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.

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