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This paper introduces a square-root velocity (SRV) representation for analyzing shapes of curves in euclidean spaces under an elastic metric. In this SRV representation, the elastic metric simplifies to the IL<sup>2</sup> metric, the reparameterization group acts by isometries, and the space of unit length curves becomes the unit sphere. The shape space of(More)
For analyzing shapes of planar, closed curves, we propose differential geometric representations of curves using their direction functions and curvature functions. Shapes are represented as elements of infinite-dimensional spaces and their pairwise differences are quantified using the lengths of geodesics connecting them on these spaces. We use a Fourier(More)
Using a differential-geometric treatment of planar shapes, we present tools for: 1) hierarchical clustering of imaged objects according to the shapes of their boundaries, 2) learning of probability models for clusters of shapes, and 3) testing of newly observed shapes under competing probability models. Clustering at any level of hierarchy is performed(More)
BACKGROUND Electroconvulsive therapy (ECT) elicits a rapid and robust clinical response in patients with refractory depression. Neuroimaging measurements of structural plasticity relating to and predictive of ECT response may point to the mechanisms underlying rapid antidepressant effects and establish biomarkers to inform other treatments. Here, we(More)
We study shapes of planar arcs and closed contours modeled on elastic curves obtained by bending, stretching or compressing line segments non-uniformly along their extensions. Shapes are represented as elements of a quotient space of curves obtained by identifying those that differ by shape-preserving transformations. The elastic properties of the curves(More)
Applications in computer vision involve statistically analyzing an important class of constrained, non-negative functions, including probability density functions (in texture analysis), dynamic time-warping functions (in activity analysis), and re-parametrization or non-rigid registration functions (in shape analysis of curves). For this one needs to impose(More)
Resting-state MRI (rs-fMRI) is a powerful procedure for studying whole-brain neural connectivity. In this study we provide the first empirical evidence of the longitudinal reliability of rs-fMRI in children. We compared rest-retest measurements across spatial, temporal and frequency domains for each of six cognitive and sensorimotor intrinsic connectivity(More)
Whether plasticity of white matter (WM) microstructure relates to therapeutic response in major depressive disorder (MDD) remains uncertain. We examined diffusion tensor imaging (DTI) correlates of WM structural connectivity in patients receiving electroconvulsive therapy (ECT), a rapidly acting treatment for severe MDD. Tract-Based Spatial Statistics(More)
Declarative memory (DM) impairments are reported in schizophrenia and in unaffected biological relatives of patients. However, the neural correlates of successful and unsuccessful encoding, mediated by the medial temporal lobe (MTL) memory system, and the influence of disease-related genetic liability remain under explored. This study employed an(More)
We propose an efficient representation for studying shapes of closed curves in R n. This paper combines the strengths of two important ideas-elastic shape metric and path-straightening methods-and results in a very fast algorithm for finding geodesics in shape spaces. The elastic metric allows for optimal matching of features between the two curves while(More)