Title: Discontinuity-Preserving Filters for Tensor Fields



			     Joachim Weickert
                    Mathematical Image Analysis Group
	       Faculty of Mathematics and Computer Science
	            Saarland University, Building 27
		       66041 Saarbrucken, Germany
		  Email: weickert@mia.uni-saarland.de
		     Web: www.mia.uni-saarland.de



Abstract:
In recent years, many discontinuity-preserving methods for nonlinear image
restoration have been developed. Not much attention, however, has been paid 
to the design of nonlinear flters for matrix-valued image data. Such tensor 
field data arise e.g. in medical applications when diffusion tensor magnetic 
resonance imaging (DT-MRI) is used, but also in motion analysis in image 
sequences and in scientific visualization problems. It is quite common that 
these matrix fields have additional properties such as symmetry or positive 
semidefiniteness. In this talk a number of PDE-based and variational methods 
for filtering tensor fields will be presented. Isotropic as well as 
anisotropic strategies are discussed and experimentally compared. It is shown 
that all proposed filters preserve the positive semidefiniteness of any 
positive semidefinite initial tensor field.