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Generating geometric 3D reconstructions from Neural Radiance Fields (NeRFs)is of great interest. However, accurate and complete reconstructions based onthe density values are challenging. The network output depends on input data,NeRF network configuration and hyperparameter. As a result, the direct usage ofdensity values, e.g. via filtering with global density thresholds, usuallyrequires empirical investigations. Under the assumption that the densityincreases from non-object to object area, the utilization of density gradientsfrom relative values is evident. As the density represents a position-dependentparameter it can be handled anisotropically, therefore processing of thevoxelized 3D density field is justified. In this regard, we address geometric3D reconstructions based on density gradients, whereas the gradients resultfrom 3D edge detection filters of the first and second derivatives, namelySobel, Canny and Laplacian of Gaussian. The gradients rely on relativeneighboring density values in all directions, thus are independent fromabsolute magnitudes. Consequently, gradient filters are able to extract edgesalong a wide density range, almost independent from assumptions and empiricalinvestigations. Our approach demonstrates the capability to achieve geometric3D reconstructions with high geometric accuracy on object surfaces andremarkable object completeness. Notably, Canny filter effectively eliminatesgaps, delivers a uniform point density, and strikes a favorable balance betweencorrectness and completeness across the scenes.

3D Density-Gradient based Edge Detection on Neural Radiance Fields (NeRFs) for Geometric Reconstruction