  This paper studies the problem of structured 3D reconstruction using
wireframes that consist of line segments and junctions, focusing on the
computation of structured boundary geometries of scenes. Instead of leveraging
matching-based solutions from 2D wireframes (or line segments) for 3D wireframe
reconstruction as done in prior arts, we present NEAT, a rendering-distilling
formulation using neural fields to represent 3D line segments with 2D
observations, and bipartite matching for perceiving and distilling of a sparse
set of 3D global junctions. The proposed {NEAT} enjoys the joint optimization
of the neural fields and the global junctions from scratch, using
view-dependent 2D observations without precomputed cross-view feature matching.
Comprehensive experiments on the DTU and BlendedMVS datasets demonstrate our
NEAT's superiority over state-of-the-art alternatives for 3D wireframe
reconstruction. Moreover, the distilled 3D global junctions by NEAT, are a
better initialization than SfM points, for the recently-emerged 3D Gaussian
Splatting for high-fidelity novel view synthesis using about 20 times fewer
initial 3D points. Project page: \url{https://xuenan.net/neat}.
