基于广义势场的三维形体多层次线骨架构建

Computing hierarchical curve-skeletons of 3D objects based on generalized potential field

在Cornea建立的基于广义势场的骨架生成算法的基础上,提出一种新的多层次线骨架构建算法。通过选取不同的r值简化边界点,减少了斥力场的计算时间。与Cornea算法不同,选取曲面变分替代曲率,并选取局部曲面变分值较高的边界点作为种子点生成多层次的骨架。由于曲面变分比曲率更适用于反映点云形体表面的性质且计算速度较快,因此该算法更适于处理点云,且具有一定的鲁棒性。同时分析了不同的r值与骨架连通性和计算时间的关系。实验结果表明,经边界点简化处理,斥力场计算时间比原来减少一半左右,且以此生成的骨架能够保持较好的光滑性和连通性。还尝试了另一种基于曲面变分简化边界点的准则,并仔细考查了高曲面变分点、邻域半径k以及不同的空间划分尺度n对多层次骨架生成的影响。

This paper presented a new algorithm to compute hierarchical curve-skeletons based on the algorithm of generalized potential field given by Cornea. The algorithm reduced the force field computing time by using different r to simplify the boundary points. The difference was that it used surface variation to replace curvature and used the boundary points with higher local surface variation as seed points to get hierarchical curve-skeletons. Because the surface variation is more applicable to reflect the properties of point-sample surface than curvature and faster to compute, it is more applicable to deal with point cloud and robust. The paper analyzed the relationship between different r and the connectivity and the computing time. The experimental results indicate that the computing time of the force field by using simplified boundary points declines about half to the original algorithm, and the resuh curve-skeletons keep good smoothness and connectivity. The paper also tried another rule to simplify the boundary points based on surface variation and studied carefully the influences of higher surface variation points, neighborhood size k and different soatial division n to the hierarchical curve-skeletons.