CN107730472A - A kind of image defogging optimized algorithm based on dark primary priori - Google Patents
A kind of image defogging optimized algorithm based on dark primary priori Download PDFInfo
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Abstract
A kind of image defogging optimized algorithm based on dark primary priori of the present invention, belongs to technical field of image processing.This method carries out certain modification to dark channel prior formula, add down-sampling coefficient x, the time required for original dark channel prior algorithm is greatly reduced, sampling under one width 1080p picture dark channel information amounts can be reduced to 360p ranks, so as to reduce transmissivity t (x) the calculating time, and the calculating time of view picture figure, in order to reach live effect, appropriate down-sampling coefficient x is chosen in the present invention, make the soc images per second that handle more than 24 width (human eye differentiates video limit 24fps), and the information of image sacrifice is in controlled range.The present invention is new to not only solve the problem of processing of video defogging is slow under high definition image quality, also provides prioritization scheme for inexpensive defogging system, makes the operation that HD video defogging can also be realized in the case of low performance soc.
Description
Technical field
It is to be related to a kind of figure specifically the present invention relates to a kind of image defogging optimized algorithm based on dark primary priori
As rapid defogging method, belong to technical field of image processing.
Background technology
The capture images under severe weather conditions, because a large amount of particles (such as mist, haze) to be suspended in air can produce to light
Absorb, scattering process, so as to cause the image quality decrease of capture, it is existing fuzzy, color distortion, the contrast decline of image etc. occur
As, not only reduce image visuality, more to successive image Processing Algorithm (such as object identification, feature extraction, graphical analysis)
Carry out cause difficulty.
At present, the defogging algorithm that computer vision field domestic and foreign scholars propose can be divided into base according to the Land use systems of information
In multiple image (or other additional informations) and it is based only upon the class of single image two.
The distribution of mist is relevant with the depth of scenery in image in foggy image, due to can be from the multiple image of same scenery
The middle depth information for refining scenery, therefore, many scholars propose the defogging based on multiple image (or other additional informations) and calculated
Method, as carried out defogging using multiple image of the same scenery under different polarization wave filter, using same scenery in different weather
Under the conditions of multiple image defogging, utilize additional scene depth information to carry out defogging.But due to the input of this kind of algorithm requirement
Information is more so that their practicality suffers restraints, such as in the system that some require real-time, it is difficult to needed for obtaining in real time
Multiple image under the conditions of the different weather wanted；And in circumstances not known, the additional depth information of scenery can not be provided.
Only also there is more progress using the defogging algorithm of single image information within nearly 2 years.In wherein a kind of defogging algorithm,
It is proposed to recover fog free images by increasing Image Warping, but such a method easily causes the color of image after recovering slightly
Aobvious distortion, and discontinuously locate that in the depth of field halo artifact (halo) can be produced.
In another defogging algorithm, based on scenery surface colourity (surfaceshading) and Medium Propagation
(mediumtransmission) with partial statistics irrelevance it is assumed that to foggy image carry out defogging, this algorithm defogging
Positive effect, but the algorithm can not handle gray level image.Later, the bright scholars of He Kai were in the base counted to a large amount of fog free images
On plinth, it is proposed that dark primary priori (darkchannelprior), and this statistical law rough estimate Medium Propagation function is utilized,
Then scratch nomography using image to be modified Medium Propagation function, and then defogging, the defogging of this algorithm are carried out to image
Effect is more significant.
And in recent years, with the continuous development of computer hardware technique, video is removed in real time in the case where there is greasy weather gas
Mist has become possibility, but because the above-mentioned algorithm calculating time is longer, it is high to processor requirement, therefore made on video definition
Compromise, market image defogging technology is all mostly in the related field definition such as video monitoring, automatic Pilot, urban transportation
360p or 480p, because the real-time demisting of equipment cost problem HD video can not solve always.
The content of the invention
The technical problem to be solved in the present invention is to provide a kind of image defogging optimized algorithm based on dark primary priori, not only
Solve the problems, such as that the processing of video defogging is slow under high definition image quality, also provides prioritization scheme for inexpensive defogging system, makes low
The operation of HD video defogging can also be realized in the case of performance soc.
