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.

我们提出了一种无监督的三维形状协同分割方法，通过从形状集合中学习一组可变形部件模板。我们的网络通过选择的部分模板组成每个形状，这些模板经过仿射变换以适应集合中的结构变化。为了最大限度地发挥部分模板的表达能力，我们引入了一个逐部位变形网络，以便对具有实质几何变化的多样部件进行建模，同时对变形能力施加约束，以确保对最初表示的部件的准确性。我们还提出了一种训练方案，有效地克服局部最小值。从体系结构上看，我们的网络是一个分支式自编码器，具有以体素形状为输入的 CNN 编码器，产生逐部位变换矩阵、潜在编码和部件存在评分，以及解码器输出的点占有率来定义重建损失。我们的网络称为 DAE-Net，可以实现无监督的三维形状协同分割，从而产生细粒度、紧凑且有意义的部件，并且在不同形状之间保持一致。我们在 ShapeNet Part 数据集、DFAUST 和 Objaverse 的动物子集上进行了大量实验，展示了优于之前方法的性能。