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Learning adapted coordinate systems for the statistical analysis of anatomical shapes. Application to Alzheimer's disease progression modeling

Alexandre Bône 1, 2 
2 ARAMIS - Algorithms, models and methods for images and signals of the human brain
SU - Sorbonne Université, Inria de Paris, ICM - Institut du Cerveau et de la Moëlle Epinière = Brain and Spine Institute
Abstract : This thesis aims to build coordinate systems for shapes i.e. finite-dimensional metric spaces where shapes are represented by vectors. The goal of building such coordinate systems is to allow and facilitate the statistical analysis of shape data sets. The end-game motivation of our work is to predict and sub-type Alzheimer’s disease, based in part on knowledge extracted from banks of brain medical images. Even if these data banks are longitudinal, their variability remains mostly due to the large and normal inter-individual variability of the brain. The variability due to the progression of pathological alterations is of much smaller amplitude. The central objective of this thesis is to develop a coordinate system adapted for the statistical analysis of longitudinal shape data sets, able to disentangle these two sources of variability. As shown in the literature, the parallel transport operator can be leveraged to achieve this desired disentanglement, for instance by defining the notion of exp-parallel curves on a manifold. Using this tool on shape spaces comes however with theoretical and computational challenges, tackled in the first part of this thesis. Finally, if shape spaces are commonly equipped with a manifold-like structure in the field of computational anatomy, the underlying classes of diffeomorphisms are however most often largely built and parameterized without taking into account the data at hand. The last major objective of this thesis is to build deformation-based coordinate systems where the parameterization of deformations is adapted to the data set of interest.
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Submitted on : Monday, October 4, 2021 - 6:42:10 PM
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Alexandre Bône. Learning adapted coordinate systems for the statistical analysis of anatomical shapes. Application to Alzheimer's disease progression modeling. Computer Vision and Pattern Recognition [cs.CV]. Sorbonne Université, 2020. English. ⟨NNT : 2020SORUS273⟩. ⟨tel-03364632v2⟩

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