The technical solution adopted by the present invention is：A kind of image defogging optimized algorithm based on dark primary priori, including it is as follows
Step：
Step 1：From video extraction foggy image I (x)；
Step 2：Mini-value filtering processing, the image G (x) after being handled are carried out to foggy image I (x)；
Step 3：Ask for image G (x) dark channel diagram Jdark；
The minimum value of each passage in image G (x) is obtained, in deposit and image G (x) size identical gray-scale maps, is obtained
Dark channel diagram Jdark；
For input picture G (x), it is as follows that its dark asks for formula：
J in formulacOne kind in image G (x) three Color Channels R, G, B is represented, Ω (x) is represented centered on coordinate x
One window, y is x passage function, and dark channel prior defines jdark(x)→0；
Step 4：Air light value A is estimated, choosing method is as follows：
1) preceding 0.1% pixel is taken according to the size of brightness from dark channel diagram；
2) in these positions that step 1) is chosen, there is maximum brightness corresponding to searching in original foggy image I (x)
Point value, as A values；
Step 5：Calculate transmissivity t (x)
Atmospherical scattering model is as follows：
I (x)=J (x) t (x)+A (1-t (x)) (2)
Wherein I (x) is treats demisting image, and J (x) is fogless image to be asked, and t (x) is image atmospheric transmissivity, and A is
Air light value,
Atmospherical scattering model (2) can be deformed into
In above formula, subscript C represents the meaning of tri- passages of R/G/B,
Formula (3) both sides are asked twice minimum operation obtain following formula：
In above formula, J (x) is fogless image to be asked, and the dark primary priori theoretical in step 3 has：
Therefore, can be derived with reference to formula (4), (5)：
But in actual life, even fine day white clouds, there is also some particles in air, therefore, see distant place
Object still can feel the influence of mist, in addition, the presence of mist allows the mankind to feel the presence of the depth of field, therefore, when defogging
Retain a certain degree of mist, it is therefore desirable to introduced in formula (6) and remove fog factor ω, ω rule of asking for is here：Calculate dark
The ratio between standard deviation of passage figure defogging result corresponding with its asks for local defogging factor ω, and ω is between 0-1；
Then formula (6) is modified to formula (7)：
The lower sampling coefficient n (n=0.25~0.5) of increase, is modified to formula (7), obtains formula (8)：
Down-sampling coefficient n is adjusted, image quality reaches best effect after making defogging processing speed and defogging；
Step 6：Image restoring
From formula (2),
By Step 4: five A, t (x) tried to achieve substitute into formula (9), it can be deduced that fogless image J (x) to be asked.
Beneficial effects of the present invention are：The present invention can be applicable in vehicle-mounted monitoring system and traffic surveillance and control system, for city
Mobile soc and desktop cpu performance gaps are big on face, realize HD video demisting in low-cost platform, will can be adopted under 1080p images
Sample, by algorithm optimization to sacrifice the cost of a small amount of image quality, lifts calculating speed, reaches inexpensive facility to 360p or 270p
The requirement of defogging real time implementation.
Brief description of the drawings
Fig. 1 is the image of before processing in example one of the present invention；
Fig. 2 is the image after being handled in example one of the present invention；
Fig. 3 is the image of before processing in example two of the present invention；
Fig. 4 is the image after being handled in example two of the present invention；
Fig. 5 is inventive algorithm flow chart.
Embodiment
Below in conjunction with the accompanying drawings and specific embodiment, the present invention is made further clear, intactly illustrated.
