Geometry Guided Adaptive Ray-Surface Intersection for LiDAR Camera Fusion Spatial Localization

In LiDAR-camera fusion measurement, conventional nearest-neighbor back-projection methods are limited by discrete point-cloud sampling and struggle to accurately recover the spatial position corresponding to image measurement points under sparse point-cloud conditions. Moreover, targets in complex industrial environments often exhibit diverse local geometric structures, making it difficult for a single surface model to effectively describe different surface characteristics. This paper proposes a Geometry-Guided Adaptive Ray-Surface Intersection measurement method, which replaces the traditional image-to-discrete-point mapping with ray-to-continuous-surface intersection. A spatial viewing ray is constructed from the image measurement point and camera optical center, and local neighborhood points are extracted through nearest projected-point back-projection. Based on curvature and normal-vector statistical features, local surfaces are classified into four geometric categories, and corresponding surface models are adaptively constructed using plane fitting, curved surface fitting, voxel-assisted plane searching, or bilinear patch fitting. The three-dimensional coordinates are then obtained through ray-model intersection. Experiments were conducted on multiple target types in an industrial equipment warehouse over a range of 5–20 m. The results show that the proposed method reduces the average measurement error from 5.63 cm of the nearest-neighbor method to 1.81 cm. When the point-cloud density decreases to 25%, the average absolute error increases by only 26.5%, compared with 92.6% and 58.7% for the nearest-neighbor and interpolation methods, respectively. These results demonstrate the effectiveness and robustness of the proposed method for LiDAR-camera fusion measurement under sparse point-cloud conditions.