  The majority of existing large 3D shape datasets contain meshes that lend
themselves extremely well to visual applications such as rendering, yet tend to
be topologically invalid (i.e, contain non-manifold edges and vertices,
disconnected components, self-intersections). Therefore, it is of no surprise
that state of the art studies in shape understanding do not explicitly use this
3D information. In conjunction with this, triangular meshes remain the dominant
shape representation for many downstream tasks, and their connectivity remain a
relatively untapped source of potential for more profound shape reasoning. In
this paper, we introduce ROAR, an iterative geometry/topology evolution
approach to reconstruct 2-manifold triangular meshes from arbitrary 3D shape
representations, that is highly suitable for large existing in-the-wild
datasets. ROAR leverages the visual prior large datasets exhibit by evolving
the geometry of the mesh via a 2D render loss, and a novel 3D projection loss,
the Planar Projection. After each geometry iteration, our system performs
topological corrections. Self-intersections are reduced following a
geometrically motivated attenuation term, and resolution is added to required
regions using a novel face scoring function. These steps alternate until
convergence is achieved, yielding a high-quality manifold mesh. We evaluate
ROAR on the notoriously messy yet popular dataset ShapeNet, and present
ShapeROAR - a topologically valid yet still geometrically accurate version of
ShapeNet. We compare our results to state-of-the-art reconstruction methods and
demonstrate superior shape faithfulness, topological correctness, and
triangulation quality. In addition, we demonstrate reconstructing a mesh from
neural Signed Distance Functions (SDF), and achieve comparable Chamfer distance
with much fewer SDF sampling operations than the commonly used Marching Cubes
approach.
