Abstract
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.
Abstract (translated)
生成神经网络辐射场(NeRF)的几何3D重构非常感兴趣。然而,基于密度值的准确和完整的重构是具有挑战性的。网络输出取决于输入数据、NeRF网络配置和超参数。因此,直接使用密度值,例如通过滤波使用全局密度阈值,通常需要经验调查。假设密度从非物体到物体区域增加,显然可以使用相对密度梯度。因为密度代表一个位置依赖性参数,可以处理 anisotropic 的,因此处理立方晶格密度场是合理的。在这方面,我们讨论基于密度梯度的几何3D重构,而梯度来自第一和第二阶导数的3D边缘检测滤波,即Sobel、卡尼和高斯洛伦兹。梯度依赖于相对相邻密度值在所有方向,因此与绝对值无关。因此,梯度过滤器能够提取沿广泛的密度范围的边缘,几乎与假设和经验调查无关。我们的方法展示了能力在物体表面和显著物体完整性的几何3D重构上实现高几何精度。值得注意的是,卡尼滤波有效地消除间隙,提供均匀的点密度,并 strike 正确性和完整性在场景之间的有利平衡。
URL
https://arxiv.org/abs/2309.14800
