Underwater-to-air distorted image correction based on the reconstructed water surface

Abstract The lights with spatial target information received by the underwater camera are refracted at the intersection with the water surface, resulting in geometric distortion of the image. Existing methods for correcting the water-to-air distorted images typically rely on a large amount of data, such as image sequences, making the restoration using a single frame challenging. To address the issue, we propose a spatial pixel correction algorithm based on the reconstructed water surface. Firstly, we introduce a gradient water surface reconstruction algorithm based on the discrete normal vector, ensuring high accuracy in the spatial position and amplitude of the reconstructed water surface. Thus, intersections of the lights with the reconstructed water surface can be solved based on the constructed water surface. Subsequently, we propose a camera’s reverse tracking algorithm, which skillfully links the images with the spatial pixel coordinates. Finally, based on the characteristics of pixel arrangement, we propose a spatial grid algorithm to separate the spatial coordinates obtained by the reverse tracking algorithm. This part can better handle the highly concentrated and over-dispersed pixels in the spatial coordinate system. The proposed correction algorithm has better correction performance. The similarity between the restored and real images is more than 80%, and the mean square error is less than 0.01.