Generating geometric 3D reconstructions from Neural Radiance Fields (NeRFs) is of great interest. However, accurate and complete reconstructions based on the density values are challenging. The network output depends on input data, NeRF network configuration and hyperparameter. As a result, the direct usage of density values, e.g. via filtering with global density thresholds, usually requires empirical investigations. Under the assumption that the density increases from non-object to object area, the utilization of density gradients from relative values is evident. As the density represents a position-dependent parameter it can be handled anisotropically, therefore processing of the voxelized 3D density field is justified. In this regard, we address geometric 3D reconstructions based on density gradients, whereas the gradients result from 3D edge detection filters of the first and second derivatives, namely Sobel, Canny and Laplacian of Gaussian. The gradients rely on relative neighboring density values in all directions, thus are independent from absolute magnitudes. Consequently, gradient filters are able to extract edges along a wide density range, almost independent from assumptions and empirical investigations. Our approach demonstrates the capability to achieve geometric 3D reconstructions with high geometric accuracy on object surfaces and remarkable object completeness. Notably, Canny filter effectively eliminates gaps, delivers a uniform point density, and strikes a favorable balance between correctness and completeness across the scenes.

翻译：从神经辐射场生成几何三维重建具有重要研究价值。然而，基于密度值实现精确且完整的重建具有挑战性。网络输出取决于输入数据、NeRF网络配置及超参数，因此直接使用密度值（例如通过全局密度阈值滤波）通常需要经验性验证。基于密度从非目标区域到目标区域递增的假设，利用相对值的密度梯度具有明显优势。由于密度为位置相关参数，可进行各向异性处理，因此对体素化三维密度场进行处理具有合理性。为此，我们提出基于密度梯度的几何三维重建方法，梯度来源于一阶与二阶三维边缘检测滤波器：Sobel、Canny及高斯拉普拉斯算子。梯度依赖于各方向的相邻密度相对值，与绝对量级无关，因此梯度滤波器能够沿宽密度范围提取边缘，几乎不依赖假设与经验验证。实验表明，本方法能够在物体表面实现高几何精度重建，并达到显著的物体完整性。值得注意的是，Canny滤波器有效消除了空洞，生成均匀点密度，并在各场景的正确性与完整性之间取得了良好平衡。