Foundations of Geometric Statistics and Their Application in the Life Sciences

Advances in Geometric Statistics for Manifold Dimension Reduction

Author(s): Xavier Pennec
Published in: Handbook of Variational Methods for Nonlinear Geometric Data, 2020, Page(s) 339-359, ISBN 978-3-030-31350-0
Publisher: Springer International Publishing
DOI: 10.1007/978-3-030-31351-7_11

Beyond Riemannian geometry: The affine connection setting for transformation groups

Author(s): Pennec, Xavier; Lorenzi, Marco
Published in: Riemannian Geometric Statistics in Medical Image Analysis, 2021, Page(s) pp.169-229, ISBN 978-0-12-814725-2
Publisher: Academic Press
DOI: 10.1016/b978-0-12-814725-2.00012-1

Manifold-valued image processing with SPD matrices

Author(s): Xavier Pennec
Published in: Riemannian Geometric Statistics in Medical Image Analysis, 2020, Page(s) 75-134, ISBN 9780-128147252
Publisher: 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

Author(s): Nicolas Guigui; Xavier Pennec
Published in: Handbook of Statistics, volume 46: Geometry and Statistics; Editors: Frank Nielsen; Arni S.R. Srinivasa Rao; C.R. Rao., Issue 46, 2022, Page(s) 285-326, ISBN 978-0-323-91345-4
Publisher: 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

Author(s): Xavier Pennec
Published in: Digital Anatomy - Applications of Virtual, Mixed and Augmented Reality, 2021, Page(s) 159-183, ISBN 978-3-030-61904-6
Publisher: 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

Author(s): Emmanuel Chevallier, Nicolas Guigui
Published in: Entropy, Issue 22/4, 2020, Page(s) 432, ISSN 1099-4300
Publisher: Multidisciplinary Digital Publishing Institute (MDPI)
DOI: 10.3390/e22040432

O(n)-invariant Riemannian metrics on SPD matrices

Author(s): Yann Thanwerdas; Xavier Pennec
Published in: Linear Algebra and its Applications, Issue Vol. 661, 2023, Page(s) 163-201, ISSN 0024-3795
Publisher: Elsevier BV
DOI: 10.1016/j.laa.2022.12.009

Theoretically and computationally convenient geometries on full-rank correlation matrices

Author(s): Yann Thanwerdas; Xavier Pennec
Published in: SIAM Journal on Matrix Analysis and Applications, Issue Vol. 43, no 4, 2022, Page(s) 1851 - 1872, ISSN 1095-7162
Publisher: SIAM
DOI: 10.48550/arxiv.2201.06282

The Measurement and Analysis of Shapes

Author(s): Benn, James; Marsland, Stephen
Published in: Annals of Global Analysis and Geometry, inPress, 62, pp.47-70., Issue 62, 2022, Page(s) 47–70, ISSN 0232-704X
Publisher: Kluwer Academic Publishers
DOI: 10.1007/s10455-022-09839-z

Permutation-Invariant Log-Euclidean Geometries on Full-Rank Correlation Matrices

Author(s): Yann Thanwerdas
Published in: SIAM Journal on Matrix Analysis and Applications, Issue 45, 2024, Page(s) 930-953, ISSN 0895-4798
Publisher: Society for Industrial and Applied Mathematics
DOI: 10.1137/22m1538144

Bures–Wasserstein Minimizing Geodesics between Covariance Matrices of Different Ranks

Author(s): Yann Thanwerdas, Xavier Pennec
Published in: SIAM Journal on Matrix Analysis and Applications, Issue 44, 2023, Page(s) 1447-1476, ISSN 0895-4798
Publisher: Society for Industrial and Applied Mathematics
DOI: 10.1137/22m149168x

Numerical Accuracy of Ladder Schemes for Parallel Transport on Manifolds

Author(s): Nicolas Guigui, Xavier Pennec
Published in: Foundations of Computational Mathematics, 2021, ISSN 1615-3375
Publisher: Springer Verlag
DOI: 10.1007/s10208-021-09515-x

Geometry of sample spaces

Author(s): Philipp Harms, Peter W. Michor, Xavier Pennec, Stefan Sommer
Published in: Differential Geometry and its Applications, Issue 90, 2023, Page(s) 102029, ISSN 0926-2245
Publisher: Elsevier BV
DOI: 10.1016/j.difgeo.2023.102029

