Rotation Invariant Spherical Harmonic Representation of 3D Shape Descriptors
Rotation Invariant Spherical Harmonic Representation of 3D Shape Descriptors
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DOI：
10.2312/sgp/sgp03/156-165
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发表时间：
2003-06
期刊：
影响因子：
12.3
通讯作者：
M. Kazhdan;T. Funkhouser;S. Rusinkiewicz
中科院分区：
文献类型：
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作者：
M. Kazhdan;T. Funkhouser;S. Rusinkiewicz
3D形状匹配的挑战之一来自于这样一个事实，即在许多应用中，如果模型的旋转不同，则应该认为它们是相同的。因此，在比较两个模型时，相似性度量隐式地提供了最佳对齐时的相似性度量。明确求解最优对准通常是不切实际的。因此，提出了两种一般方法来解决这个问题：(1)每个模型都使用旋转不变量描述符表示。(2)每个模型都由一个旋转相关的描述符来描述，该描述符与模型定义的规范坐标系对齐。在本文中，我们描述了正则对准的局限性，并讨论了一种基于球面谐波的替代方法来获得旋转不变表示。我们描述了该工具的属性，并展示了如何将其应用于许多现有的方向相关描述符，以提高它们的匹配性能。该工具的优点有两个方面：首先，它提高了许多描述符的匹配性能。其次，它降低了描述符的维数，提供了更紧凑的表示，这反过来又使两个模型的比较更有效。
One of the challenges in 3D shape matching arises from the fact that in many applications, models should be considered to be the same if they differ by a rotation. Consequently, when comparing two models, a similarity metric implicitly provides the measure of similarity at the optimal alignment. Explicitly solving for the optimal alignment is usually impractical. So, two general methods have been proposed for addressing this issue: (1) Every model is represented using rotation invariant descriptors. (2) Every model is described by a rotation dependent descriptor that is aligned into a canonical coordinate system defined by the model. In this paper, we describe the limitations of canonical alignment and discuss an alternate method, based on spherical harmonics, for obtaining rotation invariant representations. We describe the properties of this tool and show how it can be applied to a number of existing, orientation dependent descriptors to improve their matching performance. The advantages of this tool are two-fold: First, it improves the matching performance of many descriptors. Second, it reduces the dimensionality of the descriptor, providing a more compact representation, which in turn makes comparing two models more efficient.