Foundations of Geometric Statistics and Their Application in the Life Sciences

Advances in Geometric Statistics for Manifold Dimension Reduction

Autori: Xavier Pennec
Pubblicato in: Handbook of Variational Methods for Nonlinear Geometric Data, 2020, Pagina/e 339-359, ISBN 978-3-030-31350-0
Editore: Springer International Publishing
DOI: 10.1007/978-3-030-31351-7_11

Beyond Riemannian geometry: The affine connection setting for transformation groups

Autori: Pennec, Xavier; Lorenzi, Marco
Pubblicato in: Riemannian Geometric Statistics in Medical Image Analysis, 2021, Pagina/e pp.169-229, ISBN 978-0-12-814725-2
Editore: Academic Press
DOI: 10.1016/b978-0-12-814725-2.00012-1

Manifold-valued image processing with SPD matrices

Autori: Xavier Pennec
Pubblicato in: Riemannian Geometric Statistics in Medical Image Analysis, 2020, Pagina/e 75-134, ISBN 9780-128147252
Editore: Academic Press
DOI: 10.1016/B978-0-12-814725-2.00010-8

Parallel transport, a central tool in geometric statistics for computational anatomy: Application to cardiac motion modeling

Autori: Nicolas Guigui; Xavier Pennec
Pubblicato in: Handbook of Statistics, volume 46: Geometry and Statistics; Editors: Frank Nielsen; Arni S.R. Srinivasa Rao; C.R. Rao., Numero 46, 2022, Pagina/e 285-326, ISBN 978-0-323-91345-4
Editore: Elsevier - Academic Press
DOI: 10.1016/bs.host.2022.03.006

Statistical Analysis of Organs’ Shapes and Deformations: The Riemannian and the Affine Settings in Computational Anatomy

Autori: Xavier Pennec
Pubblicato in: Digital Anatomy - Applications of Virtual, Mixed and Augmented Reality, 2021, Pagina/e 159-183, ISBN 978-3-030-61904-6
Editore: Springer International Publishing
DOI: 10.1007/978-3-030-61905-3_9

A Bi-Invariant Statistical Model Parametrized by Mean and Covariance on Rigid Motions

Autori: Emmanuel Chevallier, Nicolas Guigui
Pubblicato in: Entropy, Numero 22/4, 2020, Pagina/e 432, ISSN 1099-4300
Editore: Multidisciplinary Digital Publishing Institute (MDPI)
DOI: 10.3390/e22040432

O(n)-invariant Riemannian metrics on SPD matrices

Autori: Yann Thanwerdas; Xavier Pennec
Pubblicato in: Linear Algebra and its Applications, Numero Vol. 661, 2023, Pagina/e 163-201, ISSN 0024-3795
Editore: Elsevier BV
DOI: 10.1016/j.laa.2022.12.009

Theoretically and computationally convenient geometries on full-rank correlation matrices

Autori: Yann Thanwerdas; Xavier Pennec
Pubblicato in: SIAM Journal on Matrix Analysis and Applications, Numero Vol. 43, no 4, 2022, Pagina/e 1851 - 1872, ISSN 1095-7162
Editore: SIAM
DOI: 10.48550/arxiv.2201.06282

The Measurement and Analysis of Shapes

Autori: Benn, James; Marsland, Stephen
Pubblicato in: Annals of Global Analysis and Geometry, inPress, 62, pp.47-70., Numero 62, 2022, Pagina/e 47–70, ISSN 0232-704X
Editore: Kluwer Academic Publishers
DOI: 10.1007/s10455-022-09839-z

Numerical Accuracy of Ladder Schemes for Parallel Transport on Manifolds

Autori: Nicolas Guigui, Xavier Pennec
Pubblicato in: Foundations of Computational Mathematics, 2021, ISSN 1615-3375
Editore: Springer Verlag
DOI: 10.1007/s10208-021-09515-x

Introduction to Riemannian Geometry and Geometric Statistics: from basic theory to implementation with Geomstats

