Underwater Vignetting Image Correction Based on Binary Polynomial Regularization and Latent Low-Rank Representation

Due to light attenuation and complex environments, underwater robots need to carry artificial light to improve visibility, which leads to issues such as brightness vignetting, low contrast, and color distortion in the captured underwater images. However, existing methods for enhancing underwater images often overlook the challenges caused by artificial light. To address these challenges, we construct a novel underwater vignetting image formation model and propose a correction method called UVIC. The method consists of three main modules: separating the vignetting component, separating the backscattering component, and adaptive brightness and color correction. In our model, based on the linear relationship between the image gradient and the coefficients of the binary polynomial, we introduce a binary polynomial regularization to separate the vignetting component without estimating the center of the vignetting. Additionally, the backscattering can be effectively separated by introducing a latent low-rank representation based on local consistency, without estimating atmospheric light and transmission parameters. Furthermore, we design an adaptive brightness and color correction module using the global brightness of the image L layer and the histogram distribution characteristics of the a and b layers to adjust the brightness and color bias of the image. Particularly, there are both additive and multiplicative operations, and we decompose the objective function into two submodels and solve them by the iterative reweighted least squares and alternating direction multiplier methods, respectively. Numerous experiments demonstrate that UVIC not only effectively corrects image brightness vignetting, but also improves color bias, contrast, and sharpness.