In geometry processing, symmetry is a universal type of high-level structural information of 3D models and benefits many geometry processing tasks including shape segmentation, alignment, matching, and completion. Thus it is an important problem to analyze various symmetry forms of 3D shapes. Planar reflective symmetry is the most fundamental one. Traditional methods based on spatial sampling can be time-consuming and may not be able to identify all the symmetry planes. In this paper, we present a novel learning framework to automatically discover global planar reflective symmetry of a 3D shape. Our framework trains an unsupervised 3D convolutional neural network to extract global model features and then outputs possible global symmetry parameters, where input shapes are represented using voxels. We introduce a dedicated symmetry distance loss along with a regularization loss to avoid generating duplicated symmetry planes. Our network can also identify generalized cylinders by predicting their rotation axes. We further provide a method to remove invalid and duplicated planes and axes. We demonstrate that our method is able to produce reliable and accurate results. Our neural network based method is hundreds of times faster than the state-of-the-art methods, which are based on sampling. Our method is also robust even with noisy or incomplete input surfaces.
翻译:在几何处理中,对称是3D模型高层次结构信息的通用类型,有利于许多几何处理任务,包括形状分割、对齐、匹配和完成。因此,分析各种三维形状的对称形式是一个重要问题。平面反射对称是最基本的。基于空间取样的传统方法可能耗费时间,可能无法识别所有对称平面。在本文中,我们提出了一个新的学习框架,以自动发现3D形状的全球平面反射对称。我们的框架培训了一个不受监督的三维相向神经网络,以提取全球模型特征,然后输出可能的三维形状的对称参数。对称对称是对称是最基本的。我们采用了专门的对称距离损失和调整损失,以避免产生重复的对称平面平面平面平面。我们的网络还可以通过预测其旋转轴来识别通用的圆柱体。我们进一步提供了一种方法来清除一个无效和重复的3D形状的对称。我们所使用的方法甚至能够产生可靠和不精确的对称参数。我们的网络以数百个不完全的对称方法也是以更精确的对称的。我们网络以几百个不精确的对称方法为基础。