Physics-Grounded Monocular Vehicle Distance Estimation Using Standardized License Plate Typography

Estimating the distance to a leading vehicle is a basic input to forward collision warning, adaptive cruise control, and automated emergency braking. Production systems obtain this distance from radar, laser scanners, or stereo camera pairs, which add cost, power draw, and packaging constraints. This paper asks whether a single ordinary camera can recover the same distance by using a target that is standardized in size and present on every road vehicle: the rear license plate. U.S. plates share a fixed outer size and a character height that is set by regulation and varies only narrowly between states, so the height of a plate character in the image is a direct measure of distance once the camera geometry is known. The proposed method (Typography-Based Monocular Distance Estimation) detects the plate, measures the height of its printed characters, identifies the issuing state to select the correct physical character height, and recovers distance from the camera projection. Three measurements taken from the same plate: the character height, the stroke width, and the character spacing. Together with the spacing of the two mounting holes and a single-image depth network, are combined so that a weak or corrupted measurement is given less weight automatically. The distance, its rate of change, and a time-to-collision estimate are smoothed across frames and used to raise a warning with the timing used by U.S. collision-warning regulations. The same plate that anchors the scale also identifies the vehicle, so the method returns a distance, a bearing, and an identity from one passive sensor. It reads scale from a printed standard instead of from time of flight or parallax, making it a cheap, low-maintenance complement to those sensors in a fault-tolerant perception stack, achieving the cost-effective distance estimation with error less than 0.13 m.

Dense depth estimation for autonomous driving faces a geometry-scale conflict: depth foundation models deliver pixel-aligned dense visual geometry without reliable metric scale, while projected LiDAR provides metric anchors that are sparse, noisy, and misaligned with image structures. Existing sparse-prompted methods incorporate LiDAR by regenerating depth from scratch, overriding the foundation model's coherent geometry and producing structural artifacts on visually continuous surfaces. Our key insight is that foundation models already capture geometrically coherent relative depth; no additional surface structure learning is required-only a per-pixel scale factor mapping relative geometry to metric coordinates. Based on this, we propose DrivingDepth, which treats sparse LiDAR as geometric prompts that locally calibrate a frozen foundation prior through residual pixel-wise scale correction, preserving dense visual geometry by construction. On nuScenes with 4-frame surround-view input, DrivingDepth achieves an AbsRel of 11.19 and an EdgeCR of 5.741, outperforming MapAnything (11.99/1.914) by simultaneously delivering SOTA metric accuracy and geometric consistency.

Accurate yet low-latency depth is essential for radar-camera perception in autonomous systems. Cameras provide rich appearance but lack metric scale, whereas automotive radar offers metric range but is sparse and noisy. Many pipelines are multi-stage or depend on auxiliary annotations, increasing latency and limiting portability. We introduce JustDepth, a single-stage radar-camera depth estimator trained only with radar, camera, and single-scan LiDAR. All radar returns are aggregated into a fixed-width 1D representation, decoupling runtime from point count. A Height Fusion Block fuses modalities, a lightweight GNN propagates depth globally, and a training-only confidence decoder stabilizes learning with zero test-time cost. We mitigate stripe artifacts via simple augmentations and quantify them using the Vertical-Horizontal Gradient Ratio (VHGR). On nuScenes, compared to recent state-of-the-art methods, JustDepth maintains accuracy while reducing inference time by 39.7x and stripe artifacts by 66% as measured by VHGR.