CN102831591A - Gaussian filter-based real-time defogging method for single image - Google Patents

Abstract

The invention provides a Gaussian filter-based real-time defogging method for a single image. The method is established on the basis of a physical model and can realize real-scene recovery of a degraded quality image. The method comprises the following four main steps of: step 1, calculating, inputting a dark channel image of a fogged image and estimating an overall atmosphere light value; steps 2, primarily estimating an atmosphere dissipative function; step 3, adopting Gaussian filtering to refine the atmosphere dissipative function; and step 4, recovering a scene radiancy. With the adoption of the method, defects that an existing defogging method is slower in defogging speed and cannot be applied to a real-time processing system are overcome; and the method is good in effect of an obtained defogged image and rapid in processing speed, can be applied to a real-time system, and has a better practical value and a wide application background.

Description

A kind of real-time defogging method capable of the single image based on gaussian filtering

(1) technical field:

The present invention relates to a kind of real-time defogging method capable of the single image based on gaussian filtering, be applicable to the image mist elimination under the greasy weather condition, belong to digital image processing field.

(2) background technology:

Under weather conditions such as mist, haze, the scenery visibility and the contrast of the natural scene image of outdoor shooting significantly reduce.The light of body surface reflection is by gasoloid and be suspended in molecule absorption and the scattering in the atmosphere, the scene image color degradation that causes outdoor supervisory system to be obtained, and contrast and saturation degree descend.The degeneration of outdoor image directly has influence on the outdoor use of computer vision system, like video monitoring, urban transportation, intelligent vehicle etc., therefore need handle to eliminate the influence that weather brings image and the video taken under the greasy weather condition.In fact, the image mist elimination is the research content of computer graphics and computer vision field always.At first, the image mist elimination can increase the visibility of scene significantly and eliminate the color drift that the influence owing to surround lighting brings; Secondly, no matter be rudimentary graphical analysis or senior Target Recognition, most computer vision algorithms make often supposes that input picture is the scene radiancy, does not promptly have the mist image clearly.Thereby the performance of many computer vision algorithms make can receive the radiometric influence of scene of low contrast.At last, the image mist elimination can provide scene depth information for many computer vision algorithms make.

The existence of mist is information-related with unknown scene depth to the influence of image in the outdoor image, thereby the image mist elimination is faced with very big challenge.In fact, the image mist elimination is the problem of a underconstrained, because it needs only to estimate scene radiancy, propagation in atmosphere function and overall atmosphere light the mist image exactly from having of degeneration.In recent years, the defogging method capable of single image has been obtained significant progress.Tan realizes the mist elimination of image through the method for maximization local contrast; Fattal is irrelevant through the surface emissivity degree of hypothesis propagation in atmosphere function and scene, uses the method for independent component analysis to estimate scene reflectivity rate and propagation in atmosphere function; People such as He have proposed to help secretly the priori rule based on the statistics to open air no mist image rule, and general outdoor image has been obtained good mist elimination effect.But the complexity of above algorithm is high, and processing speed is slow, can not reach the effect of real-time processing, thereby can not be applied to actual application system.

(3) summary of the invention:

1, purpose: the purpose of this invention is to provide a kind of real-time defogging method capable of the single image based on gaussian filtering, it has overcome the deficiency of prior art, and the mist elimination effect is better, and processing speed is fast, can be used in the real time processing system.

2, technical scheme:

Introduce the principle and the process of image mist elimination among the present invention below.

One, greasy weather imaging model

Atmospheric scattering model under the greasy weather condition can be described as

I(x)=J(x)t(x)+A(1-t(x))

t(x)=e ^-βd(x)

Wherein, I (x) has a mist image for input; J (x) is the scene radiancy, does not promptly have the scene image under the greasy weather gas condition; T (x) is the propagation in atmosphere function, the transmissivity of expression scene radiation; A is overall atmosphere light, is assumed to be overall constant vector usually; β is the atmospheric scattering coefficient; D (x) is a scene depth.The image mist elimination will be tried to achieve J (x), t (x) and A through I (x) exactly.In the equation of atmospheric scattering model, first J of equality right-hand member (x) t (x) representes direct attenuation term, and second A (1-t (x)) representes surround lighting.Directly attenuation term is described scene radiation and the decay in propagation medium thereof, and the surround lighting that is caused by scattered light then can cause the drift of scene color.

