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Publication Detail
A Riemannian Framework for Intrinsic Comparison of Closed Genus-Zero Shapes.
  • Publication Type:
    Journal article
  • Publication Sub Type:
  • Authors:
    Gutman BA, Fletcher PT, Cardoso MJ, Fleishman GM, Lorenzi M, Thompson PM, Ourselin S
  • Publication date:
  • Pagination:
    205, 218
  • Journal:
    Information processing in medical imaging : proceedings of the ... conference
  • Volume:
  • Medium:
  • Print ISSN:
  • Language:
  • Keywords:
    Brain, Humans, Alzheimer Disease, Image Interpretation, Computer-Assisted, Magnetic Resonance Imaging, Image Enhancement, Subtraction Technique, Models, Statistical, Sensitivity and Specificity, Reproducibility of Results, Algorithms, Computer Simulation, Pattern Recognition, Automated
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 conjugation-invariant metric arising from the L2 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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