We present a learning-based method, namely GeoUDF,to tackle the long-standing and challenging problem of reconstructing a discrete surface from a sparse point cloud.To be specific, we propose a geometry-guided learning 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 neighboring points on the surface. 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 generality. The source code is publicly available at https://github.com/rsy6318/GeoUDF.

翻译：我们提出了一种名为GeoUDF的基于学习方法，以解决从稀疏点云重建离散曲面这一长期存在的挑战性问题。具体而言，我们提出了一种几何引导的UDF及其梯度估计学习方法，该方法将查询点的无符号距离显式建模为其到表面邻近点切平面距离的可学习仿射平均值。此外，我们通过为每个点显式学习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，进一步增强了UDF估计。最后，为从预测的UDF中提取三角网格，我们提出了一种定制的基于边的移动立方体模块。我们进行了大量实验和消融研究，证明该方法在重建精度、效率和泛化性方面相较于现有最先进方法具有显著优势。源代码已在https://github.com/rsy6318/GeoUDF公开提供。