Embodiment 1：As Figure 1-5, a kind of image defogging optimized algorithm based on dark primary priori, including following step
Suddenly：
Step 1：From video extraction foggy image I (x)；
Step 2：Mini-value filtering processing, the image G (x) after being handled are carried out to foggy image I (x)；
Step 3：Ask for image G (x) dark channel diagram Jdark；
The minimum value of each passage in image G (x) is obtained, in deposit and image G (x) size identical gray-scale maps, is obtained
Dark channel diagram Jdark；
For input picture G (x), it is as follows that its dark asks for formula：
J in formulacOne kind in image G (x) three Color Channels R, G, B is represented, Ω (x) is represented centered on coordinate x
One window, y is x passage function, and dark channel prior defines jdark(x)→0；
Step 4：Air light value A is estimated, choosing method is as follows：
1) preceding 0.1% pixel is taken according to the size of brightness from dark channel diagram；
2) in these positions that step 1) is chosen, there is maximum brightness corresponding to searching in original foggy image I (x)
Point value, as A values；
Step 5：Calculate transmissivity t (x)
Atmospherical scattering model is as follows：
I (x)=J (x) t (x)+A (1-t (x)) (2)
Wherein I (x) is treats demisting image, and J (x) is fogless image to be asked, and t (x) is image atmospheric transmissivity, and A is
Air light value,
Atmospherical scattering model (2) can be deformed into
In above formula, subscript C represents the meaning of tri- passages of R/G/B,
Formula (3) both sides are asked twice minimum operation obtain following formula：
In above formula, J (x) is fogless image to be asked, and the dark primary priori theoretical in step 3 has：
Therefore, can be derived with reference to formula (4), (5)：
But in actual life, even fine day white clouds, there is also some particles in air, therefore, see distant place
Object still can feel the influence of mist, in addition, the presence of mist allows the mankind to feel the presence of the depth of field, therefore, when defogging
Retain a certain degree of mist, it is therefore desirable to introduced in formula (6) and remove fog factor ω, ω rule of asking for is here：Calculate dark
The ratio between standard deviation of passage figure defogging result corresponding with its (tests value to ask for the local defogging factor ω, ω between 0-1
0.95 image effect is best)；
Then formula (6) is modified to formula (7)：
Wherein ω is fog factor, to adjust image defogging degree, avoids the occurrence of and loses the depth of field and loss image detail
Situation；
The lower sampling coefficient n (n=0.25~0.5) of increase, is modified to formula (7), obtains formula (8)：
Down-sampling coefficient n is adjusted, image quality reaches best effect after making defogging processing speed and defogging；
Step 6：Image restoring
From formula (2),
By Step 4: five A, t (x) tried to achieve substitute into formula (9), it can be deduced that fogless image J (x) to be asked.
In described step two, the mini-value filtering that radius is 1 is carried out to image and is handled, it is therefore an objective to which image removes black surround, base
In the defogging algorithm of dark primary priori, need defogging degree high to partially white region, corresponding transmissivity t (x) is just small, dark
Region needs defogging degree low, so corresponding transmissivity t (x) needs to adjust height.So picture sky areas exist it is dark wide
Accuse board or house, then just occur that above-mentioned article joins blackening in sky, in order to solve this problem, asking for dark
Preceding we carry out the mini-value filtering that radius is 1 to image and handled, and can so bring slight halo effect certainly, but with it is black
Side problem, which is compared, just seems insignificant.
In step 4, down-sampling operation is carried out using single linear interpolation to air light value A, reduces and calculates data volume, reduce
Soc calculates the time.
