title: Morphometry of anatomical shape complexes with dense deformations and sparse parameters.
abstract: 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 modelingis 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 www.deformetrica.org.
authors: INRIA, Project-Team Aramis, Centre Paris-Rocquencourt, France; Sorbonne Universités, UPMC Université Paris 06, UMR S 1127, ICM, Paris, France; Inserm, U1127, ICM, Paris, France; CNRS, UMR 7225, ICM, Paris, France; Institut du Cerveau et de la Moëlle Épinière (ICM), Hôpital de la Pitié Salpêtrière, 75013 Paris, France.
authors: Stanley
authors: S
authors: Durrleman
authors: Scientific Computing and Imaging (SCI) Institute, University of Utah, Salt Lake City, UT 84112, USA.
authors: Marcel
authors: M
authors: Prastawa
authors: Centre de Mathématiques et Leurs Applications (CMLA), Ecole Normale Supérieure de Cachan, 94230 Cachan, France.
authors: Nicolas
authors: N
authors: Charon
authors: Brain Institute, University of Utah, Salt Lake City, UT 84112, USA.
authors: Julie R
authors: JR
authors: Korenberg
authors: Scientific Computing and Imaging (SCI) Institute, University of Utah, Salt Lake City, UT 84112, USA.
authors: Sarang
authors: S
authors: Joshi
authors: Scientific Computing and Imaging (SCI) Institute, University of Utah, Salt Lake City, UT 84112, USA.
authors: Guido
authors: G
authors: Gerig
authors: Centre de Mathématiques et Leurs Applications (CMLA), Ecole Normale Supérieure de Cachan, 94230 Cachan, France.
authors: Alain
authors: A
authors: Trouvé
mesh_terms: D001921:Brain / Q000033:anatomy & histology* / Q000473:pathology; D003627:Data Interpretation, Statistical; D004314:Down Syndrome / Q000473:pathology; D006801:Humans; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D008953:Models, Anatomic; D059906:Neuroimaging / Q000379:methods*; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity
keywords: Anatomy; Deformation; Morphometry; Shape; Statistics; Varifold