Statistical Computing on Non-Linear Spaces for Computational Anatomy

Xavier Pennec 1, * Pierre Fillard 1, 2, 3, *
Abstract : Computational anatomy is an emerging discipline that aims at analyzing and modeling the individual anatomy of organs and their biological variability across a population. However, understanding and modeling the shape of organs is made difficult by the absence of physical models for comparing different subjects, the complexity of shapes, and the high number of degrees of freedom implied. Moreover, the geometric nature of the anatomical features usually extracted raises the need for statistics on objects like curves, surfaces and deformations that do not belong to standard Euclidean spaces. We explain in this chapter how the Riemannian structure can provide a powerful framework to build generic statistical computing tools. We show that few computational tools derive for each Riemannian metric can be used in practice as the basic atoms to build more complex generic algorithms such as interpolation, filtering and anisotropic diffusion on fields of geometric features. This computational framework is illustrated with the analysis of the shape of the scoliotic spine and the modeling of the brain variability from sulcal lines where the results suggest new anatomical findings.
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Chapitre d'ouvrage
Paragios, Nikos and Duncan, Jim and Ayache, Nicholas. Handbook of Biomedical Imaging: Methodologies and Clinical Research, Springer, pp.147-168, 2015, 978-0-387-09748-0. 〈10.1007/978-0-387-09749-7_8〉
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https://hal.inria.fr/inria-00616201
Contributeur : Project-Team Asclepios <>
Soumis le : vendredi 19 juillet 2013 - 12:51:36
Dernière modification le : vendredi 22 juin 2018 - 01:20:25
Document(s) archivé(s) le : dimanche 20 octobre 2013 - 02:20:12

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Xavier Pennec, Pierre Fillard. Statistical Computing on Non-Linear Spaces for Computational Anatomy. Paragios, Nikos and Duncan, Jim and Ayache, Nicholas. Handbook of Biomedical Imaging: Methodologies and Clinical Research, Springer, pp.147-168, 2015, 978-0-387-09748-0. 〈10.1007/978-0-387-09749-7_8〉. 〈inria-00616201〉

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