  Most state-of-the-art deep geometric learning single-view reconstruction
approaches rely on encoder-decoder architectures that output either shape
parametrizations or implicit representations. However, these representations
rarely preserve the Euclidean structure of the 3D space objects exist in. In
this paper, we show that building a geometry preserving 3-dimensional latent
space helps the network concurrently learn global shape regularities and local
reasoning in the object coordinate space and, as a result, boosts performance.
We demonstrate both on ShapeNet synthetic images, which are often used for
benchmarking purposes, and on real-world images that our approach outperforms
state-of-the-art ones. Furthermore, the single-view pipeline naturally extends
to multi-view reconstruction, which we also show.
