  Recently proposed 3D object reconstruction methods represent a mesh with an
atlas - a set of planar patches approximating the surface. However, their
application in a real-world scenario is limited since the surfaces of
reconstructed objects contain discontinuities, which degrades the quality of
the final mesh. This is mainly caused by independent processing of individual
patches, and in this work, we postulate to mitigate this limitation by
preserving local consistency around patch vertices. To that end, we introduce a
Locally Conditioned Atlas (LoCondA), a framework for representing a 3D object
hierarchically in a generative model. Firstly, the model maps a point cloud of
an object into a sphere. Secondly, by leveraging a spherical prior, we enforce
the mapping to be locally consistent on the sphere and on the target object.
This way, we can sample a mesh quad on that sphere and project it back onto the
object's manifold. With LoCondA, we can produce topologically diverse objects
while maintaining quads to be stitched together. We show that the proposed
approach provides structurally coherent reconstructions while producing meshes
of quality comparable to the competitors.
