Weak Convex Decomposition by Lines-of-sight
Weak Convex Decomposition by Lines-of-sight
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DOI：
10.1111/cgf.12169
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发表时间：
2013-08-01
影响因子：
2.5
通讯作者：
Cohen-Or, Daniel
中科院分区：
文献类型：
--
作者：
Asafi, Shmuel;Goren, Avi;Cohen-Or, Daniel
我们定义一组点的凸度秩为互可见点对在点对总数中所占的部分。在弱凸性定义的基础上，引入了一种将给定形状分解为弱凸区域的谱方法。在不显式测量凸秩的情况下应用分解。该方法仅仅相当于表示全对视线的矩阵的光谱聚类。我们的方法可以直接应用于定向点云，不需要任何拓扑信息，也不需要显式的凹凸度量。我们在大量的例子上证明了我们的算法的效率，并将它们与竞争方法进行了定性比较。
We define the convexity rank of a set of points to be the portion of mutually visible pairs of points out of the total number of pairs. Based on this definition of weak convexity, we introduce a spectral method that decomposes a given shape into weakly convex regions. The decomposition is applied without explicitly measuring the convexity rank. The method merely amounts to a spectral clustering of a matrix representing the all-pairs line of sight. Our method can be directly applied on an oriented point cloud and does not require any topological information, nor explicit concavity or convexity measures. We demonstrate the efficiency of our algorithm on a large number of examples and compare them qualitatively with competitive approaches.