Improved Partial Differential Equation and Fast Approximation Algorithm for Hazy/Underwater/Dust Storm Image Enhancement

This paper presents an improved and modified partial differential equation (PDE)-based de-hazing algorithm. The proposed method combines logarithmic image processing models in a PDE formulation refined with linear filter-based operators in either spatial or frequency domain. Additionally, a fast, simplified de-hazing function approximation of the hazy image formation model is developed in combination with fuzzy homomorphic refinement. The proposed algorithm solves the problem of image darkening and over-enhancement of edges in addition to enhancement of dark image regions encountered in previous formulations. This is in addition to avoiding enhancement of sky regions in de-hazed images while avoiding halo effect. Furthermore, the proposed algorithm is utilized for underwater and dust storm image enhancement with the incorporation of a modified global contrast enhancement algorithm. Experimental comparisons indicate that the proposed approach surpasses a majority of the algorithms from the literature based on quantitative image quality metrics.