In step 5, using air light value A, fog factor ω and dark channel diagram is gone to calculate transmissivity t (x), it is of the invention here
Transmissivity t (x) computational methods are improved, improved as follows：
It is fine in terms of algorithm details before the transmittance figure ratio of defogging in HE darks, such as its sampling number of appropriate reduction,
The effect of its defogging does not have too big difference, so artwork is not asked for when asking for transmissivity, but first to original
Figure carries out linear interpolation down-sampling, such as is reduced into the 1/4 of artwork, calculates the transmissivity of small figure, passes through interpolation again afterwards
The acquisition artwork approximation transmissivity t (x) of mode, then it can also obtain required effect.Because defogging calculates main take to figure
As the estimation of transmissivity, therefore screen demisting to calculating transmissivity again after being sampled under artwork, is being greatly reduced per the time required to frame,
Requirement to defogging equipment SOC also decreases, you can with control device cost, when carrying out defogging processing to 1080p images,
The actual amount of calculation of defogging can be optimized to the amount of calculation to 360p image defoggings, therefore can realize complete with low-performance equipment (low cost)
Into the effect of the real-time demisting of high definition, key to the invention is that the selection of lower sampling coefficient of reduction is, it is necessary to an appropriate lower sampling
Coefficient, makes lower sampling time-consuming and the small figure transmissivity of calculating takes sum t and is less than the directly time-consuming T of calculating artwork transmissivity, and image
Image quality can not sacrifice too much after processing.And lower sampling coefficient n selection controls the processing time for making the platform single width figure picture
In 30ms, you can realize the requirement of real-time demisting.In formula (7) we add a down-sampling coefficient n (0.25~
0.5), simplify transmissivity t (x) amount of calculation, while take into account the quality of picture after defogging so that the equipment of low operational capability can be with
The real-time defogging of video is carried out, formula is as follows after modification：
Its concrete operation step is as follows：
1) chosen for different computing capability equipment and be adapted to down-sampling coefficient n,
2) the down-sampling coefficient n of selection is brought into formula (8), calculates transmissivity t (x)
3) down-sampling coefficient n is adjusted, image quality obtains preferable improvement after making defogging processing speed and defogging.
Inventive algorithm optimizes the calculating in the primary unknowns air light value A and transmissivity t (x) in atmospheric scattering formula
Amount simplifies so that the demisting time is greatly reduced, if down-sampling rate is n, then only has original by the amount of calculation after algorithm optimization
The 1/n of amount of calculation2, reduce soc difficulty in computation so that low performance soc can complete the high definition defogging behaviour of 1080p images
Make.
It is exemplified below：
Example one：Calculated on i3 4g platforms, performance is similar to main flow low performance soc, and it is 1080p to take image
The original image of image quality, as shown in Figure 1, 2, Fig. 1 is image before defogging, and Fig. 2 is image after processing, down-sampling coefficient 1/5, during processing
Between 20ms, meet the requirement of real-time defogging.
Example two：Calculated on i3 4g platforms, performance is similar to main flow low performance soc, and it is 1080p to take image
The original image of image quality, as shown in Figure 3,4, Fig. 3 is image before defogging, and Fig. 4 is image after processing, down-sampling coefficient 1/4, during processing
Between 28ms, meet the requirement of real-time demisting.
The present invention can be applicable in vehicle-mounted monitoring system and traffic surveillance and control system, for moving soc and desktop cpu on the market
Performance gap is big, and HD video demisting is realized in low-cost platform, can pass through 1080p image down samplings to 360p or 270p
Algorithm optimization is crossed to sacrifice the cost of a small amount of image quality, lifts calculating speed, reaches the requirement of inexpensive facility defogging real time implementation.
Above in association with accompanying drawing to the present invention embodiment be explained in detail, but the present invention be not limited to it is above-mentioned
Embodiment, can also be before present inventive concept not be departed from those of ordinary skill in the art's possessed knowledge
Put that various changes can be made.