Two, help priori secretly

Helping priori secretly is to obtain through the statistical observation to a large amount of outdoor no mist images: in the regional area of most images, some pixel has at least a Color Channel to have very low brightness value.Helping secretly of image J is defined as

$J^{\mathrm{dark}}\left(x\right)=\underset{y\∈\mathrm{\Ω}\left(x\right)}{\min }\left(\underset{c\∈\{r,g,b\}}{\min }{J}^c\left(y\right)\right)$

Wherein, J ^cCertain Color Channel of presentation video J, Ω (x) expression is a square region at center with pixel x.Statistics through to great amount of images can know, the image of clear no mist help J secretly ^DarkValue always very low and approach 0.

Three, estimate overall atmosphere light

For a width of cloth did not have the mist image, it helps image secretly should be the almost black full image of a width of cloth, but a width of cloth has the overall brightness of helping image secretly of mist image to brighten.See that from visual effect it is a guestimate to the concentration of mist that the image of helping secretly of mist image is arranged.Adopt following method to estimate overall atmosphere light among the present invention

A=I(x _k)

Wherein, $x_k=\underset{x}{\mathrm{Arg}}\mathrm{Max}\left(J^{\mathrm{Dark}}\left(x\right)\right).$

This method of estimation has better robustness than directly choosing the method for estimation of the maximum pixel value of intensity in the image as overall atmosphere light, can more accurately estimate the value of overall atmosphere light A.

Four, atmospheric dissipation Function Estimation

4.1 rough estimate

Being defined as of atmospheric dissipation function

V(x)=1-t(x)

So the atmospheric scattering model can be rewritten as

I(x)=J(x)t(x)+AV(x)

Atmospheric dissipation function representation surround lighting is the increasing function about scene depth d (x) to the extention of scene imaging.In the atmospheric scattering model, respectively each Color Channel is carried out normalization, promptly the model two ends are together divided by overall atmosphere light A ^c, obtain normalized atmospheric scattering model and do

$\frac{I^c\left(x\right)}{A^c}=\frac{J^c\left(x\right)}{A^c}t\left(x\right)+V\left(x\right)$

For the zone of brightness in the input picture greater than overall atmosphere light A; This shows that the corresponding region color overflows promptly corresponding , need carry out special processing to these zones.The present invention is limited in

in [0,1] scope through grey level stretching

$\frac{I^c\left(x\right)}{A^c}=(\frac{I^c\left(x\right)}{A^c}-\min \left(\frac{I^c\left(x\right)}{A^c}\right))/(\max \left(\frac{I^c\left(x\right)}{A^c}\right)-\min \left(\frac{I^c\left(x\right)}{A^c}\right))$

So the atmospheric scattering model can be reduced to

$\frac{I\left(x\right)}{A}=\frac{J\left(x\right)}{A}t\left(x\right)+V\left(x\right)$

Known by the above formula, atmospheric dissipation function V (x) satisfy two constraints: 1) V (x) ≥ 0, that is V (x) is positive; 2)

ie V (x) is not greater than

The minimum color components .

Suppose that propagation in atmosphere function and atmospheric dissipation function are constant in a zonule, use and

expression respectively.Atmospheric scattering model two ends are got help secretly

$\underset{y\∈\mathrm{\Ω}\left(x\right)}{\min }\left(\underset{c\∈\{r,g,b\}}{\min }\frac{I^c\left(y\right)}{A^c}\right)=\tilde{t}\left(x\right)\underset{y\∈\mathrm{\Ω}\left(x\right)}{\min }\left(\underset{c\∈\{r,g,b\}}{\min }\frac{J^c\left(y\right)}{A^c}\right)+\tilde{V}\left(x\right)$

For the image J (x) of clear no mist, it is helped image secretly and approaches 0

$\underset{y\∈\mathrm{\Ω}\left(x\right)}{\min }\left(\underset{c\∈\{r,g,b\}}{\min }{J}^c\left(y\right)\right)\→0$

