A seminar in shape theory

I had a tip from Ozan Öktem about an upcoming seminar which deals with recent developments for mathematical methods applicable to shape recognition and classification.

Here is the detailed description:

Time: Wed 2010-09-29 kl 13.15 - 15.00
Place: Room 3733 Lindstedtsvägen 25
Contact: Ozan Öktem (790 6606) or Sandra Di Rocco (790 7168)
Weblink: http://www.kth.se/sci/institutioner/math/kalender/2.21854/seminars/an-overview-of-computational-anatomy-1.65738

An overview of Computational Anatomy
Joint CIAM/Algebra and Geometry Seminar by Stéphanie Allassonnière from Centre de Mathematiques Appliquees, Ecole Polytechnique.

The seminar will provide an overview of Computational Anatomy which is an emerging discipline at the interface of geometry, statistics and image analysis, that aims to analyse and model biological shape variability at the population scale. The goal is not only to model the normal mean anatomy and its normal variations among a population, but also to discover morphological differences between normal and pathological populations, and possibly to detect, model and classify pathologies from structural abnormalities. Another goal is to correlate this variability information with other functional, genetic or structural information.

First, the goals and mathematical tools which are needed for such methods are presented. In particular, the focus will be on the deformable template framework, which assumes that the shapes that come from a given group (in term of age, sex, disease) are close to each other up to a class of deformations.

Next, the registration issue is introduced which is the central tool in this context. Its goal is to find the 'optimal' deformation that maps one shape onto another one. Some techniques which have been proposed to solve it will be presented bringing us to the Large Deformation Diffeomorphic Metric Mapping (LDDMM). This mathematically well-grounded method allows one to consider the registration of landmarks, curves, surfaces and images within the same framework.

The last part of the presentation will focus on the probabilistic and statistical questions that arise when we are provided with a population of images or shapes. The main issue is how to compute a "mean" and a "deviation" from this set. The main tools and results will be introduced whereas a more specific tutorial given the day after will discuss further issues.

Stéphanie Allassonnière received her PhD in 2007 from the Université of Paris 13 (France) in Applied Mathematics . The thesis was supervised by Alain Trouvé (ENS- Cachan) and Laurent Younes (CIS - Johns Hopkins University, Baltimore) and dealt with statistical estimation of template images using generative models. She then spent one year as a postdoctoral fellow in the CIS working with Laurent Younes and Michael Miller on statistics for medical imaging. Since 2008, she have been Assistant Professor in Ecole Polytechnique in the Applied Mathematics Department where she has continued her research on statistical analysis of images and deformations. In particular, she is studying the mathematical properties of the statistical estimators and stochastic estimation algorithms. She was recently awarded the "Prix Excellencia 2010" for her research work.