Autori: Nicolas Guigui; Nina Miolane; Xavier Pennec
Pubblicato in: Foundations and Trends® in Machine Learning, Numero Vol 16, Numero 3, 2023, Pagina/e 329-493, ISSN 1935-8237
Editore: Now Publishers Inc.
DOI: 10.1561/2200000098

Voxel-based assessments of treatment effects on longitudinal brain changes in the Multidomain Alzheimer Preventive Trial cohort

Autori: Raphaël Sivera, Nicolas Capet, Valeria Manera, Roxane Fabre, Marco Lorenzi, Hervé Delingette, Xavier Pennec, Nicholas Ayache, Philippe Robert
Pubblicato in: Neurobiology of Aging, Numero 94, 2020, Pagina/e 50-59, ISSN 0197-4580
Editore: Elsevier BV
DOI: 10.1016/j.neurobiolaging.2019.11.020

The geometry of mixed-Euclidean metrics on symmetric positive definite matrices

Autori: Yann Thanwerdas; Xavier Pennec
Pubblicato in: Differential Geometry and its Applications, Numero Vol.81, 2022, Pagina/e 101867, ISSN 0926-2245
Editore: Elsevier BV
DOI: 10.1016/j.difgeo.2022.101867

Geomstats: A Python Package for Riemannian Geometry in Machine Learning

Autori: Nina Miolane, Nicolas Guigui, Alice Le Brigant, Johan Mathe, Benjamin Hou, Yann Thanwerdas, Stefan Heyder, Olivier Peltre, Niklas Koep, Hadi Zaatiti, Hatem Hajri, Yann Cabanes, Thomas Gerald, Paul Chauchat, Christian Shewmake, Daniel Brooks, Bernhard Kainz, Claire Donnat, Susan Holmes, Xavier Pennec
Pubblicato in: JMLR - Journal of Machine Learning Research, Numero 21, 2020, Pagina/e 19-027, ISSN 1533-7928
Editore: JMLR

Parallel Transport on Kendall Shape Spaces

Autori: Nicolas Guigui, Elodie Maignant, Alain Trouvé, Xavier Pennec
Pubblicato in: Geometric Science of Information - 5th International Conference, GSI 2021, Paris, France, July 21–23, 2021, Proceedings, Numero 12829, 2021, Pagina/e 103-110, ISBN 978-3-030-80208-0
Editore: Springer International Publishing
DOI: 10.1007/978-3-030-80209-7_12

Cardiac Motion Modeling With Parallel Transport And Shape Splines

Autori: Nicolas Guigui, Pamela Moceri, Maxime Sermesant, Xavier Pennec
Pubblicato in: 2021 IEEE 18th International Symposium on Biomedical Imaging (ISBI), 2021, Pagina/e 1394-1397, ISBN 978-1-6654-1246-9
Editore: IEEE
DOI: 10.1109/isbi48211.2021.9433887

Geodesics and Curvature of the Quotient-Affine Metrics on Full-Rank Correlation Matrices

Autori: Yann Thanwerdas, Xavier Pennec
Pubblicato in: Geometric Science of Information - 5th International Conference, GSI 2021, Paris, France, July 21–23, 2021, Proceedings, Numero 12829, 2021, Pagina/e 93-102, ISBN 978-3-030-80208-0
Editore: Springer International Publishing
DOI: 10.1007/978-3-030-80209-7_11

Exploration of Balanced Metrics on Symmetric Positive Definite Matrices

Autori: Yann Thanwerdas, Xavier Pennec
Pubblicato in: Geometric Science of Information - 4th International Conference, GSI 2019, Toulouse, France, August 27–29, 2019, Proceedings, Numero 11712, 2019, Pagina/e 484-493, ISBN 978-3-030-26979-1
Editore: Springer International Publishing
DOI: 10.1007/978-3-030-26980-7_50