Because A ^cAlways be on the occasion of, so

$\underset{y\∈\mathrm{\Ω}\left(x\right)}{\min }\left(\underset{c\∈\{r,g,b\}}{\min }\frac{J^c\left(y\right)}{A^c}\right)\→0$

Thus, can obtain the rough estimate of atmospheric dissipation function

$\tilde{V}\left(x\right)=\underset{y\∈\mathrm{\Ω}\left(x\right)}{\min }\left(\underset{c\∈\{r,g,b\}}{\min }\frac{I^c\left(y\right)}{A^c}\right)$

Ω among the present invention (x) gets 1 * 1, promptly uses

minimum color component is estimated the atmospheric dissipation function

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

4.2 Refinement operation based on gaussian filtering

Because the minimum color component that in to the rough estimate of atmospheric dissipation function, uses

, cause the rough estimate

of atmospheric dissipation function also maybe be no longer continuous in the variation of non-depth of field sudden change place.Thereby need carry out the segment smoothing operation to the rough estimate

of atmospheric dissipation function, need keep the edge details of depth of field sudden change simultaneously.The present invention adopts Gauss's LPF to come refinement atmospheric dissipation function

to be expressed as

$V\left(x\right)=\frac{1}{W^g}\underset{y\∈S}{\mathrm{\Σ}}{G}_{\mathrm{\σ}}\left(\right||x-y|\left|\right)\tilde{V}\left(y\right)$

Wherein, W ^gBe normalization coefficient

$W^g=\underset{y\∈S}{\mathrm{\Σ}}{G}_{\mathrm{\σ}}\left(\right||x-y|\left|\right)$

In the formula, G _σBe Gaussian function.For with the pixel of center pixel close together, gauss low frequency filter is given bigger weight; And, give less weight for distance pixel far away.

Atmospheric dissipation function by after the refinement can be tried to achieve the propagation in atmosphere function

t(x)=1-V(x)

Five, restoration scenario radiancy

Through overall atmosphere light and propagation in atmosphere function, can recover the scene radiancy at an easy rate according to the atmospheric scattering model.Because the rough estimate of atmospheric dissipation function is counted the minimum color component of image

, thus the difference of image

and atmospheric dissipation function with very big probability near 0.In addition, be positioned at the sky of infinite distant place, propagation in atmosphere function t (x) approaches 0, so directly attenuation term J (x) t (x) approaches 0, causes the scene radiancy J that recovers to be regarded noise probably.For fear of the uncertain value of 0/0 type, the present invention takes following two measures to solve: 1) through introducing a lower bound t ₀Restriction propagation in atmosphere function t (x); 2) introducing factor k is that distant objects keeps a spot of mist.In fact, even under bright day gas condition, distant objects still can receive the influence of mist.If the mist in the image is removed fully, image will become untrue and can lose depth of view information.Come to make the scene that recovers seem truer through introducing factor k among the present invention for distant objects keeps a spot of mist.So according to the atmospheric scattering model, scene radiancy J (x) can recover through following formula

$J\left(x\right)=A\×\frac{I\left(x\right)/A-\mathrm{kV}\left(x\right)}{\max (t\left(x\right),t_0)}$

Six, improve algorithm

Experiment through to great amount of images shows, the sky in the image, the bright areas such as object and the water surface of white partially tend to take place serious distortion through color after the defogging.In fact,, can not find pixel value and approach 0 dark access points, thereby help priori secretly in these zones and be false even the pixel value of these bright areas is just very big under the condition of no mist.

