  Implicit neural representation is a recent approach to learn shape
collections as zero level-sets of neural networks, where each shape is
represented by a latent code. So far, the focus has been shape reconstruction,
while shape generalization was mostly left to generic encoder-decoder or
auto-decoder regularization.
  In this paper we advocate deformation-aware regularization for implicit
neural representations, aiming at producing plausible deformations as latent
code changes. The challenge is that implicit representations do not capture
correspondences between different shapes, which makes it difficult to represent
and regularize their deformations. Thus, we propose to pair the implicit
representation of the shapes with an explicit, piecewise linear deformation
field, learned as an auxiliary function. We demonstrate that, by regularizing
these deformation fields, we can encourage the implicit neural representation
to induce natural deformations in the learned shape space, such as
as-rigid-as-possible deformations.
