CN104318528A - Foggy weather image restoration method based on multi-scale WLS filtering - Google Patents

Abstract

The invention belongs to the field of image processing and relates to a foggy weather image restoration method based on multi-scale WLS filtering. The method comprises the steps of estimating atmosphere illumination intensity A according to a dark channel apriori principle; performing white balance on an image I according to an obtained a value of the atmosphere illumination intensity A and simplifying an atmospheric scattering model; performing rough estimation on an atmospheric dissipative function V to obtain (shown in the description); adopting the multi-scale WLS filtering to conduct fine estimation on the atmospheric dissipative function so as to obtain Vi; restoring a foggy weather image to be an ideal weather image Ri according to the obtained multi-scale atmospheric dissipative function Vi and the simplified atmospheric scattering model; adopting a tone mapping method to adjust an image dynamic range according to the restored multi-scale image Ri and performing visibility improvement to obtain a final result R. The foggy weather image restoration method based on multi-scale WLS filtering can effectively improve the contrast ratio and definition of the foggy weather image and has the advantages of being low in computation complexity, high in execution efficiency and the like.

Description

Based on the Misty Image restoration methods of multiple dimensioned WLS filtering

Technical field

The invention belongs to image processing field, be specifically related to a kind of Misty Image disposal route based on multiple dimensioned WLS (Weighted least squares, weighted least-squares method) filtering.

Background technology

Under the weather condition such as mist, haze, because the visibility of scene reduces, in image, the feature such as target contrast and color is attenuated, and this greatly limits and have impact on outwork system, as video monitoring, topographic(al) reconnaissance, automatic Pilot etc.Therefore, the realization recovered Misty Image is a problem having realistic meaning.

At present, have two classes substantially to the method that Misty Image carries out sharpening process: based on model with the algorithm of non-model.Here model refers to atmospherical scattering model, and it is a kind of physical model describing light and transmit in an atmosphere.Wherein, the algorithm based on non-model does not require the reason understanding image degradation, can only improve visual effect to a certain extent.These class methods belong to image enhancement technique category, mainly comprise: histogram method, based on the method for small echo, and based on the algorithm etc. of Retinex; Algorithm based on model carries out by understanding the immanent cause of image degradation the visibility that inverse operation improves image, this class methods process image is adopted to belong to image-recovery technique category, because they make use of the Physical Mechanism of image degradation, therefore this kind of algorithm is more reliable, and mist elimination effect is more obvious.

In recent years, the research based on model achieves larger progress, particularly achieves important breakthrough for single image mist elimination technology.Document 1 (Tarel J P, Hauti N.Fast visibility restoration from a single color or gray level image [J] .Proceedings of IEEE Conference on International Conference on Computer Vision, Kyoto, Japan, 2009:20-28) suppose that atmospheric dissipation letter approaches maximal value in feasible zone, and localized variation is mild, proposes a kind of rapid image mist elimination algorithm.The method adopts median filter method to estimate atmospheric dissipation function, and its shortcoming is that Hemifusus ternatanus ability is poor.Document 2 (He K, Sun J, Tang X.Single image haze removal using dark channel prior [C] .Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (CVPR) .New York, USA:IEEE Computer Society, 2009:1956-1963) by proposing dark primary priori theoretical to the outdoor statistical experiment without mist image, utilize this theory to obtain good mist elimination effect, and corresponding depth image can be obtained.The method possesses physics validity, but algorithm complex is high, processing speed is slow.

Summary of the invention

The object of the invention is to propose a kind of Misty Image restoration methods based on multiple dimensioned WLS filtering, atmospherical scattering model is adopted to carry out modeling to greasy weather scene, accurately solve atmospheric dissipation function, effectively remove the impact of fog in image, improve Misty Image visibility.

Provide the principle of the method for the invention below.

In foggy weather situation, the diameter of suspended particle floating in air is larger, and it not only has direct impact to incident light, also can reflect the surround lighting of surrounding.Atmospherical scattering model can be used in describing the physical characteristics that this light transmitted in the greasy weather, and this model representation is as follows:

I(x,y)＝R(x,y)e ^-βd(x,y)+A(1-e ^-βd(x,y))

Wherein, I is original image brightness, and R is the picture rich in detail brightness under desirable weather, and A is atmosphere light photograph of overall importance, and β is atmospheric scattering coefficient, and under foggy environment, it can think a constant had nothing to do with wavelength, and d is the depth of field.The present invention is in order to avoid direct solution d and β two parameters, and adopt the mode solving atmospheric dissipation function, it is expressed as:

V(x,y)＝1-e ^-βd(x,y)

Wherein, V is atmospheric dissipation function, comprises depth of view information, can represent roughly the impact of fog.In conjunction with above formula and atmospherical scattering model known, defogging process transition is calculate A and V two parameters by I, and then solves picture rich in detail R.R also can be decomposed into:

R(x,y)＝Aρ(x,y)

Wherein, ρ is scene albedo.