Do not considering to help secretly under the condition of priori, the atmospheric dissipation function does accurately

$\tilde{V}\left(x\right)=1-\frac{1-\underset{y\∈\mathrm{\Ω}\left(x\right)}{\min }\left(\underset{c\∈\{r,g,b\}}{\min }\frac{I^c\left(y\right)}{A^c}\right)}{1-\underset{y\∈\mathrm{\Ω}\left(x\right)}{\min }\left(\underset{c\∈\{r,g,b\}}{\min }\frac{J^c\left(y\right)}{A^c}\right)}$

In bright areas,

Can not be approximately 0, therefore actual atmospheric dissipation function V _Actual(x) be less than according to the atmospheric dissipation function of helping prior estimate secretly

The reason of bright areas color distortion in the no mist image that recovers is described below.Passage I ^cWith J ^cBetween the difference of color can use I ^c-A ^cWith J ^c-A ^cBetween difference represent, bright areas corresponding the wrong atmospheric dissipation function V bigger than normal that estimates, also promptly corresponding propagation in atmosphere function t less than normal.Even so I ^r, I ^g, I ^bBetween only differ several pixel values, after divided by very little propagation in atmosphere function t (although the minimum value of t is 0.1), interchannel color distortion can be exaggerated several times even ten times, makes the no mist image finally recover and the color of former figure that bigger drop arranged.Particularly when three channel direction inconsistent (passage that has is greater than A, and the passage that has is less than A), drop superposes, and the phenomenon of colour cast, i.e. color distortion can appear in the bright areas of similar sky.

In order to eliminate color distortion, must adjust the propagation in atmosphere function of bright areas, feasible estimation

More near actual t _Actual(x), do not destroy the Unified frame of helping mist elimination secretly simultaneously.Based on this, the present invention introduces parameter M, is defined as tolerance, for | I-A| thinks bright areas less than the zone of M, recomputates the propagation in atmosphere function; , think to satisfy the zone of helping priori secretly greater than the zone of M for | I-A|, keep original transmissivity constant., tolerance is reduced to original algorithm when being 0.For this reason, the present invention defines propagation in atmosphere function and atmospheric dissipation function again

t'(x)=min(max(M/|I-A|,1)·max(t(x),t ₀),1)

V'(x)=1-t'(x)

So the scene radiancy of improving the back recovery does

$J\left(x\right)=A\×\frac{I^{\′}\left(x\right)/A-{\mathrm{kV}}^{\′}\left(x\right)}{t^{\′}\left(x\right)}$

Following formula has guaranteed that the propagation in atmosphere function of bright areas is unlikely to be partial to by error very little value.Tolerance mechanism is that a kind of of former algorithm replenished and expansion in fact, make its can handle well contain the large tracts of land bright areas the mist image arranged, and meet and help the priori principle secretly.

Because the integral image behind the mist elimination becomes very dark, the present invention uses piecewise nonlinear to stretch increases the mist elimination picture contrast.

In sum, the real-time defogging method capable of a kind of single image based on gaussian filtering of the present invention, this method specifically may further comprise the steps:

Step 1: read the original mist image I (x) that has, " calculated dark channel image and estimate overall atmosphere light value A "

(1) in Microsoft Visual Studio 2008 language environments, reads one and original mist image I (x) arranged;

(2) calculate the image of helping secretly that input has the mist image

I wherein ^cCertain Color Channel of presentation video I; Ω (x) expression is the square region at center with pixel x, is of a size of 4 * 4;

(3) estimate overall atmosphere light value A=I (x _k), wherein Image I is helped in expression secretly ^Dark(x) two-dimensional coordinate of the brightest pixel in.So overall atmosphere light value is to help the corresponding original color of pixel value that the mist image is arranged of pixel the brightest in the image secretly.

Step 2: according to input the image of helping secretly of mist image is arranged, " the thick step is estimated atmospheric dissipation function V (x) "

(1) atmospheric scattering model normalization.In the atmospheric scattering model, respectively each Color Channel is carried out normalization, promptly the model two ends are together divided by overall atmosphere light A ^c, obtain normalized atmospheric scattering model

$\frac{I^c\left(x\right)}{A^c}=\frac{J^c\left(x\right)}{A^c}t\left(x\right)+V\left(x\right)$

(2) through grey level stretching

is limited in [0,1] scope

$\frac{I^c\left(x\right)}{A^c}=(\frac{I^c\left(x\right)}{A^c}-\min \left(\frac{I^c\left(x\right)}{A^c}\right))/(\max \left(\frac{I^c\left(x\right)}{A^c}\right)-\min \left(\frac{I^c\left(x\right)}{A^c}\right))$

Where,

means taking the matrix

The minimum;

indicates taking matrix

the maximum.

