CN104091307A - Frog day image rapid restoration method based on feedback mean value filtering - Google Patents

Abstract

The invention discloses a frog day image rapid restoration method based on feedback mean value filtering, for restoration processing of a frog day image. The method takes an atmosphere scattering model as a basis, comprises specific steps shown in an attached drawing 1 of the abstract of the descriptions, and mainly involves restoration of the frog day image through four steps including image preprocessing 2, atmosphere light value estimation 7, transmission graph estimation 12 and tone adjustment 14. The main technical features of the invention comprise weight graph establishing 4, mean value filtering 9, parameter repairing fuzzy edge feedback 10 and high-light area transmissivity self-adaptive correction 11. The advantages are as follows: atmosphere light values can be accurately estimated, influences exerted by a non-sky high-light area are avoided, at the same time, the complexity of the algorithm for estimating a transmission graph is low, and quite good restoration effect can be achieved within a short period. The method provided by the invention is applied to restoration processing of a degraded image under the condition of foggy weather, dusty weather and the like.

Description

Foggy day image fast restoration method based on feedback mean filtering

The technical field is as follows:

the invention relates to the technical field of digital image processing and computer vision, in particular to a foggy day image fast restoration method based on feedback mean filtering.

Background art:

under the foggy weather condition, the propagation of light can be influenced by suspended water drops in the air and scatter, and then deviate from the original propagation path, and simultaneously, the light of other light paths can enter the light path due to scattering, so that the formed image is blurred, the color is distorted, and the contrast is obviously reduced, which seriously influences the analysis and identification of human eyes or a computer vision system on the image content.

Currently, the single image defogging technology can be generally classified into an image enhancement-based defogging method and a physical model-based image restoration method. The method developed rapidly at present is an image restoration method based on a physical model, and the method can solve the fog-free image through related prior information and the physical model. The relatively representative algorithm is a single image defogging algorithm based on dark channel prior, which is provided by HE and the like, the algorithm is used for counting a large number of outdoor fog-free images, a dark channel prior rule capable of estimating fog concentration is found, scene transmittance reflecting the fog concentration can be obtained by using the rule, then the fog-free images are solved by combining a physical model of fog day imaging, the defogging effect of the algorithm is good, and the recovered images are natural in color, but the space and time complexity of the whole algorithm are higher, and the dark channel prior fails when a large-area bright area such as the sky appears in the images, and meanwhile, as a soft matting algorithm is involved in the initial transmittance optimization process, the time and space complexity of the whole algorithm is higher, and the actual application is difficult to meet. In summary, the HE algorithm has a good defogging effect, but still has the following four problems to be solved: (1) the algorithm has high time and space complexity and is difficult to meet the practical application; (2) the large-area off-white areas such as sky are easy to be distorted in restoration, and the restoration result is influenced; (3) the atmospheric light value estimation is not accurate enough, and the result is susceptible to a small-area highlight region. (4) The method has narrow application range and cannot treat the fog when the fog presents color cast except white.

The invention content is as follows:

aiming at the problems in the prior art, the invention aims to provide a feedback mean filtering-based method for quickly restoring a foggy image, and the method is used for improving the instantaneity and robustness of a defogging algorithm so as to meet the actual application requirements.

In order to achieve the purpose, the invention adopts the following technical means:

1. a foggy day image fast restoration method based on feedback mean filtering is characterized by comprising the following steps:

A) preprocessing an input image to eliminate fog color cast;

B) establishing a smooth brightness weight map Q, comprising the steps of:

b1) establishing a brightness graph L and a smooth intensity graph P, wherein the specific method comprises the following steps:

$\left\{\begin{array}{c}L\left(x\right)=\frac{1}{3}(I_r\left(x\right)+I_g\left(x\right)+I_b\left(x\right))\\ P\left(x\right)=\exp (-E\left(x\right))\end{array}\right.$

wherein I_r(x)、I_g(x)、I_b(x) Respectively representing the intensity values of three channels of the preprocessed image, E (x) representing the edge intensity value of the preprocessed image obtained by a Sobel operator, L (x) representing the intensity value of a brightness image, and P (x) representing the intensity value of a smooth intensity image;

b2) obtaining a weight map Q according to the obtained brightness map and the smooth intensity map:

Q(x)＝0.5L(x)+0.5P(x)

wherein Q (x) is the intensity value of the weight map;

C) estimating an atmospheric light value A according to the preprocessed image obtained in the step A);

