Mixture of Kernels and Iterated Semidirect Product of Diffeomorphisms Groups
Open accessAbstract
In the framework of large deformation diffeomorphic metric mapping (LDDMM), a multiscale theory for the diffeomorphism group is developed based on previous works of the authors. The purpose of this paper is (1) to develop in detail a variational approach for multiscale analysis of diffeomorphisms, (2) to generalize to several scales the the semidirect product representation, and (3) to illustrate the resulting diffeomorphic decomposition on synthetic and real images. We also show that the so-called kernel bundle method and the mixture of kernels are equivalent.
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Gutierrez et al. use a regression forest and gradient boosted trees with hand-crafted features to learn update steps for rigid and B-spline registration.
“Gutierrez et al. [9] use a regression forest and gradient boosted trees [8] based on hand-crafted features to learn update steps for a rigid and a B-spline registration model.”
From Quicksilver: Fast predictive image registration – A deep learning approach (2017) · cites this paper as [8]
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Variational problems on flows of diffeomorphisms for image matching
Dupuis, P., Grenander, U., & Miller, M. I. (1998) · Quarterly of Applied Mathematics · doi:10.1090/qam/1632326 · Cited by 447 · see citing works
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- N. Aronszajn. Theory of reproducing kernels. Trans. Amer. Math. Soc., 68:337-404, 1950.
- M. F. Beg, M. I. Miller, A. Trouvé, and L. Younes. Computing large deformation metric mappings via geodesic flows of diffeomorphisms. Int. J. Comput. Vision, 61(2):139-157, 2005.
- H. Brezis. Analyse Fonctionnelle, Théorie et Applications. Masson, Paris, 1983. English translation: Springer Verlag.
- M. Kloft, U. Brefeld, S. Sonnenburg, P. Laskov, K.-R. Müller, and A. Zien. Efficient and accurate Lp-norm multiple kernel learning. In Y. Bengio, D. Schuurmans, J. Lafferty, C. K. I. Williams, and A. Culotta, editors, Advances in Neural Infor- mation Processing Systems 22, pages 997-1005. The MIT Press, 2009.
- M. Murgasova, P. Aljabar, L. Srinivasan, S. J. Counsell, V. Doria, A. Serag, I. S. Gousias, J. P. Boardman, M. A. Rutherford, A. D. Edwards, J. V. Hajnal, and D. Rueckert. A dynamic 4d probabilistic atlas of the developing brain. Neuroim- age, 54(4):2750 -2763, 2011.
- L. Risser, F.-X. Vialard, R. Wolz, D. D. Holm, and D. Rueckert. Simultaneous fine and coarse diffeomorphic registration: Application to the atrophy measurement in alzheimer's disease. In Medical Image Computing and Computer-Assisted In- tervention -MICCAI 2010, volume 6362 of Lecture Notes in Computer Science, pages 610-617, Berlin, 2010. Springer.
- L. Risser, F.-X. Vialard, R. Wolz, M. Murgasova, D. D. Holm, and D. Rueckert. Simultaneous multiscale registration using large deformation diffeomorphic metric mapping. IEEE Trans. Med. Imaging, 2011.
- N. Singh, P. T. Fletcher, J. S. Preston, L. Ha, R. King, J. S. Marron, M. Wiener, and S. Joshi. Multivariate statistical analysis of deformation momenta relating anatomical shape to neuropsychological measures. In Medical Image Computing and Computer-Assisted Intervention -MICCAI 2010, volume 6363 of Lecture Notes in Computer Science, pages 529-537, Berlin, 2010. Springer.
- S. Sommer, F. Lauze, M. Nielsen, and X. Pennec. Kernel bundle EPDiff: Evolution equations for multi-scale diffeomorphic image registration. In Scale Space and Variational Methods in Computer Vision, Lecture Notes in Computer Science. Springer, 2011.
- S. Sommer, M. Nielsen, F. Lauze, and X. Pennec. A multi-scale kernel bundle for LDDMM: Towards sparse deformation description across space and scales. In Proceedings of IPMI 2011, Lecture Notes in Computer Science. Springer, 2011.
- J.G. Sled, A.P. Zijdenbos, and A.C. Evans. A nonparametric method for automatic correction of intensity nonuniformity in MRI data. IEEE Trans. Med. Imaging, 17(1):87 -97, 1998.
- M. Vaillant, M. I. Miller, A. Trouvé, and L. Younes. Statistics on diffeomorphisms via tangent space representations. Neuroimage, 23(1):161-169, 2004.
- F.-X. Vialard, L. Risser, D. D. Holm, and D. Rueckert. Diffeomorphic atlas estimation using kärcher mean and geodesic shooting on volumetric images. In Proceedings of Medical Image Understanding and Analysis (MIUA'11), 2011.
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Quicksilver: Fast predictive image registration – A deep learning approach
Yang, X., Kwitt, R., Styner, M., & Niethammer, M. (2017) · NeuroImage · doi:10.1016/j.neuroimage.2017.07.008 · Cited by 630 · see citing works
- Authors
- Bruveris, M., Risser, L., & Vialard, F.-X.
- Affiliations
- Imperial College London (GB)
- Institut de Mécanique des Fluides de Toulouse (FR)
- École Normale Supérieure Paris-Saclay (FR)
- Venue
- Multiscale Modeling & Simulation
- Published
- 2012-01
- Volume
- 10
- Issue
- 4
- Pages
- 1344-1368
- ISSN
- 1540-3459 (ISSN-L)
- 1540-3467
- OpenAlex
- W2038056514
- Cited by
- 25
- References
- 1
- Citations by year
- 2025: 3 · 2024: 1 · 2021: 2 · 2019: 3 · 2018: 2 · 2017: 3 · 2016: 2 · 2015: 3 · 2013: 3 · 2012: 3
- FWCI
- 2.97
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Multiscale Modeling and Simulation (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- Base Institutionnelle de Recherche de l'université Paris-Dauphine (BIRD) (University Paris-Dauphine) (submittedVersion, cc-by-sa)
- HAL (submittedVersion)
- Infoscience (Ecole Polytechnique Fédérale de Lausanne) (submittedVersion)
- Infoscience (Ecole Polytechnique Fédérale de Lausanne) (submittedVersion, cc-by-nc-nd)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Computer Science › Computer Vision and Pattern Recognition › Medical Image Segmentation Techniques
- Physical Sciences › Computer Science › Computer Vision and Pattern Recognition › Image and Signal Denoising Methods
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Topological and Geometric Data Analysis
- Keywords
- LDDMM, diffeomorphism groups, semidirect products, multiscale analysis, variational methods, diffeomorphic registration, synthetic images
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