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Title: Geometric statistics for template shape estimation in computational anatomy Authors:  Nina Miolane - Inria Stanford (France) [presenting]
Abstract: Statistics is a science that studies methods of inference from observed data which often belong to vector spaces i.e. linear spaces. In contrast, Geometric statistics generalizes statistics for data belonging to manifolds, i.e. non-linear spaces. Such non-linear data spaces emerge naturally in Computational Anatomy. Organ shapes can be modeled as the equivalence of their configurations in the 3D space under the action of rotations and translations. In this case, they are elements of a quotient space, which is a stratified manifold. Geometric Statistics on stratified manifolds allow to analyze the properties of the algorithm of template (organ) shape computation. We show that this algorithm - used for more than 15 years in the medical imaging community - has a systematic bias. We also provide correction methods.