Abstract
Predicting the future development of an anatomical shape from a single baseline observation is a challenging task. But it can be essential for clinical decision-making. Research has shown that it should be tackled in curved shape spaces, as (e.g., disease-related) shape changes frequently expose nonlinear characteristics. We thus propose a novel prediction method that encodes the whole shape in a Riemannian shape space. It then learns a simple prediction technique founded on hierarchical statistical modeling of longitudinal training data. When applied to predict the future development of the shape of the right hippocampus under Alzheimer’s disease and to human body motion, it outperforms deep learning-supported variants as well as state-of-the-art.
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Notes
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Whenever we say “smooth” we mean “infinitely often differentiable”.
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- 3.
Standard multi-layer perceptrons showed similar performance to GANs.
- 4.
We denote the coordinate representation in \(\mathbb {R}^d\) of a tangent vector v w.r.t. a fixed but arbitrary basis by [v].
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Acknowledgements
This work was partially funded by grants from the European H2020 Marie Sklodowska-Curie action (grant no. 101003403) and the Scientific and Technological Research Council of Turkey under the TUBITAK 2232 Fellowship for Outstanding Researchers (no. 118C288) (https://basira-lab.com/normnets/ & https://basira-lab.com/reprime/). We are grateful for the funding by DFG (Deutsche Forschungsgemeinschaft (DFG) through Germany’s Excellence Strategy – The Berlin Mathematics Research Center MATH+ (EXC-2046/1, project ID: 390685689)) and BMBF (Bundesministerium für Bildung und Forschung (BMBF) through BIFOLD - The Berlin Institute for the Foundations of Learning and Data (ref. 01IS18025A and ref 01IS18037A)).
Data collection and sharing for this project was funded by the ADNI (adni.loni.usc.edu) (National Institutes of Health Grant U01 AG024904) and DOD ADNI (Department of Defense award number W81XWH-12-2-0012). ADNI is funded by the National Institute on Aging, the National Institute of Biomedical Imaging and Bioengineering, and through generous contributions from the following: AbbVie, Alzheimer’s Association; Alzheimer’s Drug Discovery Foundation; Araclon Biotech; BioClinica, Inc.; Biogen; Bristol-Myers Squibb Company; CereSpir, Inc.; Cogstate; Eisai Inc.; Elan Pharmaceuticals, Inc.; Eli Lilly and Company; EuroImmun; F. Hoffmann-La Roche Ltd and its affiliated company Genentech, Inc.; Fujirebio; GE Healthcare; IXICO Ltd.; Janssen Alzheimer Immunotherapy Research & Development, LLC.; Johnson & Johnson Pharmaceutical Research & Development LLC.; Lumosity; Lundbeck; Merck & Co., Inc.; Meso Scale Diagnostics, LLC.; NeuroRx Research; Neurotrack Technologies; Novartis Pharmaceuticals Corporation; Pfizer Inc.; Piramal Imaging; Servier; Takeda Pharmaceutical Company; and Transition Therapeutics. The Canadian Institutes of Health Research is providing funds to support ADNI clinical sites in Canada. Private sector contributions are facilitated by the Foundation for the National Institutes of Health (www.fnih.org). The grantee organization is the Northern California Institute for Research and Education, and the study is coordinated by the Alzheimer’s Therapeutic Research Institute at the University of Southern California. ADNI data are disseminated by the Laboratory for Neuro Imaging at the University of Southern California.
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Türkseven, D., Rekik, I., von Tycowicz, C., Hanik, M. (2023). Predicting Shape Development: A Riemannian Method. In: Wachinger, C., Paniagua, B., Elhabian, S., Li, J., Egger, J. (eds) Shape in Medical Imaging. ShapeMI 2023. Lecture Notes in Computer Science, vol 14350. Springer, Cham. https://doi.org/10.1007/978-3-031-46914-5_17
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