D) estimating a transmission map t according to the preprocessed image obtained in the step A);

E) according to the atmospheric light value A and the transmission map t obtained through estimation, a restored foggy day image is obtained through an atmospheric scattering model;

F) the method for adjusting the restored image by adopting the self-adaptive logarithm mapping operator comprises the following steps:

<math> <mrow> <msub> <mi>L</mi> <mi>d</mi> </msub> <mo>=</mo> <mfrac> <mrow> <msub> <mi>L</mi> <mrow> <mi>d</mi> <mi>max</mi> </mrow> </msub> <mo>&times;</mo> <mn>0.01</mn> </mrow> <mrow> <mi>lg</mi> <mrow> <mo>(</mo> <msub> <mi>L</mi> <mrow> <mi>w</mi> <mi>max</mi> </mrow> </msub> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>&CenterDot;</mo> <mfrac> <mrow> <mi>ln</mi> <mrow> <mo>(</mo> <msub> <mi>I</mi> <mi>w</mi> </msub> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> <mrow> <mi>ln</mi> <mo>{</mo> <mn>2</mn> <mo>+</mo> <mn>8</mn> <msup> <mrow> <mo>(</mo> <mfrac> <msub> <mi>L</mi> <mi>w</mi> </msub> <msub> <mi>L</mi> <mrow> <mi>w</mi> <mi>max</mi> </mrow> </msub> </mfrac> <mo>)</mo> </mrow> <mfrac> <mrow> <mi>ln</mi> <mi>b</mi> </mrow> <mrow> <mi>ln</mi> <mn>0.5</mn> </mrow> </mfrac> </msup> <mo>}</mo> </mrow> </mfrac> </mrow> </math>

wherein L is_dTo output luminance, L_dmaxFor maximum output brightness allowed, L_wFor input luminance, L_wmaxB is the bias parameter, which is the maximum value in the input luminance and has a default value in the range of 0.65 to 1.2.

In the method for quickly restoring the foggy day image based on the feedback average filtering, as an optimization scheme, the preprocessing method in the step a is white balance.

In the method for quickly restoring a foggy day image based on feedback average filtering, as an optimization scheme, the specific manner of estimating the atmospheric light value a in the step C is as follows: dividing the weight map Q into M multiplied by M areas with equal size, selecting the area with the maximum weight sum in the divided areas, and selecting the maximum value in the area corresponding to the preprocessed image as the atmospheric light value A.

In the method for quickly restoring a foggy day image based on feedback mean filtering, as an optimization scheme, the specific steps of estimating the transmission map t in the step D are as follows:

A) obtaining a mean filtering result, comprising:

a1) the method for extracting the minimum channel map of the preprocessed image comprises the following specific steps:

<math> <mrow> <mi>W</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <munder> <mi>min</mi> <mrow> <mi>c</mi> <mo>&Element;</mo> <mo>{</mo> <mi>r</mi> <mo>,</mo> <mi>g</mi> <mo>,</mo> <mi>b</mi> <mo>}</mo> </mrow> </munder> <mrow> <mo>(</mo> <msubsup> <mi>I</mi> <mi>w</mi> <mi>c</mi> </msubsup> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>)</mo> </mrow> </mrow> </math>

wherein,w (x) is the corresponding minimum channel map for the intensity value of a certain channel of the preprocessed image;

a2) and performing average filtering on the minimum channel map, wherein the size of a filtering template is m multiplied by m, wherein m is max (3, N/25000), N is the total pixel number of the image, m is usually taken as an odd number, and elements in the filtering template are all 1/lambda m²Wherein λ is an adjustment parameter, and the specific filtering method is as follows:

<math> <mrow> <mi>G</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>s</mi> <mo>=</mo> <mo>-</mo> <mi>a</mi> </mrow> <mi>a</mi> </munderover> <munderover> <mi>&Sigma;</mi> <mrow> <mi>t</mi> <mo>=</mo> <mo>-</mo> <mi>a</mi> </mrow> <mi>a</mi> </munderover> <mi>w</mi> <mrow> <mo>(</mo> <mi>s</mi> <mo>,</mo> <mi>t</mi> <mo>)</mo> </mrow> <mi>f</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>+</mo> <mi>s</mi> <mo>,</mo> <mi>y</mi> <mo>+</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </math>

where f (x, y) is the value of the minimum channel map at (x, y), w is the element in the filter template, G (x, y) is the mean filter result, and a is (m-1)/2;

a3) according to the minimum channel map and the filtering result, the feedback parameter gamma is obtained by the following method:

<math> <mrow> <mi>&gamma;</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <mi>W</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </mrow> <mi>&lambda;</mi> </mfrac> <mo>-</mo> <mi>G</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </mrow> </math>

wherein λ is the tuning parameter set in step a 2);

a4) according to the filtering result and the feedback parameter, the fuzzy edge is repaired by the feedback parameter to obtain a corrected result I_edge：

<math> <mrow> <msub> <mi>I</mi> <mi>edge</mi> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfenced open='{' close=''> <mtable> <mtr> <mtd> <mi>G</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>+</mo> <mfrac> <mrow> <mi>&gamma;</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </mrow> <mi>&lambda;</mi> </mfrac> </mtd> <mtd> <mi>&gamma;</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>></mo> <mn>0.01</mn> </mtd> </mtr> <mtr> <mtd> <mi>G</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </mtd> <mtd> <mi>&gamma;</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>&lt;</mo> <mn>0.01</mn> </mtd> </mtr> </mtable> </mfenced> </mrow> </math>

Wherein λ is the adjustment parameter set in step a2), and γ (x) is the feedback parameter obtained in step a 3);

a5) obtaining an initial transmission map according to the filtering result after edge correction in the following way

<math> <mrow> <mover> <mi>t</mi> <mo>~</mo> </mover> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <mn>1</mn> <mo>-</mo> <mi>&omega;</mi> <msub> <mi>I</mi> <mi>dark</mi> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </mrow> </math>

Wherein omega is a regulating parameter, and the default value is 0.95;

B) adaptively modifying the transmittance of the highlight region, the steps comprising:

b1) judging the area of the sky area in the preprocessed image, wherein the specific mode is as follows: a threshold μ is set in the weight map Q, defined as a sky region when Q (x) > μ, and a non-sky region otherwise.

b2) Setting a tolerance K according to the proportion of the region in the whole image to adaptively correct the transmissivity, and obtaining the tolerance K by the following method:

<math> <mrow> <mi>K</mi> <mo>=</mo> <mfenced open='{' close=''> <mtable> <mtr> <mtd> <mi>&tau;A</mi> </mtd> <mtd> <mi>&omega;</mi> <mo>></mo> <mn>0.75</mn> </mtd> </mtr> <mtr> <mtd> <mfrac> <mi>A</mi> <mn>10</mn> </mfrac> </mtd> <mtd> <mi>&omega;</mi> <mo>&lt;</mo> <mn>0.75</mn> </mtd> </mtr> </mtable> </mfenced> </mrow> </math>

wherein omega is the area proportion of the sky part in the area of the selected atmospheric light value in the area, tau is the area proportion of the sky part in the whole image, and the maximum value of tau is 0.35;

b3) from the tolerance K, a corrected transmission map t (x) is obtained by:

$t\left(x\right)=\left\{\begin{array}{cc}C\left(x\right)\tilde{t}\left(x\right)& C\left(x\right)>1\\ \tilde{t}\left(x\right)& C\left(x\right)<1\end{array}\right.$

wherein C (x) is a correction parameter, andI_w(x) For the gray scale of the pre-processed image, t (x) is the final estimated transmission map intensity value.

Compared with the prior art, the invention has the following beneficial effects:

1. the foggy day image fast restoration method based on the feedback mean filtering adopts an image preprocessing scheme, and achieves the purposes of correcting fog color cast and keeping fog white through white balance, thereby expanding the processing range of degraded images and having better processing effect on images influenced by non-white fog and dust.

2. According to the foggy day image rapid restoration method based on the feedback mean filtering, a smooth brightness intensity graph is designed, the atmospheric light value selection area is determined according to the division weight graph, the influence of a local non-sky highlight area is avoided, the robustness of the estimated atmospheric light value is improved, and the restoration result is more accurate.

3. The method for quickly restoring the foggy day image based on the feedback mean filtering adopts the mean filtering on the estimation of the transmission image, so that the result is more consistent with the characteristic that fog is uniformly distributed in the same scene depth, meanwhile, the fuzzy edge generated by filtering is repaired at lower calculation cost by designing the feedback parameters, the accuracy of the estimation result is improved, meanwhile, the algorithm complexity is reduced, the calculation time and the size of the image form a linear growth relation, and the real-time application can be met through hardware acceleration.

