Geometric Paradigms for MRI Analysis with Applications to Cardioimaging and Neuroimaging

Prof. Luc Florack - Department of Mathematics & Computer Science, Eindhoven University of Technology

April 24, 2015, 2:30 p.m. - April 24, 2015, 3:30 p.m.

McConnell Bldg. Rm. 12

Magnetic Resonance Imaging (MRI) is a non-invasive and highly versatile imaging modality, with unprecedented capabilities for disclosing in-vivo anatomical and functional information. Imaging protocols as well as image analysis paradigms are traditionally set up so as to convey this information to the radiologist in a format geared towards visual interpretation, supported by software platforms for interactive “data visualization” and add-ons for quantification of visual structures. 

The advent of increasingly sophisticated acquisition schemes, producing complex highcodimensional images, prohibits a direct visual approach, calling for a radically new paradigm, with a more compelling role for theory to address notorious inverse problems. Examples of these are “diffusion weighted MRI” and spatial modulation of magnetization, or “tagging MRI”. The data produced in these cases are “non-visual images” that admit quantification and visually exploration (“visual analytics”) only by virtue of an priori axiomatic framework for their interpretation. The necessary axiomatics emerges from the interplay of the physical sciences (mathematics, physics), and often leads to a revaluation of established theories originally developed in a different context.

Image researchers worldwide are starting to embrace the new paradigm, trying to “see what one can understand” rather than trying to “understand what one can see”. Physics, a rigorous and universal description language, are indispensable in this endeavor.

In this presentation I will illustrate the above rationale in the context of a differential geometric framework for the analysis of diffusion and tagging MRI data with “off-the-shelf” physics and mathematics from early twentieth century.


Luc Florack received his MSc degree in theoretical physics in 1989 and his PhD degree in 1993 (cum laude, top 2%) at Utrecht University, The Netherlands, under the supervision of professor Max Viergever and professor Jan Koenderink. During the period 1994-1995 he was an ERCIM/HCM research fellow at INRIA Sophia-Antipolis, France, with professor Olivier Faugeras, and at INESC Aveiro, Portugal, with professor Antonio Sousa Pereira. In 1996 he was an assistant research professor at DIKU, Copenhagen, Denmark, with professor Peter Johansen, on a grant from the Danish Research Council. In 1997 he returned to Utrecht University, were he became an assistant research professor at the Department of Mathematics and Computer Science. In 2001 he moved to Eindhoven University of Technology, Department of Biomedical Engineering, where he became an associate professor in 2002. In 2007 he was appointed full professor at the Department of Mathematics and Computer Science, establishing the chair of Mathematical Image Analysis, but he retained a part-time professorship at the former department. His research covers mathematical models of structural aspects of signals, images, and movies, particularly multiscale and differential geometric representations and their applications, with a focus on complex magnetic resonance images for cardiological and neurological applications. In 2010, with support of the Executive Board of Eindhoven University of Technology, he founded the Imaging Science & Technology research group (IST/e), a cross-divisional collaboration involving several academic groups on image acquisition, biomedical and mathematical image analysis, visualization and visual analytics.