IAS Seminar "Image Processing, from Grey-Value Images to Matrix Fields"

Speaker:

Prof. Bernhard Burgeth, Fachrichtung Mathematik, Universität des Saarlandes

Abstract:

Fields of symmetric matrices are natural generalisations of grey-scale or vectorial colour images. This type of data results, for example, from diffusion tensor magnetic resonance imaging (DT-MRI), a well established non-invasive medical image acquisition technique that allows for in vivo examination of human tissue. Hence, there is a demand for filtering, processing, and analysing this type of data. An abundance of methods and algorithms to do so is at our disposal for scalar images. However, since a componentwise approach is futile, goal-oriented processing of matrix fields seems to be challenging.

In this talk we will describe a framework that permits the transfer of rather general scalar image processing methods to the setting of fields of symmetric matrices (such as DT-MRI data). Furthermore we will explain how this operator-algebraic approach can be extended to process general matrix fields, for example, fields of 3D-rotation matrices.

Numerical experiments will demonstrate the feasibility, advantages, and shortcomings of this framework for processing matrix fields.

Anyone interested is cordially invited to participate in this seminar.

Contact: Dr. Andreas Kleefeld, JSC