Double-Helix Active Geometry: LiDAR-Anchored Multi-View Depth with Selective Abstention
Consumer depth sensors such as the LiDAR scanner on recent iPhones provide metric range, but their useful range is short and their returns are sparse. We present DH-Active, a lightweight, training-free geometry back-end that treats the sensor as a metric ruler rather than the sole source of depth. Near-field returns anchor the metric relative pose of two views through PnP; visually trackable samples without a valid depth return are then triangulated under that pose. A parallax/reprojection gate abstains wherever the geometry is ill-conditioned, leaving an explicit hole and a selective score instead of forcing an estimate. The measured core front end, including spiral sampling, sparse back-projection, and hole taxonomy but excluding preprocessing and multi-view recovery, runs at 1.11 ms median latency on CPU (OpenCV using 14 threads), about 38 times faster than a DINOv2-L visual branch on GPU in our timing setup. Across two iPhone captures and the public TUM RGB-D and ARKitScenes benchmarks, held-out depth is recovered at 1.4 to 6.7 percent median relative error. In a controlled ARKitScenes protocol that uses only returns within 2 m to set scale and an independent laser scan as ground truth, DH-Active achieves 64.2 percent scene-median coverage of evaluable far-field candidates at 13.4 percent scene-median relative error; direct triangulation from the device trajectory is not usable. We also report the alternatives that failed in our tests: single-frame defocus, classical focus-stack depth, defocus-LiDAR fusion, point-to-point ICP over a good visual-inertial track, and attention-to-holes resampling. A 1.26 B learned model remains more accurate after oracle scale alignment. The contribution here is narrower: metric sparse depth, explicit abstention, zero learned parameters, and near-millisecond CPU cost.