Clark Hall 314
PhD Student in Mathematical Shape Analysis
Center for Mathematical studies and their Applications (CMLA) at ENS Cachan
Geometric Growth Models for Computational Anatomy based on Diffeomorphic Matching
Abstract: The Large Deformation Diffeomorphic Metric Mapping (LDDMM) framework has proved to be highly efficient for addressing theproblem of modeling and analysis of the variability of populations of shapes, allowing for the direct comparison and quantization of diffeomorphic morphometric changes. However, the analysis of medical imaging data also requires the processing of more complex changes, which especially appear during growth or aging phenomena. The observed organisms are subject to transformations over time that are no longer diffeomorphic, at least in a biological sense. One reason might be a gradual creation of new material uncorrelated to the preexisting one. For this purpose, we offer to extend the LDDMM framework to address the problem of non-diffeomorphic structural variations in longitudinal scenarios during a growth or degenerative process. We keep the geometric central concept of a group of deformations acting on a shape space. This action induces a pointwise expression of the dynamic of the shape. The introduction of partial mappings leads to a time-varying dynamicthat modifies the action of the group of deformations. In growth scenarios, the shape evolves via inner partial mappings induced by a growth dynamic. The underlying minimization problem requires an adapted framework to consider a new set of cost functions (penalization term on the deformation).