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In this article we present an application of variational techniques to the smoothing of 3D curves. We study 2 types of application scenarios: in the first one the curve is just given by an ordered set of 3D points and in the second one the curve represents the medial axis of a 3D volume. In this last scenario, the input of the algorithm is the 3D volume and a 3D curve representing an approximation of the volume medial axis. We propose an algorithm for 3D curve smoothing, based on the minimization of a general variational model, which includes both scenarios. We present a variety of experiments to show the performance of the proposed technique.

An Algorithm for 3D Curve Smoothing