Title: Geometric Approach to Segmentation in Diffusion Magnetic Resonance Imaging

Author: Sumit Kaushik

Defence: Monday, 29 June, 2020, 4pm, Meeting Room of the department

Supervisor: Jan Slovák

The anatomy of the biological structures in human brain plays an important role in study and diagnosis of medical conditions. The extraction of these structures in DMR images need appropriate methods and modelling. In this work, two standard segmentation methods are discussed. We have used deformable models and the dimensionality reduction method to project the data from high dimension to very small dimensions. On the projected lower dimensional data, we employed the classical k-means clustering for segmentation. Novelty in this work consists in exploitation of the similarity measures for the voxels based on the properties of Riemannian symmetric spaces, as well as quaternionic representation of transformations and their polar decompositions.

Video , thesis

Další seminář z algebry se koná 16.7.2020 od 13.00 online na platformě ZOOM. Informace pro připojení a další program semináře je zde.

Charles Walker

Characterization of Lax Orthogonal Factorization Systems

Abstrakt:
In this talk we will study the lax orthogonal factorization systems (LOFSs) of Clementino and Franco, with a particular focus on finding equivalent definitions of them. In particular, we wish to define them as a pair of classes E and M subject to some conditions. To achieve this, we will reduce the definition of a LOFS in terms of algebraic weak factorization systems (defined as a KZ 2-comonad L and KZ 2-monad R on the 2-category of arrows [2, C] with a 2-distributive law LR ⇒ RL) to a  more property-like definition (meaning a definition with less data but more conditions). To do this, we replace strict KZ 2-monads with the property-like definition of KZ pseudomonads in terms of kan-extensions due to Marmolejo and Wood. In addition, pseudo-distributive laws involving KZ pseudomonads have a property- like description which will be used. Thus one can deduce the conditions the classes E and M must satisfy. We will also consider some similarities and differences between LOFSs and (pseudo-)orthogonal factorization systems, and will extend their definitions to include universal fillers for squares which only commute up to a comparison 2-cell. This is joint work with John Bourke, and is currently a work in progress.