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An As-Invariant-As-Possible \(\text {GL}^+(3){}\)-Based Statistical Shape Model

  • Felix AmbellanEmail author
  • Stefan Zachow
  • Christoph von Tycowicz
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11846)

Abstract

We describe a novel nonlinear statistical shape model based on differential coordinates viewed as elements of \(\text {GL}^+(3){}\). We adopt an as-invariant-as possible framework comprising a bi-invariant Lie group mean and a tangent principal component analysis based on a unique \(\text {GL}^+(3){}\)-left-invariant, \(\text {O}(3){}\)-right-invariant metric. Contrary to earlier work that equips the coordinates with a specifically constructed group structure, our method employs the inherent geometric structure of the group-valued data and therefore features an improved statistical power in identifying shape differences. We demonstrate this in experiments on two anatomical datasets including comparison to the standard Euclidean as well as recent state-of-the-art nonlinear approaches to statistical shape modeling.

Keywords

Statistical shape analysis Tangent principal component analysis Lie groups Classification Manifold valued statistics 

Notes

Acknowledgments

The authors are funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy – The Berlin Mathematics Research Center MATH+ (EXC-2046/1, project ID: 390685689). Furthermore, we are grateful for the open-access OAI dataset of the Osteoarthritis Initiative, that is a public-private partnership comprised of five contracts (N01-AR-2-2258; N01-AR-2-2259; N01-AR-2-2260; N01-AR-2-2261; N01-AR-2-2262) funded by the National Institutes of Health, a branch of the Department of Health and Human Services, and conducted by the OAI Study Investigators. Private funding partners include Merck Research Laboratories; Novartis Pharmaceuticals Corporation, GlaxoSmithKline; and Pfizer, Inc. Private sector funding for the OAI is managed by the Foundation for the National Institutes of Health. This manuscript was prepared using an OAI public use data set and does not necessarily reflect the opinions or views of the OAI investigators, the NIH, or the private funding partners.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Therapy Planning Group, Zuse Institute BerlinBerlinGermany

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