Non-rigid distortion correction for underwater images

Underwater images display significant non-rigid geometric distortions due to refraction and turbulence. Owing to unknown random fluctuations, the degree of distortion varies unpredictably in different regions, posing a challenge for the recovery of underwater images. The primary objective is to restore images from a sequence of distorted frames. First, we theoretically derive the relationship satisfied by the average optical flow field. Second, addressing the scenario of insufficient frames, we propose an iterative initialization method to alleviate the impact of limited frames, obtaining a satisfactory initial image. Subsequently, to mitigate the influence of errors, we relax the average optical flow field into the model. Additionally, we introduce feasible optimization methods to solve the new model. Finally, we validate the effectiveness of our strategy through comprehensive qualitative and quantitative experiments.