Spectral-Driven Isometry-Invariant Matching of 3D Shapes
Spectral-Driven Isometry-Invariant Matching of 3D Shapes
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DOI：
10.1007/s11263-009-0250-0
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发表时间：
2010-09-01
影响因子：
19.5
通讯作者：
Saupe, Dietmar
中科院分区：
文献类型：
--
作者：
Ruggeri, Mauro R.;Patane, Giuseppe;Saupe, Dietmar
本文提出了一种三维形状匹配方法，包括一种新的表面采样技术和两种基于点的统计形状描述子的三维形状匹配算法。我们的采样技术是基于与拉普拉斯-贝尔特拉米算子的较小本征值相关的本征函数的临界点。这些临界点对于等距是不变的，并且被用作采样技术的锚点，该采样技术通过使用用于控制参考点的密度和数量的统计标准来扩展最远点采样。一旦计算出一组参考点，我们就为每个参考点构造输入表面的基于点的统计描述符（简称PSSD）。该描述符结合了测地线形状分布的近似值和描述该点处的表面的其他几何信息。然后，通过将相应的PSSD集与二分图匹配进行比较或测量邻近图的重新排序的特征向量之间的L（1）距离来计算两个表面之间的相异性。这里，重新排序由与邻近图相关联的拉普拉斯矩阵的费德勒向量给出。我们的测试表明，这两种方法都适用于变形对象的在线检索，我们的采样策略提高了等距不变的匹配方法的检索性能。最后，基于Fiedler向量的方法比二分图匹配的检索速度快，检索效果相似。
This paper presents a matching method for 3D shapes, which comprises a new technique for surface sampling and two algorithms for matching 3D shapes based on point-based statistical shape descriptors. Our sampling technique is based on critical points of the eigenfunctions related to the smaller eigenvalues of the Laplace-Beltrami operator. These critical points are invariant to isometries and are used as anchor points of a sampling technique, which extends the farthest point sampling by using statistical criteria for controlling the density and number of reference points. Once a set of reference points has been computed, for each of them we construct a point-based statistical descriptor (PSSD, for short) of the input surface. This descriptor incorporates an approximation of the geodesic shape distribution and other geometric information describing the surface at that point. Then, the dissimilarity between two surfaces is computed by comparing the corresponding sets of PSSDs with bipartite graph matching or measuring the L (1)-distance between the reordered feature vectors of a proximity graph. Here, the reordering is given by the Fiedler vector of a Laplacian matrix associated to the proximity graph. Our tests have shown that both approaches are suitable for online retrieval of deformed objects and our sampling strategy improves the retrieval performances of isometry-invariant matching methods. Finally, the approach based on the Fiedler vector is faster than using the bipartite graph matching and it has a similar retrieval effectiveness.