An as-invariant-as-possible GL+(3)-based Statistical Shape Model

Please always quote using this URN: urn:nbn:de:0297-zib-74566
  • We describe a novel nonlinear statistical shape model basedon differential coordinates viewed as elements of 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 GL+(3)-left-invariant, 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.

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Author:Felix AmbellanORCiD, Stefan ZachowORCiD, Christoph von TycowiczORCiD
Document Type:ZIB-Report
Tag:Classification; Lie groups; Manifold valued statistics; Statistical shape analysis; Tangent principal component analysis
Date of first Publication:2019/08/28
Series (Serial Number):ZIB-Report (19-46)
ISSN:1438-0064