Spline Models for Shape Trajectory Analysis
The aim of the project is the development of novel methods for the identification of systematic differences in empirically defined distributions of shape trajectories. The focus will be on the derivation of hierarchical statistical models that account for the correlation inherent to time series of shapes. To this end, we will generalize the mixed-effects framework to manifold-valued data based on Riemannian spline models. The development will be driven by applications from cardiology and archaeology. In particular, a better understanding and algorithmic treatment of shape trajectories will support the diagnosis and therapy of heart diseases and will establish a quantitative method for the dating of ornaments and thereby archaeological buildings.
Publikationen
2023 |
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Martin Hanik | Geometric Data Analysis: Advancements of the Statistical Methodology and Applications | Doctoral thesis, Freie Universität Berlin, Christof Schütte, Christoph von Tycowicz (Advisors), 2023 |
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Martin Hanik, Benjamin Ducke, Hans-Christian Hege, Friederike Fless, Christoph von Tycowicz | Intrinsic shape analysis in archaeology: A case study on ancient sundials | Journal on Computing and Cultural Heritage, 16(4), pp. 1-26, 2023 |
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arXiv DOI |
2022 |
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Esfandiar Nava-Yazdani, Hans-Christian Hege, Christoph von Tycowicz | A Hierarchical Geodesic Model for Longitudinal Analysis on Manifolds | Journal of Mathematical Imaging and Vision, 64(4), pp. 395-407, 2022 (preprint available as ) |
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Martin Hanik, Hans-Christian Hege, Christoph von Tycowicz | A Nonlinear Hierarchical Model for Longitudinal Data on Manifolds | 2022 IEEE 19th International Symposium on Biomedical Imaging (ISBI), pp. 1-5, 2022 |
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arXiv DOI |
Martin Hanik, Hans-Christian Hege, Christoph von Tycowicz | Bi-invariant Dissimilarity Measures for Sample Distributions in Lie Groups | SIAM Journal on Mathematics of Data Science, 4(4), pp. 1223-1249, 2022 |
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Adele Myers, Saiteja Utpala, Shubham Talbar, Sophia Sanborn, Christian Shewmake, Claire Donnat, Johan Mathe, Umberto Lupo, Rishi Sonthalia, Xinyue Cui, Tom Szwagier, Arthur Pignet, Andri Bergsson, Søren Hauberg, Dmitriy Nielsen, Stefan Sommer, David Klindt, Erik Hermansen, Melvin Vaupel, Benjamin Dunn, Jeffrey Xiong, Noga Aharony, Itsik Pe’er, Felix Ambellan, Martin Hanik, Esfandiar Navayazdani, Christoph von Tycowicz, Nina Miolane | ICLR 2022 Challenge for Computational Geomerty & Topology: Design and Results | Proceedings of Topology, Algebra, and Geometry in Learning, pp. 269-276, Vol.196, Proceedings of Machine Learning Research, 2022 |
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BibTeX arXiv |
Esfandiar Nava-Yazdani, Martin Hanik, Felix Ambellan, Christoph von Tycowicz | On Gradient Formulas in an Algorithm for the Logarithm of the Sasaki Metric | ZIB-Report 22-12 |
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Martin Hanik, Mehmet Arif Demirtaş, Mohammed Amine Gharsallaoui, Islem Rekik | Predicting cognitive scores with graph neural networks through sample selection learning | Brain Imaging and Behavior, Vol.16, pp. 1123-1138, 2022 |
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arXiv DOI |
Ariel Caputo, Marco Emporio, Andrea Giachetti, Marco Cristani, Guido Borghi, Andrea D'Eusanio, Minh-Quan Le, Hai-Dang Nguyen, Minh-Triet Tran, Felix Ambellan, Martin Hanik, Esfandiar Navayazdani, Christoph von Tycowicz | SHREC 2022 Track on Online Detection of Heterogeneous Gestures | Computers and Graphics, Vol.107, pp. 241-251, 2022 |
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arXiv DOI |
Martin Hanik, Christoph von Tycowicz | Triangle meshes of shadow-recieving surfaces of ancient sundials | 2022 |
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2021 |
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Felix Ambellan, Martin Hanik, Christoph von Tycowicz | Morphomatics: Geometric morphometrics in non-Euclidean shape spaces | 2021 |
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Felix Ambellan, Stefan Zachow, Christoph von Tycowicz | Rigid Motion Invariant Statistical Shape Modeling based on Discrete Fundamental Forms | Medical Image Analysis, Vol.73, 2021 |
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DOI arXiv |
Ivan Sipiran, Patrick Lazo, Cristian Lopez, Nihar Bagewadi, Benjamin Bustos, Hieu Dao, Shankar Gangisetty, Martin Hanik, Ngoc-Phuong Ho-Thi, Mike Holenderski, Dmitri Jarnikov, Arniel Labrada, Stefan Lengauer, Roxane Licandro, Dinh-Huan Nguyen, Thang-Long Nguyen-Ho, Luis A. Pérez Rey, Bang-Dang Pham, Minh-Khoi Pham, Reinhold Preiner, Tobias Schreck, Quoc-Huy Trinh, Loek Tonnaer, Christoph von Tycowicz, The-Anh Vu-Le | SHREC 2021: Retrieval of Cultural Heritage Objects | Computers and Graphics, Vol.100, pp. 1-20, 2021 |
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2020 |
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Martin Hanik, Hans-Christian Hege, Christoph von Tycowicz | Bi-invariant Two-Sample Tests in Lie Groups for Shape Analysis | Shape in Medical Imaging, pp. 44-54, 2020 |
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arXiv DOI |
Esfandiar Nava-Yazdani, Hans-Christian Hege, T. J. Sullivan, Christoph von Tycowicz | Geodesic Analysis in Kendall's Shape Space with Epidemiological Applications | Journal of Mathematical Imaging and Vision, 62(4), pp. 549-559, 2020 |
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DOI arXiv |
Martin Hanik, Hans-Christian Hege, Anja Hennemuth, Christoph von Tycowicz | Nonlinear Regression on Manifolds for Shape Analysis using Intrinsic Bézier Splines | Proc. Medical Image Computing and Computer Assisted Intervention (MICCAI), pp. 617-626, 2020 |
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arXiv DOI |
Christoph von Tycowicz | Towards Shape-based Knee Osteoarthritis Classification using Graph Convolutional Networks | 2020 IEEE 17th International Symposium on Biomedical Imaging (ISBI 2020), 2020 |
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2019 |
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Felix Ambellan, Stefan Zachow, Christoph von Tycowicz | A Surface-Theoretic Approach for Statistical Shape Modeling | Proc. Medical Image Computing and Computer Assisted Intervention (MICCAI), Part IV, pp. 21-29, Vol.11767, Lecture Notes in Computer Science, 2019 (preprint available as ZIB-Report 19-20) |
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Felix Ambellan, Stefan Zachow, Christoph von Tycowicz | An as-invariant-as-possible GL+(3)-based Statistical Shape Model | Proc. 7th MICCAI workshop on Mathematical Foundations of Computational Anatomy (MFCA), pp. 219-228, Vol.11846, Lecture Notes in Computer Science, 2019 (preprint available as ZIB-Report 19-46) |
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Felix Ambellan, Hans Lamecker, Christoph von Tycowicz, Stefan Zachow | Statistical Shape Models - Understanding and Mastering Variation in Anatomy | Biomedical Visualisation, Paul M. Rea (Ed.), Springer Nature Switzerland AG, 1, pp. 67-84, 2019, ISBN: 978-3-030-19384-3, ISBN: 978-3-030-19385-0 (preprint available as ZIB-Report 19-13) |
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