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Morphometry of Anatomical Shape Complexes with Dense Deformations and Sparse Parameters

1INRIA, Project-Team Aramis, Centre Paris-Rocquencourt, France.
2Scientific Computing and Imaging (SCI) Institute, University of Utah, Salt Lake City, UT, USA.
3Centre de Mathématiques et Leurs Applications (CMLA), Ecole Normale Supérieure de Cachan, Cachan, France.
4Brain Institute, University of Utah, Salt Lake City, UT, USA.
Elsevier Science
Publication Date:
Volume Number:
Neuroimage. 2014 Nov 1;101:35-49.
PubMed ID:
Anatomy, Deformation, Morphometry, Shape, Statistics, Varifold
Appears in Collections:
R01 HD067731/HD/NICHD NIH HHS/United States
P41 RR112553/RR/NCRR NIH HHS/United States
R01 EB076882/EB/NIBIB NIH HHS/United States
U01 NS082086/NS/NINDS NIH HHS/United States
U54 EB005149/EB/NIBIB NIH HHS/United States
Generated Citation:
Durrleman S., Prastawa M., Charon N., Korenberg J.R., Joshi S., Gerig G., Trouvé A. Morphometry of Anatomical Shape Complexes with Dense Deformations and Sparse Parameters. Neuroimage. 2014 Nov 1;101:35-49. PMID: 24973601. PMCID: PMC4871626.
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We propose a generic method for the statistical analysis of collections of anatomical shape complexes, namely sets of surfaces that were previously segmented and labeled in a group of subjects. The method estimates an anatomical model, the template complex, that is representative of the population under study. Its shape reflects anatomical invariants within the dataset. In addition, the method automatically places control points near the most variable parts of the template complex. Vectors attached to these points are parameters of deformations of the ambient 3D space. These deformations warp the template to each subject's complex in a way that preserves the organization of the anatomical structures. Multivariate statistical analysis is applied to these deformation parameters to test for group differences. Results of the statistical analysis are then expressed in terms of deformation patterns of the template complex, and can be visualized and interpreted. The user needs only to specify the topology of the template complex and the number of control points. The method then automatically estimates the shape of the template complex, the optimal position of control points and deformation parameters. The proposed approach is completely generic with respect to any type of application and well adapted to efficient use in clinical studies, in that it does not require point correspondence across surfaces and is robust to mesh imperfections such as holes, spikes, inconsistent orientation or irregular meshing. The approach is illustrated with a neuroimaging study of Down syndrome (DS). The results demonstrate that the complex of deep brain structures shows a statistically significant shape difference between control and DS subjects. The deformation-based modeling is able to classify subjects with very high specificity and sensitivity, thus showing important generalization capability even given a low sample size. We show that the results remain significant even if the number of control points, and hence the dimension of variables in the statistical model, are drastically reduced. The analysis may even suggest that parsimonious models have an increased statistical performance. The method has been implemented in the software Deformetrica, which is publicly available at

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