Surface reconstruction from a 3D point cloud is a long-standing problem in the field of computer graphics and vision, especially for point clouds that are sparse and noisy. To solve this problem, a novel method, termed LV-GCNN, that combines lossless voxelization and a graph convolutional neural network is proposed in this paper. Firstly, a lossless voxelization method for point clouds, which achieves lossless conversion from disordered point clouds to ordered volumetric maps, is proposed. Secondly, with the generated voxel, the feature pyramid is extracted through a 3D convolutional neural network. Thirdly, based on the similarity between the graph and surface mesh, the graph neural network is initialized as a unit spherical mesh. The coordinate relationship between the graph vertices and feature voxel units is used to match the corresponding hierarchical features for graph vertices. The initial spherical mesh is progressively deformed and upsampled via graph convolution and graph unpooling to achieve coarse-to-fine optimization of the surface mesh. Finally, because the deformation-based approach cannot reconstruct objects with a genus greater than zero, a genus optimization method is designed. Experiments show that the surface meshes generated by the LV-GCNN are comparable to or better than the results of state-of-the-art methods under several evaluation criteria. In addition, the reconstruction effect under different situations is discussed. Ablation experiments show the importance of several applied modules in LV-GCNN. Extra experiments show that the proposed method can achieve impressive results for point sets with diverse densities or that contain different levels of noise. The LV-GCNN results outperform other methods when the input point cloud is exceptionally sparse (256 points) or contains Gaussian noise with a standard deviation of 0.05. The chamfer distance (CD), Hausdorff distance (HD), voxel difference (VD), and depth difference (DD) of the reconstruction results of the LV-GCNN are 0.0494, 0.1457, 0.7390, and 18,402 when 256 points are used as input and are 0.0654, 0.1582, 0.6735, and 21,150 when points with noise with a standard deviation of 0.05 are used as input.

从 3D 点云重建表面是计算机图形学和视觉领域的一个长期存在的问题，尤其是对于稀疏和嘈杂的点云。为了解决这个问题，本文提出了一种结合无损体素化和图卷积神经网络的新方法，称为 LV-GCNN。首先，提出了一种点云无损体素化方法，实现了从无序点云到有序体积图的无损转换。其次，利用生成的体素，通过3D卷积神经网络提取特征金字塔。第三，基于图和面网格的相似性，将图神经网络初始化为单位球面网格。图顶点与特征体素单元之间的坐标关系用于匹配图顶点对应的层次特征。初始球形网格通过图卷积和图解池逐渐变形和上采样，以实现表面网格的粗到细优化。最后，由于基于变形的方法无法重构类大于零的对象，因此设计了类优化方法。实验表明，LV-GCNN 生成的表面网格在多个评估标准下与最先进方法的结果相当或更好。此外，还讨论了不同情况下的重建效果。消融实验显示了 LV-GCNN 中几个应用模块的重要性。额外的实验表明，所提出的方法可以为具有不同密度或包含不同噪声水平的点集取得令人印象深刻的结果。当输入点云异常稀疏（256 个点）或包含标准偏差为 0.05 的高斯噪声时，LV-GCNN 结果优于其他方法。LV-GCNN重建结果的倒角距离（CD）、豪斯多夫距离（HD）、体素差（VD）、深度差（DD）在256个点作为输入时分别为0.0494、0.1457、0.7390、18402当使用标准偏差为 0.05 的噪声点作为输入时，分别为 0.0654、0.1582、0.6735 和 21,150。当输入点云异常稀疏（256 个点）或包含标准偏差为 0.05 的高斯噪声时，LV-GCNN 结果优于其他方法。LV-GCNN重建结果的倒角距离（CD）、豪斯多夫距离（HD）、体素差（VD）、深度差（DD）在256个点作为输入时分别为0.0494、0.1457、0.7390、18402当使用标准偏差为 0.05 的噪声点作为输入时，分别为 0.0654、0.1582、0.6735 和 21,150。当输入点云异常稀疏（256 个点）或包含标准偏差为 0.05 的高斯噪声时，LV-GCNN 结果优于其他方法。LV-GCNN重建结果的倒角距离（CD）、豪斯多夫距离（HD）、体素差（VD）、深度差（DD）在256个点作为输入时分别为0.0494、0.1457、0.7390、18402当使用标准偏差为 0.05 的噪声点作为输入时，分别为 0.0654、0.1582、0.6735 和 21,150。