Stochastic Medial Axis Transform for Bayesian Extended Object Tracking

In this paper, we present novel results and insights into tracking extended objects using the Stochastic Medial Axis Transform (SMAT). Unlike conventional methods that depend on explicit shape parameterization with basic priors, SMAT employs an implicit inside-out representation by constructing maximum inscribed circles within the object. This is achieved by simultaneously fitting two Bézier curves: one that defines the medial manifold, providing the centers of the maximum inscribed circles, and the other that characterizes the scalar thickness field, assigning positive radii to these centers. This dual-curve formulation leverages the concept of inverse skeletonization and offers a flexible, parametric shape model capable of tracking diverse shapes, whether convex or non-convex, symmetric or asymmetric. Furthermore, we obtain a closed-form likelihood function in 2D space that facilitates the application of advanced recursive Bayesian state estimators. Finally, we conduct two simulation studies to demonstrate and evaluate the effectiveness of the proposed approach.