According to above-mentioned principle, the method for the invention comprises the following steps:

Step 1: estimate atmosphere illumination intensity A according to dark channel prior principle.

Step 2: the value combining the atmosphere illumination intensity A obtained, carries out white balance to image I, and simplifies atmospherical scattering model.

Step 3: according to the physical attribute of foggy environment, carries out rough estimate to atmospheric dissipation function, obtains

Step 4: adopt multiple dimensioned WLS filtering to atmospheric dissipation function carefully estimate, obtain V _i, i be greater than zero integer.

Step 5: combine the multiple dimensioned atmospheric dissipation function V obtained _i, according to simplifying atmospherical scattering model, to recover Misty Image be image R under desirable weather _i.

Step 6: combine the multiple dimensioned Recovery image R obtained _i, adopt tone-mapping algorithm adjustment output image dynamic range, carry out the lifting of visibility, obtain net result R.

Compared with prior art, the present invention has the following advantages:

(1) the present invention effectively can improve contrast and the sharpness of Misty Image, has the advantages such as computation complexity is lower, execution efficiency is stronger.Experiment proves, has the phenomenon of excessive correction after method mist elimination process described in document 1, and there is fog and remove incomplete phenomenon.The mist elimination effect of method described in document 2 is comparatively natural, but to highlight ability poor for details, performs consuming time longer.Compare the two, the method for the invention mist elimination Be very effective, maintains color of image preferably, enhances detailed information, has increased substantially picture contrast.

(2) there is important using value in the present invention in a lot of fields.Such as, all can process for gray level image and coloured image, the present invention can meet the requirement for image visibility such as video monitoring, target following, information identification.In addition, the present invention has very high practical value in fields such as freeway traffic monitoring, military surveillance, remote sensings.

Accompanying drawing explanation

Fig. 1 is the process flow diagram of the method for the invention;

Fig. 2 is the result that the embodiment of the present invention obtains: (a) original image, (b) single scale refinement result V ₁, (c) single scale mist elimination result R ₁, (d) tests net result R;

Fig. 3 ~ 5 are the present invention and prior art Contrast on effect 1 ~ 3, (a) original image, and (b) applies the result that document 1 obtains, and (c) applies the result that document 2 obtains, and (d) applies the result that the present invention obtains.

Embodiment

Below in conjunction with drawings and embodiments, the present invention will be further described.

The process flow diagram of the method for the invention as shown in Figure 1, specifically comprises the following steps:

Step 1: input original image, for Fig. 2 (a), is the Misty Image of 315 × 315 sized by this figure, adopts the method based on dark channel prior to solve global constant's atmosphere light according to A.

Dark channel prior is thought in non-sky image block, has at least a Color Channel to have very low brightness in some pixel.For a width Misty Image I, can define dark is:

$I^{\mathrm{dark}}\left(q\right)=\underset{c\∈\{R,G,B\}}{\min }\left(\underset{p\∈\mathrm{\Ω}\left(q\right)}{\min }\left(I^c\left(p\right)\right)\right)$

Wherein, I ^darkfor the dark of I, c is Color Channel index value, I ^cbe a Color Channel of I, Ω (x) is a localized mass centered by pixel q.According to dark channel prior theory, if I is the outdoor image of a width without mist, then except sky areas, I ^darkbrightness all lower and close to 0.Namely clear area (non-sky areas) I being arranged in Misty Image can be thought ^dark→ 0.

After obtaining dark result, by dark I ^darkin pixel sort from big to small by brightness value, choose sequence after brightness value front 0.1% pixel, then, the pixel of same position in the original image I of its correspondence is expressed as I _0.1%, these points are all the points that mist is the denseest, it is generally acknowledged that air illumination value is positioned at I _0.1%in scope.In order to mist elimination process is more thorough, get I _0.1%average A _mean=mean (I _0.1%) as the initial value of atmosphere light photograph.Because foggy environment is usually along with the cloudy day, causes fog to deviate from pure white color, therefore need A _meancorrect, mapped close to white (1,1,1), namely

$A=A_{\mathrm{mean}}/\underset{c\∈R,G,B}{\max }\left(A_{\mathrm{mean}}^c\right)$

Wherein, A is the air illumination value of application claims solution.

