  We propose a new representation for encoding 3D shapes as neural fields. The
representation is designed to be compatible with the transformer architecture
and to benefit both shape reconstruction and shape generation. Existing works
on neural fields are grid-based representations with latents defined on a
regular grid. In contrast, we define latents on irregular grids, enabling our
representation to be sparse and adaptive. In the context of shape
reconstruction from point clouds, our shape representation built on irregular
grids improves upon grid-based methods in terms of reconstruction accuracy. For
shape generation, our representation promotes high-quality shape generation
using auto-regressive probabilistic models. We show different applications that
improve over the current state of the art. First, we show results for
probabilistic shape reconstruction from a single higher resolution image.
Second, we train a probabilistic model conditioned on very low resolution
images. Third, we apply our model to category-conditioned generation. All
probabilistic experiments confirm that we are able to generate detailed and
high quality shapes to yield the new state of the art in generative 3D shape
modeling.