4. According to the foggy day image fast restoration method based on the feedback mean filtering, the sky area is divided by the weight map setting threshold, the transmissivity of the sky area is adaptively corrected according to the area of the sky area, and the condition that the restored sky area has color distortion is avoided.

5. The method adjusts the restoration result through the self-adaptive logarithm mapping operator, combines the image restoration method and the image enhancement method, and enables the restoration result to be bright in color, and the contrast and the definition to be improved greatly.

Description of the drawings:

FIG. 1 is a flow chart of a method for rapidly restoring a foggy day image based on feedback mean filtering according to the present invention. In the figure, 1 is an input image, 2 is image preprocessing, 3 is extracted image edges, 4 is a weight map, 5 is a selected region for determining an atmospheric light value, 6 is a region for determining a sky region, 7 is an estimated atmospheric light value, 8 is an extracted minimum channel map, 9 is a mean value filter, 10 is a feedback parameter for repairing a blurred edge, 11 is a transmittance of an adaptive correction highlight region, 12 is an estimated transmission map, 13 is a restored image, 14 is a tone adjustment, and 15 is an output image.

FIG. 2 shows the result of image preprocessing according to an embodiment of the present invention; FIG. 2(a) is an image of a foggy day input by an embodiment of the present invention; fig. 2(b) is a preprocessed image obtained by white balance according to an embodiment of the present invention.

FIG. 3 is a process for estimating an atmospheric light value according to an embodiment of the present invention; FIG. 3(a) is a luminance map calculated for the preprocessed image of FIG. 2(b) according to an embodiment of the present invention; FIG. 3(b) is a graph of the calculated smoothed intensity for the preprocessed image of FIG. 2(b) according to an embodiment of the present invention; FIG. 3(c) is a graph of weights computed for the preprocessed image of FIG. 2(b) according to an embodiment of the present invention; fig. 3(d) shows the atmospheric light value selection region determined by dividing the weight map into 3 × 3 regions.

FIG. 4 is a process of estimating an initial transmission map according to an embodiment of the present invention; FIG. 4(a) is a minimum channel map obtained by taking the minimum channel value of the preprocessed image shown in FIG. 2(b) according to an embodiment of the present invention; fig. 4(b) is a filtering result obtained by performing mean filtering on the minimum channel map; FIG. 4(c) is a diagram of the edge region to be repaired determined by the feedback parameters; fig. 4(d) is an initial transmission diagram obtained after edge repairing by feedback parameters.

FIG. 5 is a process of modifying transmittance according to an embodiment of the present invention; fig. 5(a) is a schematic view of a sky region obtained by thresholding the weight map of fig. 3(c) according to an embodiment of the invention; fig. 5(b) is a corrected transmission diagram obtained by setting a tolerance according to the area of the sky region in the embodiment of the present invention.

FIG. 6 is the end result of an embodiment of the present invention; FIG. 6(a) is a graph showing the recovery result of a foggy day image according to the embodiment of the present invention; fig. 6(b) is a diagram illustrating the result of performing tone adjustment on the restored result by the adaptive logarithm mapping operator according to the embodiment of the present invention.

FIG. 7 shows the result of processing a sand image according to an embodiment of the present invention; FIG. 7(a) is a sand degradation image; FIG. 7(b) is a graph showing the restoration result of the dust image according to the present invention.

The specific implementation mode is as follows:

the basic idea of the invention is as follows: the method comprises the steps of preprocessing a foggy day image by using an image enhancement method to eliminate fog color cast, designing a specific weight map by using the highlight and smoothness characteristics of a sky area to determine an atmospheric light value selection area, further improving the accuracy of atmospheric light value estimation, estimating a transmission map by mean value filtering with feedback parameters, obtaining the transmission map which better accords with fog distribution characteristics by using a simple and rapid method, finally solving a restored image by inverse solution according to an atmospheric scattering model, and adjusting the restored result by using a self-adaptive logarithmic mapping operator to obtain a final restored image.

The embodiments and processes of the present invention will be described in detail with reference to the accompanying drawings and examples, but the scope of the present invention should not be limited to the examples.

