# Structural Information Reconstruction of Distorted Underwater Images Using Image Registration
## 1 Introduction  
When imaging through a fluctuating air-water surface using a fixed camera, the images acquired by observing the fixed objects that are completely immersed in the water, often suffer from severe distortions due to the water surface fluctuation. Furthermore, refraction occurs when light passes through the air-water interface, especially on the wavy water surface [1, 2]. The refraction angle is affected by the refractive index of the medium and angle of incidence. In addition, the attenuation derived from the scattering and absorption of the imaging path is also an important consideration that results in observation distortion. The suspended particles in the medium, such as organic matter, mineral salt, microorganisms, etc., are constantly consuming the beam energy and changing the propagation path of light [3, 4]. Hence, underwater image restoration is more challenging than similar problems in other environments. Research on this challenging problem has been carried out for decades. Some researchers consider that the distorted wavefront due to the fluctuated surface is the important factor of image degradation. Therefore, the adaptive optics method, which is popular in astronomical imaging, was used for underwater image correction at first. [PERSON] and [PERSON] [5] assumed that the distortions are mainly low-frequency aberration and phase shift, and proposed a simplified model based on adaptive optics. There are several methods using ripple estimation technology for underwater reconstruction. A simple algorithm was proposed in [6], where it reconstructs the 3D model of water surface ripple by optical flow estimation and statistical motion features. In [7], an algorithm based on the dynamic nature of the water surface was presented, which uses cyclic waves and circular ripples to express local aberration. [PERSON] et al. [8] proposed a model-based tracking algorithm. The distortion model, based on the wave equation, is established, then the model is fitted to frames to estimate the shape of the surface and restore the underwater scene. According to Cox-Munk law [9], if the water surface is sufficiently large and still, the normal water surface will roughly assume a Gaussian distribution. Inspired by the law, some approaches focus on finding the center of the distribution of patches from the image sequence as the orthoscopic patch [10]. Many strategies related to lucky regions have been proposed to deal with the problem. In [11], the graph-embedding technology was applied to block frames and calculate the local distance between them, and the shortest path algorithm was used to select patches to form the undistorted image. [PERSON] et al. [12; 13] came up with a similar method, where the motion blur and geometric distortion were modeled respectively, and the K-means algorithm was applied to replace the shortest path algorithm. [PERSON] et al. [14] combined bispectrum analysis with lucky region selection, and smooth edge transition by using patches fusion. A restoration method based on optical flow and lucky region was proposed by [PERSON] et al. [15]. The selection of a lucky patch is realized by image measurement metric and calculating the nonlinear gain coefficient of the current frame to each point. Later in [16; 17], [PERSON] et al. improved the resolution of their algorithm by developing structure tensor oriented image quality metrics. Recently in [18], on the basis of lucky region fusion, [PERSON] et al. put forward to a method that the input of distorted frame and output of restored frame are carried out at the same time. The quality of reconstruction is ameliorated by successive updating of the subsequent distorted frame. The registration technology [19; 20; 21; 22], which is originally used to recover the atmospheric turbulence image, is applied to address this issue. [PERSON] et al. [20] presented a two-stage nonrigid registration approach to overcome the structural turbulence of waves.