A reflective symmetry descriptor for 3D models
A reflective symmetry descriptor for 3D models
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DOI：
10.1007/s00453-003-1050-5
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发表时间：
2004-01-01
期刊：
影响因子：
1.1
通讯作者：
Rusinkiewicz, S
中科院分区：
文献类型：
--
作者：
Kazhdan, M;Chazelle, B;Rusinkiewicz, S
计算二维和三维形状的反射对称性是计算机视觉和计算几何中的经典问题。大多数先前的工作都集中在寻找对称的主轴，或确定不存在。在本文中，我们引入了一个新的反射对称描述符，表示通过模型的质心的所有平面（即使它们不是对称平面）的任意3D模型的反射对称性的测量。这个新的形状描述符的主要好处是，它是在一个规范的参数化（球体）定义的，并描述了一个3D形状的全局属性。我们将展示如何获得体素网格从任意的3D形状，并使用傅立叶方法，我们提出了一种算法，计算对称描述符在O（N-4 log N）时间为N × N × N体素网格和计算多分辨率近似在O（N-3 log N）时间。在我们最初的实验中，我们发现对称描述子对噪声不敏感，并且在点采样下是稳定的。我们还发现，它在形状匹配任务中表现良好，提供了一种与现有方法正交的形状相似性度量。
Computing reflective symmetries of 2D and 3D shapes is a classical problem in computer vision and computational geometry. Most prior work has focused on finding the main axes of symmetry, or determining that none exists. In this paper we introduce a new reflective symmetry descriptor that represents a measure of reflective symmetry for an arbitrary 3D model for all planes through the model's center of mass (even if they are not planes of symmetry). The main benefits of this new shape descriptor are that it is defined over a canonical parameterization (the sphere) and describes global properties of a 3D shape. We show how to obtain a voxel grid from arbitrary 3D shapes and, using Fourier methods, we present an algorithm that computes the symmetry descriptor in O (N-4 log N) time for an N x N x N voxel grid and computes a multiresolution approximation in O (N-3 log N) time. In our initial experiments, we have found that the symmetry descriptor is insensitive to noise and stable under point sampling. We have also found that it performs well in shape matching tasks, providing a measure of shape similarity that is orthogonal to existing methods.