(3) the thick step is estimated the atmospheric dissipation function

$\tilde{V}\left(x\right)=\underset{y\∈\mathrm{\Ω}\left(x\right)}{\min }\left(\underset{c\∈\{r,g,b\}}{\min }\frac{I^c\left(y\right)}{A^c}\right)$

Here Ω (x) expression is the square region at center with pixel x, and size is taken as 1 * 1.

Step 3: " refinement atmospheric dissipation function

"

(1) adopt Gauss's LPF to come refinement atmospheric dissipation function

to be expressed as

$V\left(x\right)=\frac{1}{W^g}\underset{y\∈S}{\mathrm{\Σ}}{G}_{\mathrm{\σ}}\left(\right||x-y|\left|\right)\tilde{V}\left(y\right)$

In the following formula, W ^gBe normalization coefficient

$W^g=\underset{y\∈S}{\mathrm{\Σ}}{G}_{\mathrm{\σ}}\left(\right||x-y|\left|\right)$

Wherein, G _σBe Gaussian function, Gauss's template is of a size of 5 * 5, and σ is 0.7.

(2) calculate the propagation in atmosphere function

According to the definition of atmospheric dissipation function, can try to achieve the propagation in atmosphere function

t(x)=1-V(x)

The atmospheric dissipation function after V (x) the expression refinement wherein.

Step 4: " restoration scenario radiancy J (x) "

(1) recomputates propagation in atmosphere function and atmospheric dissipation function

t'(x)=min(max(M/|I-A|,1)·max(t(x),t ₀),1)

V'(x)=1-t'(x)

Wherein, tolerance M is 50; t ₀Be 0.1; The propagation in atmosphere function of t (x) for trying to achieve in the step 3; The minimum value in the element and 1 among the matrix * is got in min (*, 1) expression; The maximal value in the element and 1 among the matrix * is got in max (*, 1) expression; Max (t (x), t ₀) expression gets element and t among the matrix t (x) ₀In maximal value, the expression dot product.

(2) the scene radiancy of recovering does

$J\left(x\right)=A\×\frac{I^{\′}\left(x\right)/A-{\mathrm{kV}}^{\′}\left(x\right)}{t^{\′}\left(x\right)}$

Wherein, A is overall atmosphere light value; I' (x)/A representes the composograph of three Color Channels of

of the operation of process grey level stretching in the step 2; The k value is generally 0.8-0.9.

3, advantage and effect: the real-time defogging method capable of a kind of single image based on gaussian filtering of the present invention; Its advantage is: the present invention is based upon on the basis of physical model of greasy weather imaging; Algorithm is simple, and computation complexity is low, and processing speed is fast; Can recover the real scene of degraded image preferably, can be applicable in the real time processing system.

(4) description of drawings

Fig. 1 the method for the invention FB(flow block)

(5) embodiment

In order to understand technical scheme of the present invention better, below embodiment of the present invention is further described:

The present invention realizes under Microsoft Visual Studio 2008 language environments.Computing machine reads the original mist image that has; At first calculating input image helps image secretly and estimates overall atmosphere light value through helping image secretly; Then the atmospheric dissipation function is carried out rough estimate; Utilize gaussian filtering that the atmospheric dissipation function of rough estimate is carried out refinement then, use improved algorithm computation scene radiancy at last.

The present invention is a kind of single image defogging method capable based on gaussian filtering, and the flow process of this method is seen shown in Figure 1.This method may further comprise the steps:

Step 1: read the original mist image I (x) that has, " calculated dark channel image and estimate overall atmosphere light value A "

(1) in Microsoft Visual Studio 2008 language environments, reads one and original mist image I (x) arranged;

(2) calculate the image of helping secretly that input has the mist image I wherein ^cCertain Color Channel of presentation video I; Ω (x) expression is the square region at center with pixel x, is of a size of 4 * 4;

(3) estimate overall atmosphere light value A=I (x _k), wherein

Image I is helped in expression secretly ^Dark(x) two-dimensional coordinate of the brightest pixel in.So overall atmosphere light value is to help the corresponding original color of pixel value that the mist image is arranged of pixel the brightest in the image secretly.

