We present a statistical shape-analysis framework for characterizing and comparing morphological variation of the corpus callosum. The midsagittal boundary of the corpus callosum is represented by a closed curve and analyzed using an invariant shape representation. The shape space of callosal curves is endowed with a Riemannian metric. Shape distances are given by the length of shortest paths (geodesics) that are invariant to shape-confounding transformations. The statistical framework enables computation of shape averages and covariances on the shape space in an intrinsic manner (unique to the shape space). The statistical framework makes use of the tangent principal component approach to achieve dimension reduction on the space of corpus callosum shapes. The advantages of this approach are - it is fully automatic, invariant, and avoids the use of landmarks to define shapes. We applied our method to determine the effects of sex, age, schizophrenia and schizophrenia-related genetic liability on callosal shape in a large sample of patients and controls and their first-degree relatives (N=218). Results showed significant age, sex, and schizophrenia effects on both global and local callosal shape structure.
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