Step 2: by atmosphere light according to carrying out white balance to image, simultaneously atmospherical scattering model is simplified.

Protoatmosphere scattering model is expressed as:

I(x,y)＝R(x,y)e ^-βd(x,y)+A(1-e ^-βd(x,y))

Wherein, I is original image brightness, and R is the picture rich in detail brightness under desirable weather, and A is atmosphere light photograph of overall importance, and β is atmospheric scattering coefficient, and under foggy environment, it can think a constant had nothing to do with wavelength, and d is the depth of field.In order to avoid direct solution d and β two parameters, adopt the mode solving atmospheric dissipation function, it is expressed as:

V(x,y)＝1-e ^-βd(x,y)

Wherein, V is atmospheric dissipation function, comprises depth of view information, can represent roughly the impact of fog.

Be expressed as by the simplification atmospherical scattering model obtained after white balance process:

I'(x.y)＝I(x,y)/A＝ρ(x,y)(1-V(x,y))+V(x,y)

Wherein, I' is the image after white balance process; ρ is scene albedo, and:

R(x,y)＝Aρ(x,y)

The object of white balance process avoids the phenomenon of integral image colour cast to occur.

Step 3: rough estimate is carried out to V.

According to the physical attribute of greasy weather scene, 2 constraint conditions below V demand fulfillment:

(1)0≤V(x,y)≤1

(2) V (x, y) is not more than I'(x, y) Minimal color weight

By above-mentioned constraint, each pixel of the Misty Image after white balance can be defined as the rough estimate result of atmospheric dissipation function at the Minimal color weight of RGB tri-passages that is:

$\tilde{V}(x,y)=\underset{c\∈\{R,G,B\}}{\min }\left(I^{\′}(x,y)\right)$

For a width gray-scale map, then have now do not possess the characteristics such as atmospheric dissipation function local smoothing method, need further refinement.

Step 4: adopt multiple dimensioned WLS filtering to obtain rough estimate carry out refinement, solve desirable atmospheric dissipation function V.

WLS filtering can be expressed as and minimize following cost function:

$\mathrm{\Σ}[{(V(x,y)-\tilde{V}(x,y))}^2+{\mathrm{\λ}}_i(g_x\left(\tilde{V}(x,y)\right){\left(\frac{\∂V(x,y)}{\∂x}\right)}^2+g_y\left(\tilde{V}(x,y)\right){\left(\frac{\∂V(x,y)}{\∂y}\right)}^2)]$

Wherein, formula left end Section 1 is data item, and this target minimizes input picture with the difference of output image V; Section 2 is level and smooth project, and this reaches level and smooth object, λ by the partial derivative in x and the y direction minimizing V _ifor regulating parameter, i is yardstick index value.G is level and smooth weights, is defined as:

$g_x\left(\tilde{V}(x,y)\right)={({\left|\frac{\∂\ln \left(\tilde{V}(x,y)\right)}{\∂x}\right|}^{{\mathrm{\γ}}_i}-\mathrm{\ϵ})}^{-1},g_y\left(\tilde{V}(x,y)\right)={({\left|\frac{\∂\ln \left(\tilde{V}(x,y)\right)}{\∂y}\right|}^{{\mathrm{\γ}}_i}+\mathrm{\ϵ})}^{-1}$

Wherein, ε is a very little constant, and prevent divisor from being zero, the present invention fixes ε=0.00001, γ _ifor the sensitivity parameter of regulating gradient change.Matrix form can be changed into by after the least energy formula discretize of WLS:

${(V-\tilde{V})}^T(V-\tilde{V})+{\mathrm{\λ}}_i(V^T{D}_x^T{A}_x{D}_{x}V+V^T{D}_y^T{A}_y{D}_{y}V)$

Wherein, A _xand A _yabout refinement weights g _xand g _ydiagonal matrix; D _xand D _ybe the forward difference matrix in x and y direction, and with for backward difference matrix, minimizing of above formula can be converted into following equations:

$(E+{\mathrm{\λ}}_{i}G)V=\tilde{V}$

Wherein, E representation unit matrix, for sparse Laplacian matrix.Above formula can obtain the V after thinning processing by linear solution _i.The present invention adopts different λ _iand γ _iparameter is carried out multiple dimensioned atmospheric dissipation function and is solved, observe through many experiments and find, as yardstick quantity i=3, the result of acquisition is ideal, as I>3, it is less that visual effect promotes degree, and add computation complexity, therefore, under normal circumstances, yardstick quantity is set as 3 by the present invention, i.e. i=3, below step also will be introduced with this yardstick quantity.

