coin *Neural 3D Morphable Models*. We quantitatively evaluate our methods on several popular datasets: human faces with different expressions (COMA [@coma]) and identities (Mein3D [@booth2018large]) and human bodies with shape ad pose variation (DFAUST [@dfaust:CVPR:2017]). Our model achieves state-of-the-art reconstruction results, outperforming the widely used linear 3D Morphable Model [@vetterMM] and the COMA autoencoder [@coma], as well other graph convolutional operators, including the initial formulation of the spiral operator [@spirals]. We also qualitatively assess our framework showing ‘shape arithmetic’ in the latent space of the autoencoder and by synthesising facial identities via a spiral convolution Wasserstein GAN.

Related Work
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**Generative models for arbitrary shapes:** Perhaps the most common approaches for generating arbitrary shapes are **volumetric CNNs** [@wu20153d; @qi2016volumetric; @maturana2015voxnet] acting on 3D voxels. For example, voxel regression from images [@girdhar2016learning], denoising autoencoders [@sharma2016vconv] and voxel-GANs [@wu2016learning] have been proposed. Among the key drawbacks of volumetric methods are their inherent high computational complexity and that they yield coarse and redundant representations. **Point clouds** are a simple and lightweight alternative to volumetric representation recently gaining popularity. Several methods have been proposed for representation learning of fixed-size point clouds [@achlioptas2017learning] using the PointNet [@qi2017pointnet] architecture. In [@yang2018foldingnet], point clouds of arbitrary size 