Abstract
The Large Deformation Diffeomorphic Metric Mapping (LDDMM) framework acting on currents is a conceptually powerful tool for matching highly varying shapes. In the classical approach, the numerical treatment is based on currents representing individual particles, and couples the discretization of shape and deformation. This design restricts the capabilities of LDDMM. In this work, we propose to decouple current and deformation discretization by using conforming adaptive finite elements. We show how to efficiently (a) compute the temporal evolution of discrete \(m\)-current attributes for any \(m\), and (b) incorporate multiple scales into the matching process. This effectively leads to more flexibility, which is demonstrated in several numerical experiments on anatomical shapes.
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Notes
This work extends the authors’ contribution to the Proceedings of the Third International Workshop on Mathematical Foundations of Computational Anatomy—Geometrical and Statistical Methods for Modeling Biological Shape Variability in Günther et al. (2011).
Pelvic bone data by courtesy of Markus Heller, Julius Wolff Institute and Center for Musculoskeletal Surgery Charité—Universitätsmedizin Berlin, Germany. Mandible data by courtesy of Max Zinser, Universitätsklinikum Köln, Germany.
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Acknowledgments
This work was supported by the German DFG Research Center Matheon, Project F2. We thank Stanley Durrleman from the University of Utah for the fruitful discussion and helpful suggestions at the initial phase of this paper. Furthermore, we thank Malik Kirchner for implementing parts of the required tools.
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Günther, A., Lamecker, H. & Weiser, M. Flexible Shape Matching with Finite Element Based LDDMM. Int J Comput Vis 105, 128–143 (2013). https://doi.org/10.1007/s11263-012-0599-3
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DOI: https://doi.org/10.1007/s11263-012-0599-3