Arsigny, Vincent (2006) Processing data in Lie groups: An algebraic approach. Application to non-linear registration and diffusion tensor MRI. PhD thesis INRIA Sophia-Antipolis, projet ASCLEPIOS, INRIA Sophia-Antipolis - Projet ASCLEPIOS, EP/X p.222.
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Alternative Locations: http://www.imprimerie.polytechnique.fr/Theses/Files/Arsigny.pdf
| Item Type: | PhD Thesis (PhD) |
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| Thesis Supervisor: | Nicholas, Ayache |
| Date: | November 2006 |
| Board of examiners: | Bloch, Isabelle and Gallier, Jean and Faugeras, Olivier and Mallat, Stéphane and Xavier, Pennec |
| Ecole Doctorale: | ED 447 ECOLE DOCTORALE DE L'ECOLE POLYTECHNIQUE |
| Discipline: | INRIA Sophia-Antipolis, projet ASCLEPIOS |
| Collection (Fonds): | EP/X |
| Institution: | EP/X |
| Department: | INRIA Sophia-Antipolis - Projet ASCLEPIOS |
| Subjects: | 2. Information and Communication Sciences and Technologies |
| Uncontrolled Keywords: | Riemannian geometry, Lie groups, Log-Euclidean metrics, Polyaffine transformations, Bi-invariant means, Diffeomorphisms, Non-rigid registration, Dt-mri, Tensors, Statistics, Fréchet means, Magnetic resonance imaging., géométrie Riemannienne, groupes de Lie, Métriques log-euclidiennes, Transformations polyaffine, Moyennes bi-invariantes, Difféomorphismes, Recalage non-linéaire, Irm-td, Tenseurs, Statistiques, moyennes de Fréchet, Imagerie par résonance magnétique. |
Table of content
1. Introduction
2. Fundamental Mathematical Tools
3. Log-Euclidean Metrics on Tensors
4. Log-Euclidean Processing of Diffusion Tensors
5. Original Polyrigid and Polyaffine Transformations
6. Log-Euclidean Polyaffine Transformations
7. Bi-Invariant Means in Lie Groups
8. Statistics on Diffeomorphisms in a Log-Euclidean Framework
9. Conclusions and Perspectives
| ID Code: | 2291 |
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| Deposited By: | Laurence Vidament |
| Deposited On: | 30 March 2007 |
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