In this embodiment, a computer with a CPU of 2.79Ghz and a memory of 1.75G is used to perform simulation on a Matlab2010 platform, and an image with 600 × 450 pixels shown in fig. 2(a) is used as an input image to perform defogging processing, where the average time of multiple processing is 2.5s, and a specific flow is shown in fig. 1, and includes the following steps:

A) in this embodiment, the input image is preprocessed by using white balance, and the specific steps are as follows:

a1) obtaining a white balance correction coefficient, the step comprising:

obtaining the gray scale map of the input image, and obtaining the correction coefficient alpha of the corresponding color channel through the input image and the gray scale map_c：

<math> <mrow> <msub> <mi>&alpha;</mi> <mi>c</mi> </msub> <mo>=</mo> <mfrac> <msub> <mi>Y</mi> <mi>m</mi> </msub> <msub> <mi>M</mi> <mi>c</mi> </msub> </mfrac> <mo>;</mo> <mi>c</mi> <mo>&Element;</mo> <mo>{</mo> <mi>r</mi> <mo>,</mo> <mi>g</mi> <mo>,</mo> <mi>b</mi> <mo>}</mo> </mrow> </math>

Wherein, Y_mFor all pixels of a grey-scale image of the input imageMean intensity value, M_cThe average intensity value of part of pixels in each color channel is satisfied that the intensity value in the corresponding channel is greater than 0.9Y_mamIn which Y is_maxThe maximum value in the gray scale image of the input image is obtained, and finally, the color channel values of the input image are respectively multiplied by the corresponding correction coefficients alpha_cTo obtain a white balanced image

In the step, the relative difference between the three channels is reduced under the condition that the total chromaticity of the input image is kept unchanged, so that the purpose of correcting the integral color cast of the image is achieved, but the correction coefficient alpha is usually smaller than 1, so that the processed image is integrally dark, and the integral brightness of the white balance image needs to be linearly improved at the moment.

a2) The step of linearly boosting the brightness of the white balance image comprises the following steps:

<math> <mrow> <msub> <mi>I</mi> <mi>w</mi> </msub> <mo>=</mo> <mrow> <mo>(</mo> <mfrac> <msub> <mi>I</mi> <mi>max</mi> </msub> <msub> <mi>W</mi> <mi>max</mi> </msub> </mfrac> <mo>+</mo> <mi>&epsiv;</mi> <mo>)</mo> </mrow> <msub> <mover> <mi>I</mi> <mo>~</mo> </mover> <mi>w</mi> </msub> </mrow> </math>

wherein, I_maxFor maximum intensity values in the input image, W_maxFor white-balanced processed imagesThe maximum intensity value in (1) is epsilon, which is an adjustment coefficient and has a value range of 0 to 0.1, in this embodiment, 0.05, I_wIs the final pre-processed image. FIG. 2(b) shows the present embodimentThe processed image.

B) Establishing a smooth brightness weight graph:

b1) establishing a brightness map L and a smooth intensity map P, specifically as follows:

$\left\{\begin{array}{c}L\left(x\right)=\frac{1}{3}(I_r\left(x\right)+I_g\left(x\right)+I_b\left(x\right))\\ P\left(x\right)=\exp (-E\left(x\right))\end{array}\right.$

wherein I_r(x)、I_g(x)、I_b(x) The intensity values of the three channels of the preprocessed image are respectively, E (x) is the edge intensity value of the preprocessed image obtained by a Sobel operator, L (x) is the intensity value of a brightness image, and P (x) is the intensity value of a smooth intensity image.

b2) Obtaining a weight map Q according to the obtained brightness map and the smooth intensity map:

Q(x)＝0.5L(x)+0.5P(x)

the method mainly starts from the characteristics that the sky area has high brightness, few edge details and high area smoothness, and a weight map is established by the characteristics to prepare for estimating the atmospheric light value and adaptively adjusting the sky area transmissivity.

C) And estimating an atmospheric light value:

in this embodiment, the weight map is divided into 3 × 3 equal regions, and the region with the largest weight-weighted sum is selected as the candidate region of the atmospheric light value, and the maximum value is selected as the value of the atmospheric light a in the region corresponding to the preprocessed image, where the value of a is a constant. The step can select the area containing the maximum sky area as the alternative area of the atmospheric light value, thereby avoiding the influence of the local non-sky highlight area on the selection of the atmospheric light and increasing the accuracy of the atmospheric light value estimation. Fig. 3 shows the process of obtaining the weight map and selecting the atmospheric light value according to the present embodiment.

