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.

翻译：我们提出一种无监督的3D形状共分割方法，该方法从形状集合中学习一组可形变部件模板。为适应集合中的结构变化，我们的网络通过仿射变换后的部件模板子集来组合每个形状。为最大化部件模板的表达能力，我们引入逐部件形变网络，在约束形变能力以保持对原始部件忠实性的同时，实现对具有显著几何变化的多样化部件的建模。我们还提出一种有效克服局部极小值的训练方案。在架构上，我们的网络是分支型自编码器：CNN编码器以体素形状为输入，生成逐部件变换矩阵、潜变量编码和部件存在分数；解码器输出点占用率以定义重建损失。我们的网络被命名为形变自编码器DAE-Net，能够实现无监督的3D形状共分割，产生跨不同形状一致的细粒度、紧凑且有意义的部件。我们在ShapeNet Part数据集、DFAUST数据集以及Objaverse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。