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

Author(s): Nicolas Guigui; Nina Miolane; Xavier Pennec
Published in: Foundations and Trends® in Machine Learning, Issue Vol 16, Issue 3, 2023, Page(s) 329-493, ISSN 1935-8237
Publisher: Now Publishers Inc.
DOI: 10.1561/2200000098

Classifying histograms of medical data using information geometry of beta distributions

Author(s): Alice Le Brigant, Nicolas Guigui, Sana Rebbah, Stéphane Puechmorel
Published in: IFAC-PapersOnLine, Issue 54, 2021, Page(s) 514-520, ISSN 2405-8963
Publisher: International Federation of Automatic Control.
DOI: 10.1016/j.ifacol.2021.06.110

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

Author(s): Raphaël Sivera, Nicolas Capet, Valeria Manera, Roxane Fabre, Marco Lorenzi, Hervé Delingette, Xavier Pennec, Nicholas Ayache, Philippe Robert
Published in: Neurobiology of Aging, Issue 94, 2020, Page(s) 50-59, ISSN 0197-4580
Publisher: Elsevier BV
DOI: 10.1016/j.neurobiolaging.2019.11.020

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

Author(s): Yann Thanwerdas; Xavier Pennec
Published in: Differential Geometry and its Applications, Issue Vol.81, 2022, Page(s) 101867, ISSN 0926-2245
Publisher: Elsevier BV
DOI: 10.1016/j.difgeo.2022.101867

Graph alignment exploiting the spatial organization improves the similarity of brain networks

Author(s): Anna Calissano, Theodore Papadopoulo, Xavier Pennec, Samuel Deslauriers‐Gauthier
Published in: Human Brain Mapping, Issue 45, 2024, Page(s) e26554, ISSN 1065-9471
Publisher: John Wiley & Sons Inc.
DOI: 10.1002/hbm.26554

Geomstats: A Python Package for Riemannian Geometry in Machine Learning

Author(s): 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
Published in: JMLR - Journal of Machine Learning Research, Issue 21, 2020, Page(s) 19-027, ISSN 1533-7928
Publisher: JMLR

Parallel Transport on Kendall Shape Spaces

Author(s): Nicolas Guigui, Elodie Maignant, Alain Trouvé, Xavier Pennec
Published in: Geometric Science of Information - 5th International Conference, GSI 2021, Paris, France, July 21–23, 2021, Proceedings, Issue 12829, 2021, Page(s) 103-110, ISBN 978-3-030-80208-0
Publisher: Springer International Publishing
DOI: 10.1007/978-3-030-80209-7_12

Rethinking the Riemannian Logarithm on Flag Manifolds as an Orthogonal Alignment Problem

Author(s): Tom Szwagier, Xavier Pennec
Published in: Lecture Notes in Computer Science, Geometric Science of Information, Issue Proc of Geometric Science of Information (GSI 2023) - LNCS 14071, 2023, Page(s) 375-383
Publisher: Springer Nature Switzerland
DOI: 10.1007/978-3-031-38271-0_37

Cardiac Motion Modeling With Parallel Transport And Shape Splines

Author(s): Nicolas Guigui, Pamela Moceri, Maxime Sermesant, Xavier Pennec
Published in: 2021 IEEE 18th International Symposium on Biomedical Imaging (ISBI), 2021, Page(s) 1394-1397, ISBN 978-1-6654-1246-9
Publisher: IEEE
DOI: 10.1109/isbi48211.2021.9433887

Towards Quotient Barycentric Subspaces

Author(s): Anna Calissano, Elodie Maignant, Xavier Pennec
Published in: Lecture Notes in Computer Science, Geometric Science of Information, Issue LNCS 14071, 2023, Page(s) 366-374
Publisher: Springer Nature Switzerland
DOI: 10.1007/978-3-031-38271-0_36

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

Author(s): Yann Thanwerdas, Xavier Pennec
Published in: Geometric Science of Information - 5th International Conference, GSI 2021, Paris, France, July 21–23, 2021, Proceedings, Issue 12829, 2021, Page(s) 93-102, ISBN 978-3-030-80208-0
Publisher: Springer International Publishing
DOI: 10.1007/978-3-030-80209-7_11

