An Extrinsic Calibration Method With Closed-Form Solution for Underwater Opti-Acoustic Imaging System

Forward-looking sonar (FLS) and camera are widely used sensors in multimodal systems for underwater environments. The extrinsic calibration is a precondition for this kind of multimodal systems to fuse optical and acoustic information. Due to the very different imaging formation mechanisms and models of 3-D-to-2-D projection for imaging sonar and optical camera, the multimodal correspondence and the sonar-pose recovery from a 2-D sonar image are two main issues in extrinsic calibration work. In this article, we propose an extrinsic calibration method for the opti-acoustic imaging system combining a camera and an FLS in underwater environment. The proposed method includes an estimation process yielding closed-form expressions to determine the sonar pose with respect to the calibration board, which enables the estimation of extrinsic parameters to be directly computed from sensor measurements and the knowledge of calibration-board structure. A calibration board with two sets of feature arrays is used to generate two 2-D-to-3-D correspondences, which circumvents the 2-D-to-2-D multimodal correspondence problem. An iterative optimization process is provided to further improve the performance, while the extra computation time is negligible. Both simulated and actual experiments show that the method outperforms the existing iterative method based on bundle adjustment.