Covariance-Based Descriptors for Efficient 3D Shape Matching, Retrieval, and Classification
Covariance-Based Descriptors for Efficient 3D Shape Matching, Retrieval, and Classification
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DOI：
10.1109/tmm.2015.2457676
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发表时间：
2015-07
影响因子：
7.3
通讯作者：
Hedi Tabia;Hamid Laga
中科院分区：
文献类型：
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作者：
Hedi Tabia;Hamid Laga
现有技术的3D形状分类和检索算法（下文称为形状分析）通常基于比较捕获3D对象的主要几何和拓扑性质的签名或描述符。然而，现有的描述符都没有在所有形状类上实现最佳性能。在这篇文章中，我们探索，第一次，使用协方差矩阵的描述符，而不是描述符本身，在3D形状分析。与基于直方图的技术不同，基于协方差的3D形状分析使得能够将不同类型的特征和模态融合和编码成紧凑的表示。然而，协方差矩阵是对称正定（SPD）矩阵的非线性流形的元素，因此\BBL 2度量不适合它们的比较和聚类。在这篇文章中，我们研究了SPD矩阵的黎曼流形上的测地距离，并将其作为三维形状匹配和识别的度量。然后，我们：（1）引入协方差袋（BoC）矩阵和空间敏感BoC的概念作为对传统特征袋框架的SPD矩阵的黎曼流形的推广，以及（2）将用于3D形状的监督分类的标准核方法推广到协方差矩阵空间。我们评估了所提出的BoC矩阵框架和基于协方差的内核方法的性能，并在各种3D形状匹配、检索和分类设置中与基于几何的对应方法相比，证明了它们的优越性。
State-of-the-art 3D shape classification and retrieval algorithms, hereinafter referred to as shape analysis, are often based on comparing signatures or descriptors that capture the main geometric and topological properties of 3D objects. None of the existing descriptors, however, achieve best performance on all shape classes. In this article, we explore, for the first time, the usage of covariance matrices of descriptors, instead of the descriptors themselves, in 3D shape analysis. Unlike histogram -based techniques, covariance-based 3D shape analysis enables the fusion and encoding of different types of features and modalities into a compact representation. Covariance matrices, however, are elements of the non-linear manifold of symmetric positive definite (SPD) matrices and thus \BBL2 metrics are not suitable for their comparison and clustering. In this article, we study geodesic distances on the Riemannian manifold of SPD matrices and use them as metrics for 3D shape matching and recognition. We then: (1) introduce the concepts of bag of covariance (BoC) matrices and spatially-sensitive BoC as a generalization to the Riemannian manifold of SPD matrices of the traditional bag of features framework, and (2) generalize the standard kernel methods for supervised classification of 3D shapes to the space of covariance matrices. We evaluate the performance of the proposed BoC matrices framework and covariance -based kernel methods and demonstrate their superiority compared to their descriptor-based counterparts in various 3D shape matching, retrieval, and classification setups.