Claims (1)
- A kind of 1. image defogging optimized algorithm based on dark primary priori, it is characterised in that：Comprise the following steps：Step 1：From video extraction foggy image I (x)；Step 2：Mini-value filtering processing, the image G (x) after being handled are carried out to foggy image I (x)；Step 3：Ask for image G (x) dark channel diagram Jdark；The minimum value of each passage in image G (x) is obtained, in deposit and image G (x) size identical gray-scale maps, is helped secretly Road figure Jdark；For input picture G (x), it is as follows that its dark asks for formula：<mrow> <msup> <mi>j</mi> <mrow> <mi>d</mi> <mi>a</mi> <mi>r</mi> <mi>k</mi> </mrow> </msup> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <munder> <mrow> <mi>m</mi> <mi>i</mi> <mi>n</mi> </mrow> <mrow> <mi>y</mi> <mo>&Element;</mo> <mi>&Omega;</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </mrow> </munder> <mrow> <mo>(</mo> <munder> <mrow> <mi>m</mi> <mi>i</mi> <mi>n</mi> </mrow> <mrow> <mi>c</mi> <mo>&Element;</mo> <mrow> <mo>(</mo> <mi>r</mi> <mo>,</mo> <mi>g</mi> <mo>,</mo> <mi>b</mi> <mo>)</mo> </mrow> </mrow> </munder> <msup> <mi>j</mi> <mi>c</mi> </msup> <mo>(</mo> <mi>y</mi> <mo>)</mo> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow>J in formulacOne kind in image G (x) three Color Channels R, G, B is represented, Ω (x) represents a window centered on coordinate x Mouthful, y is x passage function, and dark channel prior defines jdark(x)→0；Step 4：Air light value A is estimated, choosing method is as follows：1) preceding 0.1% pixel is taken according to the size of brightness from dark channel diagram；2) in these positions that step 1) is chosen, the corresponding point with maximum brightness is found in original foggy image I (x) Value, as A values；Step 5：Calculate transmissivity t (x)Atmospherical scattering model is as follows：I (x)=J (x) t (x)+A (1-t (x)) (2)Wherein I (x) is treats demisting image, and J (x) is fogless image to be asked, and t (x) is image atmospheric transmissivity, and A is air Light value,Atmospherical scattering model (2) can be deformed into<mrow> <mfrac> <mrow> <msup> <mi>I</mi> <mi>c</mi> </msup> <mrow> <mo>(</mo> <mi>X</mi> <mo>)</mo> </mrow> </mrow> <msup> <mi>A</mi> <mi>c</mi> </msup> </mfrac> <mo>=</mo> <mi>t</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mfrac> <mrow> <msup> <mi>J</mi> <mi>c</mi> </msup> <mrow> <mo>(</mo> <mi>X</mi> <mo>)</mo> </mrow> </mrow> <msup> <mi>A</mi> <mi>c</mi> </msup> </mfrac> <mo>+</mo> <mn>1</mn> <mo>-</mo> <mi>t</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </mrow>In above formula, subscript C represents the meaning of tri- passages of R/G/B,Formula (3) both sides are asked twice minimum operation obtain following formula：<mrow> <munder> <mrow> <mi>m</mi> <mi>i</mi> <mi>n</mi> </mrow> <mrow> <mi>y</mi> <mo>&Element;</mo> <mi>&Omega;</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </mrow> </munder> <mrow> <mo>(</mo> <munder> <mrow> <mi>m</mi> <mi>i</mi> <mi>n</mi> </mrow> <mi>c</mi> </munder> <mfrac> <mrow> <msup> <mi>I</mi> <mi>c</mi> </msup> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </mrow> <msup> <mi>A</mi> <mi>c</mi> </msup> </mfrac> <mo>)</mo> </mrow> <mo>=</mo> <mi>t</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <munder> <mrow> <mi>m</mi> <mi>i</mi> <mi>n</mi> </mrow> <mrow> <mi>y</mi> <mo>&Element;</mo> <mi>&Omega;</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </mrow> </munder> <mrow> <mo>(</mo> <munder> <mrow> <mi>m</mi> <mi>i</mi> <mi>n</mi> </mrow> <mi>c</mi> </munder> <mfrac> <mrow> <msup> <mi>J</mi> <mi>c</mi> </msup> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </mrow> <msup> <mi>A</mi> <mi>c</mi> </msup> </mfrac> <mo>)</mo> </mrow> <mo>+</mo> <mn>1</mn> <mo>-</mo> <mi>t</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> </mrow>In above formula, J (x) is fogless image to be asked, and the dark primary priori theoretical in step 3 