Skeletonization of three-dimensional object using generalized potential field

The medial axis transform (MAT) is a skeletal representation of an object w hich has been shown to be useful in interrogation, animation, finite elemen t mesh generation, path planning, and feature recognition. In this paper, t he potential-based skeletonization approach for 2D MAT [1], which identifie s object skeleton as potential valleys using a Newtonian potential model in place of the distance function, is generalized to three dimensions. The ge neralized potential functions given in [2], which decay faster with distanc e 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. Accordin g to the simulation results, the skeletons obtained with the proposed appro ach are closely related to the corresponding MAT skeletons. While the media l axis (surface) is 2D in general for a 3D object, the potential valleys, b eing one-dimensional, form a more realistic skeleton. Other desirable attri butes of the algorithm include stability against perturbations of the objec t boundary, the flexibility to obtain partial skeleton directly, and low ti me complexity.