center for robotics and embedded systems University of Southern California Viterbi School of Engineering

We present Nonlinear Spherical Shells (NSS) as a non-iterative model-free method for constructing approximate principal curves skeletons in volumes of $d$ dimensional data points. NSS leverages existing model-free techniques for nonlinear dimension to remove nonlinear artifacts in data. With nonlinearities removed and topology preserved, data embedded by such procedures are assumed to have properties amenable to simple skeletonization procedures. Given these assumptions, NSS is able extract points in the ``middle'' of the volume data and hierarchically link them into principal curves, or a set of 1-manifolds connected at junctions.


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