The recent neural implicit representation-based methods have greatly advanced the state of the art for solving the long-standing and challenging problem of reconstructing a discrete surface from a sparse point cloud. These methods generally learn either a binary occupancy or signed/unsigned distance field (SDF/UDF) as surface representation. However, existing SDF/UDF-based methods use neural networks to implicitly regress the distance in a purely data-driven manner, thus limiting the accuracy and generalizability to some extent. In contrast, we propose the first geometry-guided method for UDF and its gradient estimation that explicitly formulates the unsigned distance of a query point as the learnable affine averaging of its distances to the tangent planes of neighbouring points. Besides, we model the local geometric structure of the input point clouds by explicitly learning a quadratic polynomial for each point. This not only facilitates upsampling the input sparse point cloud but also naturally induces unoriented normal, which further augments UDF estimation. Finally, to extract triangle meshes from the predicted UDF we propose a customized edge-based marching cube module. We conduct extensive experiments and ablation studies to demonstrate the significant advantages of our method over state-of-the-art methods in terms of reconstruction accuracy, efficiency, and generalizability. The source code is publicly available at https://github.com/rsy6318/GeoUDF.

翻译：近年基于神经隐式表示的方法显著推进了从稀疏点云重建离散表面这一长期挑战性问题的研究进展。这类方法通常学习二值占用场或符号/无符号距离场（SDF/UDF）作为表面表示。然而，现有基于SDF/UDF的方法采用神经网络以纯数据驱动方式隐式回归距离场，在一定程度上限制了精度和泛化能力。对此，本文首次提出基于几何引导的UDF及其梯度估计方法，通过将查询点的无符号距离显式建模为邻近点切平面距离的可学习仿射平均值。此外，我们通过显式学习每个点的二次多项式来建模输入点云的局部几何结构。这不仅有助于对输入稀疏点云进行上采样，还能自然诱导出无向法向量，进一步增强UDF估计。最终，为从预测的UDF中提取三角网格，我们提出定制化的边基行进立方体模块。通过大规模实验与消融研究，证明本方法在重建精度、效率和泛化能力上相较于现有最优方法具有显著优势。源代码已发布于https://github.com/rsy6318/GeoUDF。