Nina Miolane

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We use tools from geometric statistics to analyze the usual estimation procedure of a template shape. This applies to shapes from landmarks, curves, surfaces, images etc. We demonstrate the asymptotic bias of the template shape estimation using the stratified geometry of the shape space. We give a Taylor expansion of the bias with respect to a parameter σ(More)
Usual statistics are defined, studied and implemented on Euclidean spaces. But what about statistics on other mathematical spaces, like manifolds with additional properties: Lie groups, Quotient spaces, Stratified spaces etc? How can we describe the interaction between statistics and geometry? The structure of Quotient space in particular is widely used to(More)
In computational anatomy, organ’s shapes are often modeled as deformations of a reference shape, i.e., as elements of a Lie group. To analyze the variability of the human anatomy in this framework, we need to perform statistics on Lie groups. A Lie group is a manifold with a consistent group structure. Statistics on Riemannian manifolds have been well(More)
In the era of big data, one may apply generic learning algorithms for medical computer vision. But such algorithms are often ”black-boxes” and as such, hard to interpret. We still need new constructive models, which could eventually feed the big data framework. Where can one find inspiration for new models in medical computer vision? The emerging field of(More)
Bijan Afsari Young Joon Ahn Andrés Almansa Andreas Alpers L. Alvarez Eric Andres Michel Antunes Erchan Aptoula Pablo Arias Ery Arias-Castro Jean-Francois Aujol George Azzopardi Martin Bähr Lu Bai Peter Balazs Coloma Ballester Joao Barreto Thomas Batard Joost Batenburg Étienne Baudrier Amir Beck Alexander Beigl Martin Benning Ronny Bergmann Bejamin Berkels(More)
Geometric statistics for Computational Anatomy This thesis develops Geometric Statistics for the quantitative analysis of organ shapes in Computational Anatomy. Statistics is a science that studies methods of inference from data which often belong to vector spaces, i.e. linear spaces. In contrast, Geometric statistics generalizes statistics for data(More)
Lie groups appear in many fields fromMedical Imaging to Robotics. In Medical Imaging and particularly in Computational Anatomy, an organ’s shape is often modeled as the deformation of a reference shape, in other words: as an element of a Lie group. In this framework, if one wants to model the variability of the human anatomy, e.g. in order to help diagnosis(More)
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