Riemannian Locally Linear Embedding with Application to Kendall Shape Spaces

Author(s): Elodie Maignant, Alain Trouvé, Xavier Pennec
Published in: Lecture Notes in Computer Science, Geometric Science of Information, Issue LNCS 14071, 2023, Page(s) 12-20
Publisher: Springer Nature Switzerland
DOI: 10.1007/978-3-031-38271-0_2

Exploration of Balanced Metrics on Symmetric Positive Definite Matrices

Author(s): Yann Thanwerdas, Xavier Pennec
Published in: Geometric Science of Information - 4th International Conference, GSI 2019, Toulouse, France, August 27–29, 2019, Proceedings, Issue 11712, 2019, Page(s) 484-493, ISBN 978-3-030-26979-1
Publisher: Springer International Publishing
DOI: 10.1007/978-3-030-26980-7_50

Symmetric Algorithmic Components for Shape Analysis with Diffeomorphisms

Author(s): Nicolas Guigui, Shuman Jia, Maxime Sermesant, Xavier Pennec
Published in: Geometric Science of Information - 4th International Conference, GSI 2019, Toulouse, France, August 27–29, 2019, Proceedings, Issue 11712, 2019, Page(s) 759-768, ISBN 978-3-030-26979-1
Publisher: 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

Author(s): Yann Thanwerdas, Xavier Pennec
Published in: Geometric Science of Information - 4th International Conference, GSI 2019, Toulouse, France, August 27–29, 2019, Proceedings, Issue 11712, 2019, Page(s) 502-510, ISBN 978-3-030-26979-1
Publisher: 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

Author(s): Emmanuel Chevallier; Nicolas Guigui
Published in: Proc. of SPIGL 2020: Geometric Structures of Statistical Physics, Information Geometry, and Learning, 2021, Page(s) 96–106
Publisher: Springer
DOI: 10.1007/978-3-030-77957-3_5

Introduction to Geometric Learning in Python with Geomstats

Author(s): 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
Published in: Proceedings of the 19th Python in Science Conference, 2020, Page(s) 48-57
Publisher: SciPy
DOI: 10.25080/majora-342d178e-007

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

Author(s): Nicolas Guigui, Xavier Pennec
Published in: Geometric Science of Information - 5th International Conference, GSI 2021, Paris, France, July 21–23, 2021, Proceedings, Issue 12829, 2021, Page(s) 119-126, ISBN 978-3-030-80208-0
Publisher: Springer International Publishing
DOI: 10.1007/978-3-030-80209-7_14

Characterization of Invariant Inner Products

Author(s): Yann Thanwerdas, Xavier Pennec
Published in: Lecture Notes in Computer Science, Geometric Science of Information, Issue Proc of Geometric Science of Information (GSI 2023) - LNCS 14071, 2023, Page(s) 384-391
Publisher: Springer Nature Switzerland
DOI: 10.1007/978-3-031-38271-0_38

Tangent Phylogenetic PCA

Author(s): Morten Akhøj, Xavier Pennec, Stefan Sommer
Published in: Lecture Notes in Computer Science, Image Analysis, Issue Proc of Scandinavian Conference on Image Analysis 2023, LNCS13886, 2023, Page(s) 77-90
Publisher: Springer Nature Switzerland
DOI: 10.1007/978-3-031-31438-4_6

Investigation of the Impact of Normalization on the Study of Interactions Between Myocardial Shape and Deformation

Author(s): Maxime Di Folco, Nicolas Guigui, Patrick Clarysse, Pamela Moceri, Nicolas Duchateau
Published in: Lecture Notes in Computer Science, Functional Imaging and Modeling of the Heart, Issue LNCS 12738, 2024, Page(s) 223-231
Publisher: Springer International Publishing
DOI: 10.1007/978-3-030-78710-3_22

Riemannian and stratified geometries on covariance and correlation matrices

Author(s): Thanwerdas, Yann
Published in: Issue 2022-05-22, 2022
Publisher: Universite Côte d'Azur

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

Author(s): Guigui, Nicolas
Published in: Issue 2023-11-18, 2021
Publisher: Univresité Côte d'Azur

Riemannian Geometric Statistics in Medical Image Analysis

Author(s): Xavier Pennec, Stefan Sommer, Tom Fletcher
Published in: 2020, ISBN 9780-128147252
Publisher: 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

Author(s): 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
Published in: Lecture Notes in Computer Science (LNCS), Issue 11846, 2019, ISBN 978-3-030-33226-6
Publisher: Springer
DOI: 10.1007/978-3-030-33226-6

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