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Topology Preserving Atlas Construction from Shape Data without Correspondence using Sparse Parameters

Institution:
1INRIA/ICM, Pitié Salpêtrière Hospital, Paris, France.
2SCI Institute, University of Utah, Salt Lake City, UT, USA.
3Brain Institute, University of Utah, Salt Lake City, UT, USA.
4CMLA - Ecole Normale Sup ́rieure de Cachan, Cachan, France.
Publisher:
Int Conf Med Image Comput Comput Assist Interv. MICCAI 2012
Publication Date:
Oct-2012
Journal:
Med Image Comput Comput Assist Interv
Volume Number:
15
Issue Number:
Pt 3
Pages:
223-30
Citation:
Int Conf Med Image Comput Comput Assist Interv. 2012 Oct;15(Pt 3):223-30.
PubMed ID:
23286134
PMCID:
PMC3758250
Appears in Collections:
NA-MIC
Sponsors:
R01 HD067731/HD/NICHD NIH HHS/United States
P41 RR112553/RR/NCRR NIH HHS/United States
R01 EB007688/EB/NIBIB NIH HHS/United States
U54 EB005149/EB/NIBIB NIH HHS/United States
Generated Citation:
Durrleman S., Prastawa M., Korenberg J.R., Joshi S., Trouvé A., Gerig G. Topology Preserving Atlas Construction from Shape Data without Correspondence using Sparse Parameters. Int Conf Med Image Comput Comput Assist Interv. 2012 Oct;15(Pt 3):223-30. PMID: 23286134. PMCID: PMC3758250.
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Statistical analysis of shapes, performed by constructing an atlas composed of an average model of shapes within a population and associated deformation maps, is a fundamental aspect of medical imaging studies. Usual methods for constructing a shape atlas require point correspondences across subjects, which are difficult in practice. By contrast, methods based on currents do not require correspondence. However, existing atlas construction methods using currents suffer from two limitations. First, the template current is not in the form of a topologically correct mesh, which makes direct analysis on shapes difficult. Second, the deformations are parametrized by vectors at the same location as the normals of the template current which often provides a parametrization that is more dense than required. In this paper, we propose a novel method for constructing shape atlases using currents where topology of the template is preserved and deformation parameters are optimized independently of the shape parameters. We use an L1-type prior that enables us to adaptively compute sparse and low dimensional parameterization of deformations. We show an application of our method for comparing anatomical shapes of patients with Down's syndrome and healthy controls, where the sparse parametrization of diffeomorphisms decreases the parameter dimension by one order of magnitude.

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