has：<mrow> <msup> <mi>J</mi> <mrow> <mi>d</mi> <mi>a</mi> <mi>r</mi> <mi>k</mi> </mrow> </msup> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>min</mi> <mrow> <mo>(</mo> <munder> <mrow> <munder> <mrow> <mi>m</mi> <mi>i</mi> <mi>n</mi> </mrow> <mi>c</mi> </munder> <msup> <mi>J</mi> <mi>c</mi> </msup> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </mrow> <mrow> <mi>y</mi> <mo>&Element;</mo> <mi>&Omega;</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </mrow> </munder> <mo>)</mo> </mrow> <mo>=</mo> <mn>0</mn> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>5</mn> <mo>)</mo> </mrow> </mrow>Therefore, can be derived with reference to formula (4), (5)：<mrow> <mi>t</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <mn>1</mn> <mo>-</mo> <munder> <mrow> <mi>m</mi> <mi>i</mi> <mi>n</mi> </mrow> <mrow> <mi>y</mi> <mo>&Element;</mo> <mi>&Omega;</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </mrow> </munder> <mrow> <mo>(</mo> <munder> <mrow> <mi>m</mi> <mi>i</mi> <mi>n</mi> </mrow> <mi>c</mi> </munder> <mfrac> <mrow> <msup> <mi>J</mi> <mi>C</mi> </msup> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </mrow> <msup> <mi>A</mi> <mi>c</mi> </msup> </mfrac> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>6</mn> <mo>)</mo> </mrow> </mrow>But in actual life, even fine day white clouds, there is also some particles in air, therefore, see the object of distant place Or the influence of mist can be felt, in addition, the presence of mist allows the mankind to feel the presence of the depth of field, therefore, retained when defogging A certain degree of mist, it is therefore desirable to introduced in formula (6) and remove fog factor ω, ω rule of asking for is here：Calculate dark The ratio between standard deviation of defogging result corresponding with its is schemed to ask for local defogging factor ω, and ω is between 0-1；Then formula (6) is modified to formula (7)：<mrow> <mi>t</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <mn>1</mn> <mo>-</mo> <munder> <mrow> <mi>&omega;</mi> <mi>m</mi> <mi>i</mi> <mi>n</mi> </mrow> <mrow> <mi>y</mi> <mo>&Element;</mo> <mi>&Omega;</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </mrow> </munder> <mrow> <mo>(</mo> <munder> <mrow> <mi>m</mi> <mi>i</mi> <mi>n</mi> </mrow> <mi>c</mi> </munder> <mfrac> <mrow> <msup> <mi>J</mi> <mi>C</mi> </msup> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </mrow> <msup> <mi>A</mi> <mi>c</mi> </msup> </mfrac> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>7</mn> <mo>)</mo> </mrow> </mrow>The lower sampling coefficient n (n=0.25~0.5) of increase, is modified to formula (7), obtains formula (8)：<mrow> <mi>t</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <mn>1</mn> <mo>-</mo> <munder> <mrow> <mi>&omega;</mi> <mi>m</mi> <mi>i</mi> <mi>n</mi> </mrow> <mrow> <mi>y</mi> <mo>&Element;</mo> <mi>&Omega;</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </mrow> </munder> <mrow> <mo>(</mo> <munder> <mrow> <mi>m</mi> <mi>i</mi> <mi>n</mi> </mrow> <mi>c</mi> </munder> <mfrac> <mrow> <msup> <mi>J</mi> <mi>C</mi> </msup> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </mrow> <mrow> <msup> <mi>nA</mi> <mi>c</mi> </msup> </mrow> </mfrac> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>8</mn> <mo>)</mo> </mrow> </mrow>Down-sampling coefficient n is adjusted, image quality reaches best effect after making defogging processing speed and defogging；Step 6：Image restoringFrom formula (2),<mrow> <mi>J</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <mi>I</mi> <mrow> <mo>(</mo> <mi>X</mi> <mo>)</mo> </mrow> <mo>-</mo> <mi>A</mi> </mrow> <mrow> <mi>t</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>+</mo> <mi>A</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>9</mn> <mo>)</mo> </mrow> </mrow>By Step 4: five A, t (x) tried to achieve substitute into formula (9), it can be deduced that fogless image J (x) to be asked.
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