  3D morphable models are widely used for the shape representation of an object
class in computer vision and graphics applications. In this work, we focus on
deep 3D morphable models that directly apply deep learning on 3D mesh data with
a hierarchical structure to capture information at multiple scales. While great
efforts have been made to design the convolution operator, how to best
aggregate vertex features across hierarchical levels deserves further
attention. In contrast to resorting to mesh decimation, we propose an attention
based module to learn mapping matrices for better feature aggregation across
hierarchical levels. Specifically, the mapping matrices are generated by a
compatibility function of the keys and queries. The keys and queries are
trainable variables, learned by optimizing the target objective, and shared by
all data samples of the same object class. Our proposed module can be used as a
train-only drop-in replacement for the feature aggregation in existing
architectures for both downsampling and upsampling. Our experiments show that
through the end-to-end training of the mapping matrices, we achieve
state-of-the-art results on a variety of 3D shape datasets in comparison to
existing morphable models.
