A Riemannian framework for intrinsic comparison of closed Genus-Zero shapes

Boris A. Gutman, P. Thomas Fletcher, M. Jorge Cardoso, Greg M. Fleishman, Marco Lorenzi, Paul M. Thompson, Sebastien Ourselin

Research output: Contribution to journalConference articlepeer-review

3 Scopus citations

Abstract

We present a framework for intrinsic comparison of surface metric structures and curvatures. This work parallels the work of Kurtek et al. on parameterization-invariant comparison of genus zero shapes. Here, instead of comparing the embedding of spherically parameterized surfaces in space, we focus on the first fundamental form. To ensure that the distance on spherical metric tensor fields is invariant to parameterization, we apply the conjugationinvariant metric arising from the L2norm on symmetric positive definite matrices. As a reparameterization changes the metric tensor by a congruent Jacobian transform, this metric perfectly suits our purpose. The result is an intrinsic comparison of shape metric structure that does not depend on the specifics of a spherical mapping. Further, when restricted to tensors of fixed volume form, the manifold of metric tensor fields and its quotient of the group of unitary diffeomorphisms becomes a proper metric manifold that is geodesically complete. Exploiting this fact, and augmenting the metric with analogous metrics on curvatures, we derive a complete Riemannian framework for shape comparison and reconstruction. A by-product of our framework is a near-isometric and curvature-preserving mapping between surfaces. The correspondence is optimized using the fast spherical fluid algorithm. We validate our framework using several subcortical boundary surface models from the ADNI dataset.

Original languageEnglish
Pages (from-to)205-218
Number of pages14
JournalLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume9123
DOIs
StatePublished - 2015
Externally publishedYes
Event24th International Conference on Information Processing in Medical Imaging, IPMI 2015 - Isle of Skye, United Kingdom
Duration: 28 Jun 20153 Jul 2015

Keywords

  • Cortical surface
  • Riemannian metric
  • Shape analysis
  • Surface registration

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