Automatic Targetless Extrinsic Calibration for an Optical–Acoustic Stereo Imaging System

The accurate extrinsic calibration is essential for integrating optical and acoustic imaging sensors in underwater robotic systems, enabling precise multimodal perception in challenging aquatic environments. However, existing calibration methods typically depend on artificial targets or manual cross-modal feature matching, which are often impractical or unreliable in real-world underwater scenarios. To address these limitations, this article proposes a targetless extrinsic calibration method for optical–acoustic stereo imaging systems, which automatically estimates and refines extrinsic parameters without the need for predefined targets. The proposed method comprises a three-stage pipeline. First, the camera motion is estimated via visual structure-from-motion (SfM), while the sonar motion is recovered using the proposed acoustic bundle adjustment (ABA) algorithm and the symmetric dual-pose ambiguity elimination strategy, both specifically designed to address the unique nonlinear projection model of imaging sonar. Finally, to further improve accuracy, 3-D acoustic landmarks are utilized to formulate 3-D–2-D reprojection constraints, and a nonlinear optimization minimizes the geometric error to refine the extrinsic parameters. The proposed method is extensively validated in both simulated and real-world underwater environments. Experimental results demonstrate accurate and robust performance under varying noise levels and system configurations, with the final calibration results accurately satisfying the epipolar constraints of optical–acoustic stereo imaging systems.