Colloquium CS: Prof. Dr. Bernhard Burgeth

Title: Anisotropic Evolution Processes for Matrix Fields

Abstract:
There are some well-established anisotropic filters for scalar images
based on partial differential equations (PDEs), notably coherence
enhancing diffusion filtering, but also adaptive morphological filters
induced by anisotropic dilation and erosion.
In this talk we discuss a general framework that allows for an efficient
transfer of these processes to fields of symmetric matrices.
This encompasses an appropriate matrix-valued PDE-formulation
as well as proper numerical solution schemes.
In numerical experiments on real and synthetic 3D data we explore the
performance of the matrix-valued counterparts of the aforementioned
filters.