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Multi-shape Registration with Constrained Deformations

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Geometric Science of Information (GSI 2021)

Abstract

Based on a Sub-Riemannian framework, deformation modules provide a way of building large diffeomorphic deformations satisfying a given geometrical structure. This allows to incorporate prior knowledge about object deformations into the model as a means of regularisation [10]. However, diffeomorphic deformations can lead to deceiving results if the deformed object is composed of several shapes which are close to each other but require drastically different deformations. For the related Large Deformation Diffemorphic Metric Mapping, which yields unstructured deformations, this issue was addressed in [2] introducing object boundary constraints. We develop a new registration problem, marrying the two frameworks to allow for different constrained deformations in different coupled shapes.

Rosa Kowalewski is supported by a scholarship from the EPSRC Centre for Doctoral Training in Statistical Applied Mathematics at Bath (SAMBa), under the project EP/S022945/1.

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Notes

  1. 1.

    Data courtesy of Alain Trouvé.

  2. 2.

    For a more detailed description of how these modules are built, we refer to [10].

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Correspondence to Rosa Kowalewski or Barbara Gris .

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Kowalewski, R., Gris, B. (2021). Multi-shape Registration with Constrained Deformations. In: Nielsen, F., Barbaresco, F. (eds) Geometric Science of Information. GSI 2021. Lecture Notes in Computer Science(), vol 12829. Springer, Cham. https://doi.org/10.1007/978-3-030-80209-7_10

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  • DOI: https://doi.org/10.1007/978-3-030-80209-7_10

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