Haze Image Enhancement Algorithm Based On Partial Differential Equation

Images are the effective carrier of information.However,in fact,images captured under the natural condition are more or less blurred or missing pieces of key information,which causes inconvenience for practical application.Therefore,image processing technologies are widely used in practice.In particular,image enhancement is an important part of image processing technology.This paper mainly focus on image enhancement algorithm based on partial differential equation,through the analysis of the characteristics of fractional order differential and partial differential equation and the degradation process of haze image,then the atmospheric physical scattering model is introduced into our algorithm.First of all,an integer order partial differential equation model is established;then,a fractional order partial differential equation model is established combining the preponderance of the fractional differential.(1)Describing the formation mechanism of haze image.Calculating gradient on both sides of atmospheric scattering physical model,and turning the image from space domain to frequency domain,then energy functional of image recovery will be obtained,as well as the partial differential equation model through variational method.Using the dark channel prior,two transmission maps based patch dark channel and point dark channel can be estimated,respectively,then each of them are processed by fast wavelet transform.Afterwards,the high-frequency component which comes from the point transmission map and low-frequency component which comes from the patch transmission map are extracted.Then,inverse fast wavelet transform is used to obtain the fusion transmission,and Gaussian kernel is suggested to burr it.Finally,a high quality image can be obtained by finite difference method.Experiments on haze traffic images show that our algorithm can remove fog effectively,at the same time improve the sharpness and brightness of the image.(2)Considering the widespread application of fractional-order differential,a haze image enhancement model based on space fractional-order partial differential equation is obtained.Firstly,taking fractional derivative on both sides of the atmospheric physics scattering model,then obtain the corresponding partial differential equation by gradient descent method.Our method improves the weakness that image will be dark when using atmospheric scattering physical model directly,and halo phenomenon will occur when the image has a large area of the sky area;Compared to the image enhancement based on integer order partial differential equation model,image recovered by our method contains more details information,vehicle outline and the distance between vehicles is clearer,and the sky area is closer to the real image,at the same time,the contrast and brightness of image are increased and visual effect is better.