We proposed a generalized method, NeuralSSD, for reconstructing a 3D implicit surface from the widely-available point cloud data. NeuralSSD is a solver-based on the neural Galerkin method, aimed at reconstructing higher-quality and accurate surfaces from input point clouds. Implicit method is preferred due to its ability to accurately represent shapes and its robustness in handling topological changes. However, existing parameterizations of implicit fields lack explicit mechanisms to ensure a tight fit between the surface and input data. To address this, we propose a novel energy equation that balances the reliability of point cloud information. Additionally, we introduce a new convolutional network that learns three-dimensional information to achieve superior optimization results. This approach ensures that the reconstructed surface closely adheres to the raw input points and infers valuable inductive biases from point clouds, resulting in a highly accurate and stable surface reconstruction. NeuralSSD is evaluated on a variety of challenging datasets, including the ShapeNet and Matterport datasets, and achieves state-of-the-art results in terms of both surface reconstruction accuracy and generalizability.

翻译：我们提出了一种通用方法——NeuralSSD，用于从广泛可用的点云数据中重建三维隐式表面。NeuralSSD是一种基于神经伽辽金方法的求解器，旨在从输入点云中重建更高质量和更精确的表面。隐式方法因其能够精确表示形状以及在处理拓扑变化时的鲁棒性而受到青睐。然而，现有隐式场的参数化方法缺乏明确的机制来确保表面与输入数据之间的紧密贴合。为解决这一问题，我们提出了一种新颖的能量方程，以平衡点云信息的可靠性。此外，我们引入了一种新的卷积网络，该网络学习三维信息以实现更优的优化结果。这种方法确保了重建表面紧密贴合原始输入点，并从点云中推断出有价值的归纳偏置，从而实现高精度且稳定的表面重建。NeuralSSD在多个具有挑战性的数据集（包括ShapeNet和Matterport数据集）上进行了评估，并在表面重建精度和泛化能力方面均达到了最先进的水平。