Density-Adaptive Point Transformer Region-Based Convolutional Neural Network with Evidential Uncertainty for 3D Object Detection

LiDAR return density falls approximately with the inverse square of range, so a pedestrian at fifty meters may yield fewer returns than the smallest neighborhood a multiscale detector is configured to aggregate over. Multiscale point transformers sum features from several fixed receptive fields with uniform weight, which forces background and ground returns into object descriptors at exactly the ranges where detection of vulnerable road users (VRUs) matters most. We present a density-adaptive point transformer with a region-based convolutional neural network (DAPT-RCNN), a two-stage detector organized around local point density as an explicit and exploitable signal. Density-adaptive multiscale aggregation (DAMS) replaces the fixed sum over K  = {5, 10, 20} with per-point convex weights predicted from a differentiable estimate of local volumetric density and sensor range, annealed from a uniform prior so that scale specialization is learned rather than imposed. Curvature-aware neighbor weighting (CAN-W) modulates each neighbor’s contribution by the analytic surface variation of its local patch, preserving the high-curvature limb and wheel geometry that separates pedestrians and cyclists from background clutter; it adds one scalar per sampling layer and is initialized as an exact identity. An evidential refinement head (EU-Head) replaces deterministic box regression with a normal-inverse-gamma formulation whose evidence strength is conditioned on the point count of each proposal, so that boxes fitted to very few returns report wide predictive intervals rather than unwarranted confidence. We further introduce a beam-decimation evaluation protocol that synthesizes 32-, 16- and 8-beam scans from 64-beam KITTI data by ring-index selection, and an accuracy-retention ratio measuring graceful degradation rather than peak accuracy alone. On the KITTI test set, domain-adaptive pretraining with a region-based convolutional neural network (DAPT-RCNN) attains 70.98% mean average precision (mAP) and, on the nuScenes validation set, 56.72% with gains of +2.6 to +4.0 AP points on pedestrians and cyclists beyond forty meters. Under 16-beam decimation, it retains 77.5% of its 64-beam accuracy against 72.6% for the fixed-scale baseline. The expected calibration error on the confidence branch falls from 0.087 for a deterministic head and 0.112 for Monte-Carlo dropout to 0.041, at a single forward pass rather than eight. Because these results are obtained on public benchmarks rather than on-road trials, we present them as evidence of stable behavior across the range of point densities represented in these benchmarks, and as an indication of potential benefit for advanced driver-assistance and roadside perception systems, rather than as a demonstration of in-service reliability.