Step 5: asking for atmosphere light intensity A and atmospheric dissipation function V _ibasis on, directly can recover the brightness of image of scene under desirable weather condition:

$R_i(x,y)=\frac{I(x,y)-k{V}_i(x,y)}{1-V_i(x,y)}\×A$

Wherein, k (0<k<1) is for recovering regulating parameter, and for controlling the degree of mist elimination, the present invention is fixedly installed k=0.95.Multiple dimensioned picture rich in detail R is obtained through solving of above formula _i, wherein, the atmospheric dissipation function example under single yardstick is as shown in Fig. 2 (b), and the single yardstick picture rich in detail result of its correspondence is as shown in Fig. 2 (c).

Step 6: adopt multiple dimensioned tone-mapping algorithm to improve mist elimination result, shows tone and details and controls.Known i=3, obtaining mist elimination result by above-mentioned steps is R _i.First the conversion of color space is carried out, by image R _iby RGB color space conversion to CIELAB color space, only to the brightness space L process of image.Suppose R ₁misty Image recovery effects best, then establish layer based on b, i.e. b=R ₁if, two levels of detail d ¹with d ², i.e. d ¹=R ₁-R ₂, d ²=R ₂-R ₃.Then tone mapping formula is defined as:

$R_p=\mathrm{\&mu;}+C({\mathrm{\&delta;}}_0,\mathrm{\&eta;}{b}_p-\mathrm{\&mu;})+C({\mathrm{\&delta;}}_1,d_p^1)+C({\mathrm{\&delta;}}_2,d_p^2)$

Wherein, p represents pixel, and μ is the average of brightness of image scope, and C is S type adjustment function, and for regulating dynamic range, i.e. C (a, u)=1/ (1+exp (-au)), η is exposure parameter, δ ₀, δ ₁with δ ₂for gain parameter.By R ₁based on layer ensure mist elimination treatment effect, merge levels of detail d ¹with d ², carried out well supplementing to final result.

After above-mentioned process, by image by CIELAB color space conversion to RGB color space, last Misty Image restoration result R can be obtained.As shown in Fig. 2 (d), after the inventive method process, the fog in original input image obtains good removal, and the features such as the details of image and color obtain obvious enhancing.

For verifying the validity of the method for the invention, the effect of method described in application the method for the invention and application document 1,2 being carried out to Misty Image Recovery processing compares.Select size be 315 × 315 Misty Image as recovery object, the optimum configurations that the present invention relates to is λ ₁=0.1, λ ₂=0.5, λ ₃=0.8, γ ₁=γ ₂=γ ₃=1.2 (three scale parameters), δ ₀=4, δ ₁=1, δ ₂=10, η=1 (tone-mapping algorithm parameter).The experimental result that Fig. 3, Fig. 4 and Fig. 5 obtain after being through three kinds of algorithm process, input picture size is respectively 290 × 380,600 × 450 and 600 × 400.From Fig. 3 ~ 5, be all significantly improved by the mist image definition after mist elimination process, fog all obtains good removal.Relatively the mist elimination effect of several method, has the phenomenon of excessive correction after method mist elimination process described in document 1, and as Fig. 3, the result after process is comparatively unnatural.And the method adopts self-adapting window, easily occur the situation of residual fog, as Fig. 4, near the building after process, adularescent fog does not remove completely; The mist elimination effect of method described in document 2 is comparatively natural, but to highlight ability poor for details.Compare the two, the method for the invention mist elimination Be very effective, maintains color of image preferably, enhances detailed information, has increased substantially picture contrast.

Claims (7)

1., based on the Misty Image restoration methods of multiple dimensioned WLS filtering, it is characterized in that comprising the following steps:

Step 1: estimate atmosphere illumination intensity A according to dark channel prior principle;

Step 2: the value combining the atmosphere illumination intensity A obtained, carries out white balance to image I, and simplifies atmospherical scattering model;

Step 3: according to the physical attribute of foggy environment, carries out rough estimate to atmospheric dissipation function V, obtains

Step 4: adopt multiple dimensioned weighted least-squares method WLS filtering carefully to estimate atmospheric dissipation function, obtain V _i, i be greater than zero integer;

Step 5: combine the multiple dimensioned atmospheric dissipation function V obtained _i, according to simplifying atmospherical scattering model, to recover Misty Image be image R under desirable weather _i;

Step 6: combine the multiple dimensioned Recovery image R obtained _i, adopt tone-mapping algorithm adjustment dynamic range of images, carry out the lifting of visibility, obtain net result R.

