Refractive three-dimensional reconstruction for underwater stereo digital image correlation.

Measuring the three-dimensional (3D) deformation of submerged objects through different media with the stereo digital image correlation (stereo-DIC) method involves the refractive optical imaging problem where the non-linear transmission of light is induced by a change of medium density. The problem invalidates the underlying single viewpoint assumption of the perspective model in regular stereo-DIC, thereby resulting in erroneous measurements of 3D shape and deformation. In this work, we propose a refractive stereo-DIC method that overcomes the problem by considering light refraction in 3D reconstruction. We formulate a full refractive reconstruction geometry description based on Snell's law of flat refraction and the regular triangulation. This allows the true shape to be effectively reconstructed by tracing and establishing the refracted ray-paths based on the regular 3D reconstruction, without reformulating the camera model and image formation. The refractive stereo-DIC is finally established by integrating the refractive 3D reconstruction into the regular DIC framework for measuring accurate 3D shape and deformation of submerged objects. We experiment the proposed approach with underwater 3D shape and deformation measurements. Both results prove its feasibility and correctness, further heralding our approach as a flexible solution that could readily extend the stereo-DIC to fluid-immersed 3D deformation characterization.