Euclidean skeletons using closest points

In this paper, we present an efficient algorithm for computing the Euclidean skeleton of an object directly from a point cloud representation on an underlying grid. The key point of this algorithm is to identify those grid points that are (approximately) on the skeleton using the closest point information of a grid point and its neighbors. The three main ingredients of the algorithm are: (1) computing closest point information efficiently on a grid, (2) identifying possible skeletal points based on the number of closest points of a grid point and its neighbors with smaller distances, (3) applying a distance ordered homotopic thinning process to remove the non-skeletal points while preserving the end points or the edge points of the skeleton. Computational examples in 2D and 3D are presented.

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