2. the Misty Image restoration methods based on multiple dimensioned WLS filtering according to claim 1, it is characterized in that, described in step 1, the evaluation method of atmosphere illumination intensity A is as follows:

Dark channel prior is thought in non-sky image block, has at least a Color Channel to have very low brightness in some pixel; For a width Misty Image I, definition dark is:

$I^{\mathrm{dark}}\left(q\right)=\underset{c\&Element;\{R,G,B\}}{\min }\left(\underset{p\&Element;\mathrm{\&Omega;}\left(q\right)}{\min }\left(I^c\left(p\right)\right)\right)$

Wherein, I ^darkfor the dark of I, c is Color Channel index value, I ^cbe a Color Channel of I, Ω is a localized mass centered by pixel q; According to dark channel prior theory, if I is the outdoor image of a width without mist, then except sky areas, I ^darkbrightness all lower and close to 0, be namely arranged in the clear area I of Misty Image ^dark→ 0;

By dark I ^darkin pixel sort from big to small by brightness value, choose sequence after brightness value front 0.1% pixel, then, the pixel of same position in the original image I of its correspondence is expressed as I _0.1%, these points are all the points that mist is the denseest, think that air illumination value is positioned at I _0.1%in scope; In order to mist elimination process is more thorough, get I _0.1%average A _mean=mean (I _0.1%) as the initial value of atmosphere light photograph; Because foggy environment is usually along with the cloudy day, fog is caused to deviate from pure white color, for this is to A _meancorrect, mapped close to white (1,1,1), that is:

$A=A_{\mathrm{mean}}/\underset{c\&Element;R,G,B}{\max }\left(A_{\mathrm{mean}}^c\right)$

Wherein, A is the required air illumination value separated.

3. the Misty Image restoration methods based on multiple dimensioned WLS filtering according to claim 1, it is characterized in that, carry out white balance described in step 2 to image I, and the method simplifying atmospherical scattering model is as follows:

Protoatmosphere scattering model is expressed as:

I(x,y)＝R(x,y)e ^-βd(x,y)+A(1-e ^-βd(x,y))

Wherein, I is original image brightness, and R is the picture rich in detail brightness under desirable weather, and A is atmosphere light photograph of overall importance, and β is atmospheric scattering coefficient, and under foggy environment, it can think a constant had nothing to do with wavelength, and d is the depth of field; In order to avoid direct solution d and β two parameters, adopt the mode solving atmospheric dissipation function, it is expressed as:

V(x,y)＝1-e ^-βd(x,y)

Wherein, V is atmospheric dissipation function, comprises depth of view information, can represent roughly the impact of fog;

Be expressed as by the simplification atmospherical scattering model obtained after white balance process:

I'(x.y)＝I(x,y)/A＝ρ(x,y)(1-V(x,y))+V(x,y)

Wherein, I' is the image after white balance process, and ρ is scene albedo; And:

R(x,y)＝Aρ(x,y)。

4. the Misty Image restoration methods based on multiple dimensioned WLS filtering according to claim 1, is characterized in that, according to the physical attribute of foggy environment described in step 3, the method for atmospheric dissipation function V being carried out to rough estimate is as follows:

According to the physical attribute of greasy weather scene, 2 constraint conditions below V demand fulfillment:

(1)0≤V(x,y)≤1

(2) V (x, y) is not more than I'(x, y) Minimal color weight

By above-mentioned constraint, each pixel of the Misty Image after white balance is defined as the rough estimate result of atmospheric dissipation function at the Minimal color weight of RGB tri-passages that is:

$\tilde{V}(x,y)=\underset{c\&Element;\{R,G,B\}}{\min }\left(I^{\&prime;}(x,y)\right)$

For a width gray-scale map, then have now do not possess the characteristics such as atmospheric dissipation function local smoothing method, need further refinement.

