Dagstuhl Annual Report January - December 2011

The International Conference and Research Center for Computer Science is a non-profit organization. Its objective is to promote world-class research in computer science and to host research seminars which enable new ideas to be showcased, problems to be discussed and the course to be set for future development in this field. The work being done to run this informatics center is documented in this report for the business year 2011

Visualization and Processing of Tensors and Higher Order Descriptors for Multi-Valued Data (Dagstuhl Seminar 11501)

This report documents the program and the outcomes of Dagstuhl Seminar 11501 "Visualization and Processing of Tensors and Higher Order Descriptors for Multi-Valued Data", taking place December 11-16, 2011. The Seminar gathered 26 senior and younger researchers from various countries in the unique atmosphere offered by Schloss Dagstuhl. The focus of the seminar was to discuss modern and emerging methods for analysis and visualization of tensor and higher order descriptors from medical imaging and engineering applications. Abstracts of the talks are collected in this report

4th Order Symmetric Tensors and Positive ADC Modelling

International audienceHigh Order Cartesian Tensors (HOTs) were introduced in Generalized DTI (GDTI) to overcome the limitations of DTI. HOTs can model the apparent diffusion coefficient (ADC) with greater accuracy than DTI in regions with fiber heterogeneity. Although GDTI HOTs were designed to model positive diffusion, the straightforward least square (LS) estimation of HOTs doesn't guarantee positivity. In this chapter we address the problem of estimating 4th order tensors with positive diffusion profiles. Two known methods exist that broach this problem, namely a Riemannian approach based on the algebra of 4th order tensors, and a polynomial approach based on Hilbert's theorem on non-negative ternary quartics. In this chapter, we review the technicalities of these two approaches, compare them theoretically to show their pros and cons, and compare them against the Euclidean LS estimation on synthetic, phantom and real data to motivate the relevance of the positive diffusion profile constraint