A planar-reflective symmetry transform for 3D shapes
A planar-reflective symmetry transform for 3D shapes
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DOI：
10.1145/1179352.1141923
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发表时间：
2006-07
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影响因子：
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通讯作者：
Joshua Podolak;Philip Shilane;Aleksey Golovinskiy;S. Rusinkiewicz;T. Funkhouser
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文献类型：
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作者：
Joshua Podolak;Philip Shilane;Aleksey Golovinskiy;S. Rusinkiewicz;T. Funkhouser
对称是许多应用程序的重要提示，包括对象对齐、识别和分割。在本文中，我们描述了一个平面反射对称变换（PRST），它捕获了一个形状相对于所有可能平面的反射对称的连续度量。这种转换结合并扩展了之前的工作，即专注于3D网格中相对于质心的全局对称性和相对于2D图像中点的局部对称性。给出了一种计算曲面变换的有效蒙特卡罗采样算法，并证明了该算法在一般变换下是稳定的。我们还提供了一种迭代优化算法来精确地找到变换的局部最大值。我们使用变换定义了两个新的几何属性，对称中心和主对称轴，并证明了它们在正则坐标系中对物体的对齐是有用的。最后，我们证明了对称变换在计算机图形学中的几种应用是有用的，包括形状匹配、网格分割和自动视点选择。
Symmetry is an important cue for many applications, including object alignment, recognition, and segmentation. In this paper, we describe a planar reflective symmetry transform (PRST) that captures a continuous measure of the reflectional symmetry of a shape with respect to all possible planes. This transform combines and extends previous work that has focused on global symmetries with respect to the center of mass in 3D meshes and local symmetries with respect to points in 2D images. We provide an efficient Monte Carlo sampling algorithm for computing the transform for surfaces and show that it is stable under common transformations. We also provide an iterative refinement algorithm to find local maxima of the transform precisely. We use the transform to define two new geometric properties, center of symmetry and principal symmetry axes, and show that they are useful for aligning objects in a canonical coordinate system. Finally, we demonstrate that the symmetry transform is useful for several applications in computer graphics, including shape matching, segmentation of meshes into parts, and automatic viewpoint selection.