  In this work we propose a method based on geometric deep learning to predict
the complete surface of the liver, given a partial point cloud of the organ
obtained during the surgical laparoscopic procedure. We introduce a new data
augmentation technique that randomly perturbs shapes in their frequency domain
to compensate the limited size of our dataset. The core of our method is a
variational autoencoder (VAE) that is trained to learn a latent space for
complete shapes of the liver. At inference time, the generative part of the
model is embedded in an optimisation procedure where the latent representation
is iteratively updated to generate a model that matches the intraoperative
partial point cloud. The effect of this optimisation is a progressive non-rigid
deformation of the initially generated shape. Our method is qualitatively
evaluated on real data and quantitatively evaluated on synthetic data. We
compared with a state-of-the-art rigid registration algorithm, that our method
outperformed in visible areas.
