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

  • 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.
Author:Felix AmbellanORCiD, Stefan ZachowORCiD, Christoph von TycowiczORCiD
Document Type:In Proceedings
Parent Title (English):Proc. 7th MICCAI workshop on Mathematical Foundations of Computational Anatomy (MFCA)
First Page:219
Last Page:228
Series:Lecture Notes in Computer Science
Year of first publication:2019