Step 2: according to input the image of helping secretly of mist image is arranged, " the thick step is estimated atmospheric dissipation function V (x) "

(1) atmospheric scattering model normalization.In the atmospheric scattering model, respectively each Color Channel is carried out normalization, promptly the model two ends are together divided by overall atmosphere light A ^c, obtain normalized atmospheric scattering model

$\frac{I^c\left(x\right)}{A^c}=\frac{J^c\left(x\right)}{A^c}t\left(x\right)+V\left(x\right)$

(2) through grey level stretching

is limited in [0,1] scope

$\frac{I^c\left(x\right)}{A^c}=(\frac{I^c\left(x\right)}{A^c}-\min \left(\frac{I^c\left(x\right)}{A^c}\right))/(\max \left(\frac{I^c\left(x\right)}{A^c}\right)-\min \left(\frac{I^c\left(x\right)}{A^c}\right))$

Where,

means taking the matrix

The minimum;

indicates taking matrix

the maximum.

(3) the thick step is estimated the atmospheric dissipation function

$\tilde{V}\left(x\right)=\underset{y\∈\mathrm{\Ω}\left(x\right)}{\min }\left(\underset{c\∈\{r,g,b\}}{\min }\frac{I^c\left(y\right)}{A^c}\right)$

Here Ω (x) expression is the square region at center with pixel x, and size is taken as 1 * 1.

Step 3: " refinement atmospheric dissipation function

"

(1) adopt Gauss's LPF to come refinement atmospheric dissipation function

to be expressed as

$V\left(x\right)=\frac{1}{W^g}\underset{y\∈S}{\mathrm{\Σ}}{G}_{\mathrm{\σ}}\left(\right||x-y|\left|\right)\tilde{V}\left(y\right)$

In the following formula, W ^gBe normalization coefficient

$W^g=\underset{y\∈S}{\mathrm{\Σ}}{G}_{\mathrm{\σ}}\left(\right||x-y|\left|\right)$

Wherein, G _σBe Gaussian function, Gauss's template is of a size of 5 * 5, and σ is 0.7.

(2) calculate the propagation in atmosphere function

According to the definition of atmospheric dissipation function, can try to achieve the propagation in atmosphere function

t(x)=1-V(x)

The atmospheric dissipation function after V (x) the expression refinement wherein.

Step 4: " restoration scenario radiancy J (x) "

(1) recomputates propagation in atmosphere function and atmospheric dissipation function

t'(x)=min(max(M/|I-A|,1)·max(t(x),t ₀),1)

V'(x)=1-t'(x)

Wherein, tolerance M is 50; t ₀Be 0.1; The propagation in atmosphere function of t (x) for trying to achieve in the step 3; The minimum value in the element and 1 among the matrix * is got in min (*, 1) expression; The maximal value in the element and 1 among the matrix * is got in max (*, 1) expression; Max (t (x), t ₀) expression gets element and t among the matrix t (x) ₀In maximal value, the expression dot product.

(2) the scene radiancy of recovering does

$J\left(x\right)=A\×\frac{I^{\′}\left(x\right)/A-{\mathrm{kV}}^{\′}\left(x\right)}{t^{\′}\left(x\right)}$

Wherein, A is overall atmosphere light value; I' (x)/A representes the composograph of three Color Channels of

of the operation of process grey level stretching in the step 2; The k value is generally 0.8-0.9.

In order to verify validity of the present invention, use said method to handle to the mist image is arranged, obtained mist elimination effect preferably.The maximum advantage of the present invention is that algorithm is simple; Computation complexity is low; Processing speed is fast; The image of in Microsoft Visual Studio 2008 language environments, handling one 600 * 400 only needs 31ms, and the image of handling 523 * 598 only needs 50ms, can be applied in the real time processing system.

From experimental result, the method among the present invention has solved the recovery problem of the degraded image of taking under the greasy weather condition well, and processing speed is fast, can be applicable in the real time processing system, has broad application prospects and is worth.

