perform filtering and denoising processes.
Prominent examples are PDEs that steer morphological operations or govern isotropic and anisotropic diffusion processes.
In this contribution we will propose a generic framework that allows us to find the matrix-valued counterparts of such PDEs.
This framework relies on an operator algebraic point of view on symmetric matrices and exploits their rich algebraic structure. 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 confirm the effectiveness of this generic matrix-valued framework.
Joint work with Stephan Didas and Joachim Weickert.
URL: www.ricam.oeaw.ac.at/specsem/ssqbm/participants/abstracts/index.php
This page was made with 100% valid HTML & CSS - Send comments to Webmaster
Today's date and time is 04/20/24 - 05:58 CEST and this file (/specsem/ssqbm/participants/abstracts/index.php) was last modified on 12/18/12 - 11:01 CEST