# Neural 3D Morphable Models: Spiral Convolutional Networks for 3D Shape Representation Learning and Generation

## TL;DR

This paper introduces a novel spiral convolutional operator for 3D mesh data, enabling more effective shape representation and generation by explicitly modeling local vertex orderings, leading to state-of-the-art results in 3D shape modeling.

## Contribution

The paper proposes a new graph convolutional operator that enforces local vertex orderings on 3D meshes, improving shape modeling over existing methods.

## Key findings

- Achieves state-of-the-art results on 3D shape datasets.
- Outperforms linear Morphable Models and other graph operators.
- Provides a lightweight, topology-aware convolutional approach.

## Abstract

Generative models for 3D geometric data arise in many important applications in 3D computer vision and graphics. In this paper, we focus on 3D deformable shapes that share a common topological structure, such as human faces and bodies. Morphable Models and their variants, despite their linear formulation, have been widely used for shape representation, while most of the recently proposed nonlinear approaches resort to intermediate representations, such as 3D voxel grids or 2D views. In this work, we introduce a novel graph convolutional operator, acting directly on the 3D mesh, that explicitly models the inductive bias of the fixed underlying graph. This is achieved by enforcing consistent local orderings of the vertices of the graph, through the spiral operator, thus breaking the permutation invariance property that is adopted by all the prior work on Graph Neural Networks. Our operator comes by construction with desirable properties (anisotropic, topology-aware, lightweight, easy-to-optimise), and by using it as a building block for traditional deep generative architectures, we demonstrate state-of-the-art results on a variety of 3D shape datasets compared to the linear Morphable Model and other graph convolutional operators.