Landmark-Guided Elastic Shape Analysis of Spherically-Parameterized Surfaces

dc.contributor.authorKurtek, Sebastianen_US
dc.contributor.authorSrivastava, Anujen_US
dc.contributor.authorKlassen, Ericen_US
dc.contributor.authorLaga, Hamiden_US
dc.contributor.editorI. Navazo, P. Poulinen_US
dc.date.accessioned2015-02-28T15:25:49Z
dc.date.available2015-02-28T15:25:49Z
dc.date.issued2013en_US
dc.description.abstractWe 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 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 elastic deformations, and on surfaces with missing parts. We also provide multiple examples of averaging and symmetrizing 3D models.en_US
dc.description.seriesinformationComputer Graphics Forumen_US
dc.identifier.issn1467-8659en_US
dc.identifier.urihttps://doi.org/10.1111/cgf.12063en_US
dc.publisherThe Eurographics Association and Blackwell Publishing Ltd.en_US
dc.subjectI.3.5 [Computer Graphics]en_US
dc.subjectComputational Geometry and Object Modelingen_US
dc.subjectBoundary Representationsen_US
dc.titleLandmark-Guided Elastic Shape Analysis of Spherically-Parameterized Surfacesen_US
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