BeamScene: A Physically Consistent Framework with Beam-Footprint Geometry for 3D LiDAR Scene Completion

Autonomous vehicles depend on LiDAR for metrically accurate 3D perception, yet a single scan is sparse, and occluded regions are left almost empty. LiDAR scene completion recovers the missing geometry, but diffusion-based completion requires many network evaluations per scan, and recent single-pass methods place candidate points, choose feature scales, and supervise visibility with hand-set rules that are unrelated to how the sensor samples the scene. We present BeamScene, a single-pass framework that derives each of these decisions from one quantity, the beam footprint of every return, obtained from its range and the angular resolution of the sensor. The Beam-Footprint-Aware Candidate Constructor (BFCC) allocates an exact, bounded candidate budget in proportion to the footprint, spreads candidates in the ray-orthogonal tangent plane, and keeps every measured return as an immutable anchor. The Footprint-Aligned Shared-Scale Encoder (FASSE) shares sparse kernels across eight voxel resolutions and both input branches, and weights the resolutions with a parameter-free footprint-to-grid gate. The Frustum-Ray Visibility Objective (FRVO) adds frustum-local entropic transport and differentiable first-return and free-space terms during training only. On SemanticKITTI, BeamScene raises voxel IoU at $0.2\mathrm{m}$ and $0.1\mathrm{m}$ from $19.45$ and $6.30$ (LiNeXt) to $24.91$ and $8.74$, in a regime where Chamfer distance has largely saturated; its refined variant is the best of all compared methods on all six metrics of both SemanticKITTI and KITTI-360. The coarse model has $1.12$M parameters, $43.7\%$ fewer than LiNeXt, and runs in $0.234\mathrm{s}$ per scan, $17$–$99\times$ faster than diffusion-based completion.