Improved partial differential equation and fast approximation algorithm for hazy/underwater/dust storm image enhancement

Abstract

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 dehazed 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.Keywords: Logarithmic image processing; illumination-reflectance model; filter kernel-based enhancement; filter-based dynamic range compression; power law-based illumination correction; partial differential equations. A d v a n c e s i n I m a g e a n d V i d e o P r o c e s s i n g ; V o l u m e 7 , N o . 3 , J u n e 2 0 1 9 S o c i e t y f o r S c i e n c e a n d E d u c a t i o n , U n i t e d K i n g d o m 13the Laplacian-based soft mapping procedure in the original DCP, He et al proposed the guided filter to reduce the runtime [5]. However, the guided filter does not preserve fine structures according to Li and Zheng [6]. Thus, they proposed a novel globally guided image filtering (G-GIF) composed of both global structure transfer filter and global edge-preserving smoothing filters for image fine structure preservation-based de-hazing [6].Recently, fusion [7] [8] [9] [10] [11] and deep learning-based approaches [12] have become increasingly popular and widespread [2] due to faster and greater computing resources. However, a vast amount of images is required in the training stage in addition to considerable computing resources and runtime for the deep learning approaches. The fusion-based methods are relatively much more involved than the purely enhancement-based approaches but effective in most cases. Also, the restoration methods require tuning of several parameters for different images to obtain best results. Brief overview and backgroundThe haze in images can be likened to illumination in dark or shadowy images [17] since the end result of uneven illumination and haze is the reduction in image visibility and contrast. Thus, by maximizing contrast, the visibility of the image scene is enhanced, reducing the haze or uneven illumination. This Uche A. Nnolim; Improved Partial Differential Equation and Fast Approximation Algorithm for Hazy/Underwater/Dust Storm Image Enhancement