In geometry processing, symmetry is the universal high level structural information of the 3d models and benefits many geometry processing tasks including shape segmentation, alignment, matching, completion, \textit{e.g.}. Thus it is an important problem to analyze various forms of the symmetry of 3D shapes. The 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 isotropic shapes 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. \LX{Our neural network based method is hundreds of times faster than the state-of-the-art method, which is based on sampling.} Our method is also robust even with noisy or incomplete input surfaces.

本文提出了一种基于卷积神经网络的无监督学习框架，以自动发现三维形状的全局平面镜像对称性，并可识别广义圆柱体旋转轴。该方法相较于现有基于采样的方法快数百倍，即使在有噪音或不完整的输入表面数据下也很稳健。

PRS-Net：三维模型平面镜像对称性检测网络