5. the Misty Image restoration methods based on multiple dimensioned WLS filtering according to claim 1, is characterized in that, adopts WLS filtering to atmospheric dissipation function described in step 4 carry out the thin method estimated as follows:

WLS filtering is expressed as and minimizes following cost function:

$\mathrm{\&Sigma;}[{(V(x,y)-\tilde{V}(x,y))}^2+{\mathrm{\&lambda;}}_i(g_x\left(\tilde{V}(x,y)\right){\left(\frac{\&PartialD;V(x,y)}{\&PartialD;x}\right)}^2+g_y\left(\tilde{V}(x,y)\right){\left(\frac{\&PartialD;V(x,y)}{\&PartialD;y}\right)}^2)]$

Wherein, formula left end Section 1 is data item, and this target minimizes input picture with the difference of output image V; Section 2 is level and smooth project, and this reaches level and smooth object, λ by the partial derivative in x and the y direction minimizing V _ifor regulating parameter, i is yardstick index value; G is level and smooth weights, is defined as:

$g_x\left(\tilde{V}(x,y)\right)={({\left|\frac{\&PartialD;\ln \left(\tilde{V}(x,y)\right)}{\&PartialD;x}\right|}^{{\mathrm{\&gamma;}}_i}+\mathrm{\&epsiv;})}^{-1},$ $g_y\left(\tilde{V}(x,y)\right)={({\left|\frac{\&PartialD;\ln \left(\tilde{V}(x,y)\right)}{\&PartialD;y}\right|}^{{\mathrm{\&gamma;}}_i}+\mathrm{\&epsiv;})}^{-1}$

Wherein, ε is a very little constant, prevents divisor from being zero, γ _ifor the sensitivity parameter of regulating gradient change; Matrix form is changed into by after the least energy formula discretize of WLS:

${(V-\tilde{V})}^T(V-\tilde{V})+{\mathrm{\&lambda;}}_i(V^T{D}_x^T{A}_x{D}_{x}V+V^T{D}_y^T{A}_y{D}_{y}V)$

Wherein, A _xand A _yabout refinement weights g _xand g _ydiagonal matrix; D _xand D _ybe the forward difference matrix in x and y direction, and with for backward difference matrix, minimizing of above formula can be converted into following equations:

$(E+{\mathrm{\&lambda;}}_{i}G)V=\tilde{V}$

Wherein, E representation unit matrix, for sparse Laplacian matrix; Above formula can obtain the V after thinning processing by linear solution _i; Adopt different λ _iand γ _iparameter is carried out multiple dimensioned atmospheric dissipation function and is solved, and as yardstick quantity i=3, the result of acquisition is ideal, as I>3, it is less that visual effect promotes degree, and add computation complexity, therefore yardstick quantity is set as 3, i.e. i=3.

6. according to the Misty Image restoration methods based on multiple dimensioned WLS filtering in Claims 1 to 5 described in any one, it is characterized in that, recovering Misty Image described in step 5 is image R under desirable weather _imethod as follows:

Asking for atmosphere light intensity A and atmospheric dissipation function V _ibasis on, directly recover the brightness of image of scene under desirable weather condition:

$R_i(x,y)=\frac{I(x,y)-{\mathrm{kV}}_i(x,y)}{1-V_i(x,y)}\&times;A$

Wherein, k is for recovering regulating parameter, and 0<k<1, for controlling the degree of mist elimination.

7. the Misty Image restoration methods based on multiple dimensioned WLS filtering according to claim 6, is characterized in that, adjust output image dynamic range described in step 6, the method for carrying out visibility lifting is as follows:

First the conversion of color space is carried out, by image R _iby RGB color space conversion to CIELAB color space, only to the brightness space L process of image; Suppose R ₁misty Image recovery effects best, then establish layer based on b, i.e. b=R ₁if, two levels of detail d ¹with d ², i.e. d ¹=R ₁-R ₂, d ²=R ₂-R ₃; Then tone mapping formula is defined as:

$R_p=\mathrm{\&mu;}+C({\mathrm{\&delta;}}_0,{\mathrm{\&eta;b}}_p-\mathrm{\&mu;})+C({\mathrm{\&delta;}}_1,d_p^1)+C({\mathrm{\&delta;}}_2,d_p^2)$

Wherein, p represents pixel, and μ is the average of brightness of image scope, and C is S type adjustment function, and for regulating dynamic range, i.e. C (a, u)=1/ (1+exp (-au)), η is exposure parameter, δ ₀, δ ₁with δ ₂for gain parameter;

After above-mentioned process, by image by CIELAB color space conversion to RGB color space, last Misty Image restoration result R can be obtained.