  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.
