Skeletonization of three-dimensional object using generalized potential field

The medial axis transform (MAT) is a skeletal representation of an object which has been shown to be useful in interrogation, animation, finite element mesh generation, path planning, and feature recognition. In this paper, the potential-based skeletonization approach for 2D MAT [1], which identifies object skeleton as potential valleys using a Newtonian potential model in place of the distance function, is generalized to three dimensions. The generalized potential functions given in [2], which decay faster with distance than the Newtonian potential, is used for the 3D case. The efficiency of the proposed approach results from the fact that these functions and their gradients can be obtained in closed forms for polyhedral surfaces. According to the simulation results, the skeletons obtained with the proposed approach are closely related to the corresponding MAT skeletons. While the medial axis (surface) is 2D in general for a 3D object, the potential valleys, being one-dimensional, form a more realistic skeleton. Other desirable attributes of the algorithm include stability against perturbations of the object boundary, the flexibility to obtain partial skeleton directly, and low time complexity.