Landmark-Guided Elastic Shape Analysis of Spherically-Parameterized Surfaces

Sebastian Kurtek, Anuj Srivastava, Eric Klassen, Hamid Laga

Top: geodesic paths between two surfaces with missing parts. Bottom: symmetrization of highly articulated shape.

Abstract.  We argue that full surface correspondence (registration) and optimal deformations (geodesics) are two related problems and propose a framework that solves them simultaneously. We  build on the Riemannian shape analysis of anatomical and star-shaped surfaces of Kurtek et al. and focus on  articulated complex shapes that undergo elastic deformations and that may contain missing parts. Our core contribution is the re-formulation of Kurtek et al.'s approach as a constrained optimization over all possible re-parameterizations of the surfaces, using a sparse set of corresponding landmarks. We introduce a landmark-constrained basis, which we use to numerically solve this optimization and therefore establish full surface registration and geodesic deformation between the two surfaces. The length of the geodesic provides a measure of dissimilarity between surfaces. The advantages of this approach are: (1) simultaneous computation of full correspondence and geodesic between two surfaces, given a sparse set of matching landmarks (2) ability to handle more comprehensive deformations than nearly isometric, and (3) the  geodesics and the geodesic lengths can be further used for symmetrizing 3D shapes and for computing their statistical averages. We validate the framework on challenging cases of large isometric and/or elastic deformations, and on surfaces with missing parts. We also provide multiple examples of averaging and symmetrizing 3D models.

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Bibtex:
@article{kurtek_eg2013,
  author    = {Sebastian Kurtek and Anuj Srivastava and Eric Klassen and Hamid Laga},
  title       = {Landmark-Guided Elastic Shape Analysis of Spherically-Parameterized Surfaces},
  journal   = {Computer Graphics Forum (Proceedings of Eurographics 2013},
  volume   = {32},
  number   = {2},
  year       = {2013},
  pages     = {429-438}
 }

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Hamid Laga,
Apr 8, 2013, 9:09 AM