Correction of underwater images via fast centroid method and Wasserstein regularization

Abstract

Removing geometric distortion in images captured through turbulent media, like air and water, presents a substantial challenge. Previous studies have proposed a variational model that integrates optical flow with total variation (TV) regularization to address distortion. However, total variation regularization introduces an inherent bias-while it can recover the structure of the signal, it also leads to a reduction in the signal’s amplitude. In this paper, we extensively utilize histogram information, employing the Wasserstein distance as a constraint to reduce bias introduced by total variation regularization, thereby enhancing the quality of the restored images. The core concept involves minimizing the discrepancy between the histograms of the restored and distorted images using the Wasserstein distance. Moreover, for severely distorted underwater images, a fast centroid method is employed as a preprocessing step for the frames with distortion. Ultimately, experimental results demonstrate that the proposed model can mitigate the bias introduced by TV regularization and obtain high-quality restored images.