3D Density-Gradient based Edge Detection on Neural Radiance Fields
  (NeRFs) for Geometric Reconstruction
Miriam Jäger Boris Jutzi
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.