Fourth-Order Partial Differential Equation Framelet Fusion-Based Colour Correction and Contrast Enhancement for Underwater Images

Abstract

A framelet augmented fourth-order forward-reverse partial differential equation (PDE)-fusion-based algorithm is proposed for underwater image enhancement. The algorithm combines framelet domain transform-based fusion of modified base, detail and amplified detail layers in a PDE-based formulation. The extracted layers via framelet decomposition with adaptive threshold computation comprise the detail and approximation components of the images, which are amplified, attenuated and aggregated. Additions include a modified global contrast enhancement/color correction function and a suitable color space transformation to enhance difficult underwater images with flat non-overlapping color channel histograms. Also, gradient domain fusion of several color corrected image layers and fuzzy rule-based enhancement is combined in the proposed PDE-based fusion framework. Furthermore, variational illumination correction was also employed for better enhancement of dark underwater images. Experimental comparisons indicate that the proposed approaches yield better overall visual and numerical results in most cases when compared with state-of-the-art methods.