Modeling 3D Surfaces with a Locally Conditioned Atlas

Recently proposed methods for reconstructing 3D objects use a mesh with an atlas consisting of planar patches that approximate the object's surface. However, in real-world scenarios, the surfaces of reconstructed objects exhibit discontinuities that degrade the mesh's quality. Therefore, conducting additional research on methods to overcome discontinuities and improve mesh quality is always advantageous. This paper proposes to address the limitation by maintaining local consistency around patch vertices. We present LoCondA, a Locally Conditioned Atlas that represents a 3D object hierarchically as a generative model. The model initially maps the point cloud of an object onto a sphere and subsequently enforces the mapping to be locally consistent on both the sphere and the target object through the use of a spherical prior. Using this method, the mesh can be sampled on the sphere and then projected back onto the manifold of the object, yielding diverse topologies that can be seamlessly connected. The experimental results demonstrate that this approach produces structurally coherent reconstructions with meshes of comparable quality to those of competitors.