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Geodesic Shape Spaces of Surfaces of Genus Zero

Abstract : We construct shape spaces of elastic spherical surfaces immersed in Euclidean space Rk. The spaces are equipped with geodesic metrics that depend on the tension and rigidity of the surfaces. We develop algorithms to calculate geodesics and geodesic distances, as well as tools to quantify local shape similarities and contrasts, thus obtaining a local-global formulation. We give examples of geodesic interpolations and illustrations of the use of the model in brain mapping.
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https://hal.inria.fr/inria-00632879
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Submitted on : Sunday, October 16, 2011 - 10:22:56 PM
Last modification on : Tuesday, November 29, 2022 - 12:06:07 PM
Long-term archiving on: : Thursday, November 15, 2012 - 9:46:25 AM

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Xiuwen Liu, Washington Mio, Yonggang Shi, Ivo Dinov. Geodesic Shape Spaces of Surfaces of Genus Zero. 2nd MICCAI Workshop on Mathematical Foundations of Computational Anatomy, Oct 2008, New-York, United States. pp.105-116. ⟨inria-00632879⟩

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