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.

翻译：现有的大规模三维形状数据集大多包含网格，这些网格虽非常适合渲染等视觉应用，但往往存在拓扑无效性（即包含非流形边和顶点、不连通组件、自相交）。因此，当前形状理解领域的前沿研究并未显式利用这些三维信息并不令人意外。与此同时，三角网格仍是许多下游任务中主导的形状表示方式，而其连通性作为更深入形状推理的潜在来源仍相对未被充分开发。本文提出ROAR——一种迭代式几何/拓扑演化方法，能够从任意三维形状表示重建二维流形三角网格，特别适用于现有的大规模野外数据集。ROAR利用大规模数据集固有的视觉先验，通过二维渲染损失和新型三维投影损失（平面投影）来演化网格几何。每次几何迭代后，系统执行拓扑修正：通过基于几何动因的衰减项减少自相交，并利用新颖的面片评分函数为需要区域增加分辨率。这些步骤交替进行直至收敛，最终生成高质量流形网格。我们在臭名昭著但广泛使用的ShapeNet数据集上评估ROAR，并推出ShapeROAR——一个保持拓扑有效且几何精确的ShapeNet改进版本。我们将结果与最先进的重建方法对比，展示了更优的形状保真度、拓扑正确性和三角剖分质量。此外，我们演示了从神经有符号距离函数（SDF）重建网格的过程，在显著减少SDF采样操作的前提下，达到了与常用Marching Cubes方法相当的Chamfer距离。