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Publication Detail
A Riemannian framework for intrinsic comparison of closed Genus-Zero shapes
  • Publication Type:
    Journal article
  • Publication Sub Type:
    Conference Proceeding
  • Authors:
    Gutman BA, Thomas Fletcher P, Jorge Cardoso M, Fleishman GM, Lorenzi M, Thompson PM, Ourselin S
  • Publication date:
    01/01/2015
  • Pagination:
    205, 218
  • Journal:
    Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
  • Volume:
    9123
  • Status:
    Published
  • Print ISSN:
    0302-9743
Abstract
© Springer International Publishing Switzerland 2015. 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 L 2 norm 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.
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