Claims (1)

1. real-time defogging method capable based on the single image of gaussian filtering, it is characterized in that: these method concrete steps are following:

Step 1: read the original mist image I (x) that has, calculated dark channel image and estimate overall atmosphere light value A:

(1) in Microsoft Visual Studio 2008 language environments, reads one and original mist image I (x) arranged;

(2) calculate the image of helping secretly that input has the mist image

Wherein, I ^cCertain Color Channel of presentation video I; Ω (x) expression is the square region at center with pixel x, is of a size of 4 * 4;

(3) estimate overall atmosphere light value A=I (x _k), wherein

Image I is helped in expression secretly ^Dark(x) two-dimensional coordinate of the brightest pixel in is so overall atmosphere light value is to help the corresponding original color of pixel value that the mist image is arranged of pixel the brightest in the image secretly;

Step 2: according to input the image of helping secretly of mist image is arranged, the thick step is estimated atmospheric dissipation function V (x):

(1) atmospheric scattering model normalization; In the atmospheric scattering model, respectively each Color Channel is carried out normalization, promptly the model two ends are together divided by overall atmosphere light A ^c, obtain normalized atmospheric scattering model

$\frac{I^c\left(x\right)}{A^c}=\frac{J^c\left(x\right)}{A^c}t\left(x\right)+V\left(x\right);$

(2) through grey level stretching

is limited in [0,1] scope

$\frac{I^c\left(x\right)}{A^c}=(\frac{I^c\left(x\right)}{A^c}-\min \left(\frac{I^c\left(x\right)}{A^c}\right))/(\max \left(\frac{I^c\left(x\right)}{A^c}\right)-\min \left(\frac{I^c\left(x\right)}{A^c}\right))$

Where, indicates taking matrix

The minimum;

indicates taking matrix

The maximum value;

(3) the thick step is estimated the atmospheric dissipation function

$\tilde{V}\left(x\right)=\underset{y\∈\mathrm{\Ω}\left(x\right)}{\min }\left(\underset{c\∈\{r,g,b\}}{\min }\frac{I^c\left(y\right)}{A^c}\right)$

Here Ω (x) expression is the square region at center with pixel x, and size is taken as 1 * 1;

Step 3: refinement atmospheric dissipation function

(1) adopt Gauss's LPF to come refinement atmospheric dissipation function to be expressed as

$V\left(x\right)=\frac{1}{W^g}\underset{y\∈S}{\mathrm{\Σ}}{G}_{\mathrm{\σ}}\left(\right||x-y|\left|\right)\tilde{V}\left(y\right)$

In the following formula, W ^gBe normalization coefficient

$W^g=\underset{y\∈S}{\mathrm{\Σ}}{G}_{\mathrm{\σ}}\left(\right||x-y|\left|\right)$

Wherein, G _σBe Gaussian function, Gauss's template is of a size of 5 * 5, and σ is 0.7;

(2) calculate the propagation in atmosphere function

According to the definition of atmospheric dissipation function, try to achieve the propagation in atmosphere function

t(x)=1-V(x)

Wherein, the atmospheric dissipation function after V (x) the expression refinement;

Step 4: restoration scenario radiancy J (x)

(1) recomputates propagation in atmosphere function and atmospheric dissipation function

t'(x)=min(max(M/|I-A|,1)·max(t(x),t ₀),1)

V'(x)=1-t′(x)

Wherein, tolerance M is 50; t ₀Be 0.1; The propagation in atmosphere function of t (x) for trying to achieve in the step 3; The minimum value in the element and 1 among the matrix * is got in min (*, 1) expression; The maximal value in the element and 1 among the matrix * is got in max (*, 1) expression; Max (t (x), t ₀) expression gets element and t among the matrix t (x) ₀In maximal value, the expression dot product;

(2) the scene radiancy of recovering does

$J\left(x\right)=A\×\frac{I^{\′}\left(x\right)/A-{\mathrm{kV}}^{\′}\left(x\right)}{t^{\′}\left(x\right)}$

Wherein, A is overall atmosphere light value; I' (x)/A representes the composograph of three Color Channels of

of the operation of process grey level stretching in the step 2; The k value is generally 0.8-0.9.

Images