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Foundations of Geometric Statistics and Their Application in the Life Sciences

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Publications

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

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, 22/4, 2020, Page(s) 432, ISSN 1099-4300
Publisher: Multidisciplinary Digital Publishing Institute (MDPI)
DOI: 10.3390/e22040432

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

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, 94, 2020, Page(s) 50-59, ISSN 0197-4580
Publisher: Elsevier BV
DOI: 10.1016/j.neurobiolaging.2019.11.020

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, 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

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

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, 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

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, 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, 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, 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

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, 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

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), 11846, 2019, ISBN 978-3-030-33226-6
Publisher: Springer
DOI: 10.1007/978-3-030-33226-6