Two-Stage Probabilistic 3D Reconstruction of Underwater Objects via Range-Adaptive Sonar and Optical Fusion in Turbid Environments

This paper presents a two-stage probabilistic 3D reconstruction method for underwater objects in turbid environments that effectively utilizes complementary spatial information from sonar and optical measurements acquired by autonomous underwater vehicles (AUVs). The proposed method adapts to the different observation ranges of sonar and optical sensors through a two-stage strategy: Stage 1 establishes a prior occupancy map using sonar measurements alone when objects are beyond optical range; Stage 2 refines the reconstruction by probabilistically fusing optical constraints with sonar measurements when objects become optically visible. The key technical contributions are: (1) for Stage 1 sonar-only reconstruction, volumetric candidate voxel search that identifies all voxels within full 3D spherical shell segments defined by finite azimuth, elevation, and range resolutions. This volumetric representation is essential for enabling subsequent high-resolution fusion with optical measurements in Stage 2. Computational efficiency is achieved through a hierarchical divide-and-conquer algorithm. (2) Probabilistic sensor model explicitly considering voxel interdependencies and reachability to distinguish between object-occupied regions, verified free space, and occluded regions. (3) For Stage 2 optical-sonar fusion, constraint-based probabilistic matching that identifies all intersecting sonar pixels along optical rays, preventing erroneous reconstruction when optical measurements capture only a partial object views due to the limited observation range. Simulations and experiments demonstrate that the proposed method achieves superior reconstruction accuracy compared to sonar-only, optical-only, and conventional fusion methods, with particular robustness to increasing water turbidity.