Symmetric Algorithmic Components for Shape Analysis with Diffeomorphisms

Autori: Nicolas Guigui, Shuman Jia, Maxime Sermesant, Xavier Pennec
Pubblicato in: Geometric Science of Information - 4th International Conference, GSI 2019, Toulouse, France, August 27–29, 2019, Proceedings, Numero 11712, 2019, Pagina/e 759-768, ISBN 978-3-030-26979-1
Editore: Springer International Publishing
DOI: 10.1007/978-3-030-26980-7_79

Is Affine-Invariance Well Defined on SPD Matrices? A Principled Continuum of Metrics

Autori: Yann Thanwerdas, Xavier Pennec
Pubblicato in: Geometric Science of Information - 4th International Conference, GSI 2019, Toulouse, France, August 27–29, 2019, Proceedings, Numero 11712, 2019, Pagina/e 502-510, ISBN 978-3-030-26979-1
Editore: Springer International Publishing
DOI: 10.1007/978-3-030-26980-7_52

Wrapped statistical models on manifolds: motivations, the case SE(n), and generalization to symmetric spaces

Autori: Emmanuel Chevallier; Nicolas Guigui
Pubblicato in: Proc. of SPIGL 2020: Geometric Structures of Statistical Physics, Information Geometry, and Learning, 2021, Pagina/e 96–106
Editore: Springer
DOI: 10.1007/978-3-030-77957-3_5

Introduction to Geometric Learning in Python with Geomstats

Autori: Nina Miolane, Nicolas Guigui, Hadi Zaatiti, Christian Shewmake, Hatem Hajri, Daniel Brooks, Alice Le Brigant, Johan Mathe, Benjamin Hou, Yann Thanwerdas, Stefan Heyder, Olivier Peltre, Niklas Koep, Yann Cabanes, Thomas Gerald, Paul Chauchat, Bernhard Kainz, Claire Donnat, Susan Holmes, Xavier Pennec
Pubblicato in: Proceedings of the 19th Python in Science Conference, 2020, Pagina/e 48-57
Editore: SciPy
DOI: 10.25080/majora-342d178e-007

A Reduced Parallel Transport Equation on Lie Groups with a Left-Invariant Metric

Autori: Nicolas Guigui, Xavier Pennec
Pubblicato in: Geometric Science of Information - 5th International Conference, GSI 2021, Paris, France, July 21–23, 2021, Proceedings, Numero 12829, 2021, Pagina/e 119-126, ISBN 978-3-030-80208-0
Editore: Springer International Publishing
DOI: 10.1007/978-3-030-80209-7_14

Riemannian and stratified geometries on covariance and correlation matrices

Autori: Thanwerdas, Yann
Pubblicato in: Numero 2022-05-22, 2022
Editore: Universite Côte d'Azur

Computational methods for statistical estimation on Riemannian manifolds and application to the study of cardiac deformations

Autori: Guigui, Nicolas
Pubblicato in: Numero 2023-11-18, 2021
Editore: Univresité Côte d'Azur

Riemannian Geometric Statistics in Medical Image Analysis

Autori: Xavier Pennec, Stefan Sommer, Tom Fletcher
Pubblicato in: 2020, ISBN 9780-128147252
Editore: Academic Press
DOI: 10.1016/C2017-0-01561-6

Multimodal Brain Image Analysis and Mathematical Foundations of Computational Anatomy - 4th International Workshop, MBIA 2019, and 7th International Workshop, MFCA 2019, Held in Conjunction with MICCAI 2019, Shenzhen, China, October 17, 2019, Proceedings

Autori: Dajiang Zhu, Jingwen Yan, Heng Huang, Li Shen, Paul M. Thompson, Carl-Fredrik Westin, Xavier Pennec, Sarang Joshi, Mads Nielsen, Tom Fletcher, Stanley Durrleman, Stefan Sommer
Pubblicato in: Lecture Notes in Computer Science (LNCS), Numero 11846, 2019, ISBN 978-3-030-33226-6
Editore: Springer
DOI: 10.1007/978-3-030-33226-6

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