Tensor maps for synchronizing heterogeneous shape collections
Tensor maps for synchronizing heterogeneous shape collections
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DOI：
10.1145/3306346.3322944
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发表时间：
2019-07
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影响因子：
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通讯作者：
Qi-Xing Huang;Zhenxiao Liang;Haoyu Wang;Simiao Zuo;C. Bajaj
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文献类型：
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作者：
Qi-Xing Huang;Zhenxiao Liang;Haoyu Wang;Simiao Zuo;C. Bajaj
在管理几何形状集合时，建立几何形状之间高质量的对应映射已被证明是一个根本性问题。先前的研究工作主要集中在计算成对形状之间的高效映射，并展示了联合映射同步的可量化优势，即利用形状集合来改进（去噪）成对映射，以确保一致性和正确性。然而，这些现有的映射同步技术对输入的形状集合有很强的假设条件，比如所有输入形状都属于同一类别，并且/或者大多数输入的成对映射是正确的。在本文中，我们提出了一种多重映射同步方法，该方法以异构形状集合作为输入，同时输出一致的密集成对形状映射。我们通过使用一种基于张量的全新表示法来实现映射同步，从而达成目标，这种表示法比之前所有基于矩阵的表示法都更高效、更稳健。我们在广泛的几何形状数据集以及形状聚类和形状协同分割应用中，证明了该方法的实用性。
Establishing high-quality correspondence maps between geometric shapes has been shown to be the fundamental problem in managing geometric shape collections. Prior work has focused on computing efficient maps between pairs of shapes, and has shown a quantifiable benefit of joint map synchronization, where a collection of shapes are used to improve (denoise) the pairwise maps for consistency and correctness. However, these existing map synchronization techniques place very strong assumptions on the input shapes collection such as all the input shapes fall into the same category and/or the majority of the input pairwise maps are correct. In this paper, we present a multiple map synchronization approach that takes a heterogeneous shape collection as input and simultaneously outputs consistent dense pairwise shape maps. We achieve our goal by using a novel tensor-based representation for map synchronization, which is efficient and robust than all prior matrix-based representations. We demonstrate the usefulness of this approach across a wide range of geometric shape datasets and the applications in shape clustering and shape co-segmentation.