We present an unsupervised 3D shape co-segmentation method which learns a set of deformable part templates from a shape collection. To accommodate structural variations in the collection, our network composes each shape by a selected subset of template parts which are affine-transformed. To maximize the expressive power of the part templates, we introduce a per-part deformation network to enable the modeling of diverse parts with substantial geometry variations, while imposing constraints on the deformation capacity to ensure fidelity to the originally represented parts. We also propose a training scheme to effectively overcome local minima. Architecturally, our network is a branched autoencoder, with a CNN encoder taking a voxel shape as input and producing per-part transformation matrices, latent codes, and part existence scores, and the decoder outputting point occupancies to define the reconstruction loss. Our network, coined DAE-Net for Deforming Auto-Encoder, can achieve unsupervised 3D shape co-segmentation that yields fine-grained, compact, and meaningful parts that are consistent across diverse shapes. We conduct extensive experiments on the ShapeNet Part dataset, DFAUST, and an animal subset of Objaverse to show superior performance over prior methods. Code and data are available at https://github.com/czq142857/DAE-Net.

翻译：我们提出了一种无监督的三维形状共分割方法，该方法从形状集合中学习一组可变形部件模板。为了适应集合中的结构变化，我们的网络通过选取经过仿射变换的模板部件子集来组合每个形状。为最大化部件模板的表达能力，我们引入了每个部件的变形网络，以支持具有显著几何变化的多样化部件建模，同时施加变形能力约束以确保对原始表示部件的保真度。我们还提出了一种训练方案以有效克服局部最小值问题。从架构上看，我们的网络是一个分支型自编码器，其CNN编码器以体素形状为输入，输出每个部件的变换矩阵、潜在编码和部件存在得分，解码器则输出点占有率以定义重建损失。我们将该网络命名为DAE-Net（Deforming Auto-Encoder的缩写），它能实现无监督的三维形状共分割，获得跨多样化形状一致、细粒度、紧凑且具有语义意义的部件。我们在ShapeNet Part数据集、DFAUST数据集以及Objaverse中的动物子集上进行了大量实验，结果表明其性能优于现有方法。代码与数据已开源至https://github.com/czq142857/DAE-Net。