Mathematical Modeling And Algorithm On Single Image And Video Dehazing

The haze removal for hazy image can effectively reduce the sensitivity of the optical imaging system for bad weather,which has extensive range of application.From the view of mathematics,recovering the image degraded by the haze is an inverse problem in the mathematical imaging.This type of problem is generally difficult to be solved due to it is ill-posed.One of methods to solve this problem is making several priors and assumptions for image or the physical imaging model.This paper focuses on researching the mathematical modeling and algorithms in the single image and video dehazing and attempts to solve some problems existed in present researches that the edge of the recovered image is distorted;the dehazing algorithm cannot be applied to the hazy image with a large area of overcast sky or white object region and is inefficient in computation,especially in the video dehazing.The main works in this paper include:(1)the mathematical model and algorithms based on optimized theory are studied to mitigate the distortion of the edge of the recovered image;(2)designing a fast approximate algorithm to improve the efficiency of the dehazing algorithm;(3)a novel dehazing model is proposed to remove the haze in the hazy image with a large area of overcast sky region or white object;(4)for the challenging video dehazing task,an efficient and practical dehazing model,as well as the algorithm,are proposed to restore the hazy video.Firstly,by analyzing the efficiency and weakness of the dark channel prior model in single image dehazing in detail,this paper concludes that the dark channel prior and the assumption that the gray value of the transmission in the local patch is constant are the main reasons causing the distortion of the edge and the unnatural sky region or white object in the recovered image.Therefore,refining the rough transmission obtained by the dark channel prior model is crucial for the dehazing framework based on the dark channel prior.Two methods are used to solve the above problems in this paper.One is by adequately smoothing the rough transmission from the dark channel prior model to remove the large variation of the gradient and keep better continuity of the refined transmission.Depending on this designing of smoothing,a variational model for the single image dehazing is proposed to keep the recovered image having better characteristics of continuity and fidelity.The other is to develop a model to restore the exact edge of the rough transmission.A self-adaptive weighted least squares model which has ability of recovering the exact edge is proposed by introducing the gradient of the hazy image as parameters to control the operation of smoothing.Secondly,because the above transmission refining model can be essentially resolved by solving a linear equation system,this paper develops a fast approximate algorithm to solve the linear equation system by transforming the linear equation system into several tridiagonal linear systems which have high computational efficiency.This algorithm is an effective linear time algorithm and has excellent performance on optimizing the rough transmission.The experimental results show that the average running time of the algorithm has an improvement of over 20 times than that of the current algorithms.Thirdly,this paper believes that the smoothness prior is a key information for image and video dehazing.By introducing the smoothness prior and “the gray-world hypothesis”,two constraints are added into the dehazing model to prevent the refined transmission value from trending toward two extreme cases “0”and “1”that would make the physical imaging model bring the distortion of the recovered image.This novel model can be applied to the dehazing problem of the image with a large area of overcast sky region or white object and produces better dehazing effect.Finally,for the video dehazing,this paper proposes a bi-guided image filtering model to remove the haze of video.Inspired by the guided image filtering that has high computational efficiency,the bi-guided image filtering estimates the transmission of the later frame of video by approximating to the transmission of the first frame and the former frame of video simultaneously.The new technique has not only high computational efficiency,but also can keep better continuity on the video frames,which is an efficient and practical algorithm for the video dehazing.