D) And a transmission map estimation step:

taking the preprocessed image obtained in the step A) as a processing object, and estimating a transmission map according to the following steps:

d1) estimating an initial transmission map, the steps comprising:

11) the method for extracting the minimum channel map of the preprocessed image comprises the following specific steps:

<math> <mrow> <mi>W</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <munder> <mi>min</mi> <mrow> <mi>c</mi> <mo>&Element;</mo> <mo>{</mo> <mi>r</mi> <mo>,</mo> <mi>g</mi> <mo>,</mo> <mi>b</mi> <mo>}</mo> </mrow> </munder> <mrow> <mo>(</mo> <msubsup> <mi>I</mi> <mi>w</mi> <mi>c</mi> </msubsup> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>)</mo> </mrow> </mrow> </math>

wherein,for preprocessing the intensity value of a certain channel of the image, W (x) is the corresponding minimum channel map.

12) The minimum channel map is filtered by spatial means, the size of the filtering template is m × m, where m is max (3, N/25000), N is the total number of pixels of the image, m is usually an odd number, and in this embodiment is 11, and all elements in the template are 1/λ m²Wherein λ is a settable adjustment parameter, which is 1.2 in this embodiment, and the specific method of mean filtering is as follows:

<math> <mrow> <mi>G</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>s</mi> <mo>=</mo> <mo>-</mo> <mi>a</mi> </mrow> <mi>a</mi> </munderover> <munderover> <mi>&Sigma;</mi> <mrow> <mi>t</mi> <mo>=</mo> <mo>-</mo> <mi>a</mi> </mrow> <mi>a</mi> </munderover> <mi>w</mi> <mrow> <mo>(</mo> <mi>s</mi> <mo>,</mo> <mi>t</mi> <mo>)</mo> </mrow> <mi>f</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>+</mo> <mi>s</mi> <mo>,</mo> <mi>y</mi> <mo>+</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </math>

where f (x, y) is the value of the minimum channel map at (x, y), w is the element in the filter template, G (x, y) is the mean filter result, and a is (m-1)/2. It should be noted that the mean filtering in this step can be implemented by performing a two-dimensional convolution of the image matrix and the template matrix.

13) According to the minimum channel map and the filtering result, the feedback parameter gamma is obtained by the following method:

<math> <mrow> <mi>&gamma;</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <mi>W</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </mrow> <mi>&lambda;</mi> </mfrac> <mo>-</mo> <mi>G</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </mrow> </math>

where λ is the tuning parameter set in step 12).

14) According to the filtering result and the feedback parameter, the filtering result I after the edge correction is obtained in the following way_edge：

<math> <mrow> <msub> <mi>I</mi> <mi>edge</mi> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfenced open='{' close=''> <mtable> <mtr> <mtd> <mi>G</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>+</mo> <mfrac> <mrow> <mi>&gamma;</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </mrow> <mi>&lambda;</mi> </mfrac> </mtd> <mtd> <mi>&gamma;</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>></mo> <mn>0.01</mn> </mtd> </mtr> <mtr> <mtd> <mi>G</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </mtd> <mtd> <mi>&gamma;</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>&lt;</mo> <mn>0.01</mn> </mtd> </mtr> </mtable> </mfenced> </mrow> </math>

Wherein lambda is the adjusting parameter set in the step 12), the step obtains the areas with larger distortion caused by mean value filtering by setting a threshold value for the feedback parameter, and the areas are usually the edge areas with larger scene depth change.

15) Obtaining an initial transmission map according to the filtering result after edge correction in the following way

<math> <mrow> <mover> <mi>t</mi> <mo>~</mo> </mover> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <mn>1</mn> <mo>-</mo> <mi>&omega;</mi> <msub> <mi>I</mi> <mi>dark</mi> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </mrow> </math>

Wherein omega is a regulating parameter, and the default value is 0.95. Fig. 4 shows a process of acquiring an initial transmission map according to the present embodiment.

d2) Modifying the transmission map, the steps comprising:

21) the sky area is defined by setting a threshold value mu in the weight map Q, and the transmissivity is adaptively corrected according to the set tolerance K of the proportion of the area to the whole image. In this embodiment, the default value of μ is 0.9, when q (x) > μ is defined as a sky region, otherwise, it is a non-sky region, and the tolerance K is obtained as follows:

<math> <mrow> <mi>K</mi> <mo>=</mo> <mfenced open='{' close=''> <mtable> <mtr> <mtd> <mi>&tau;A</mi> </mtd> <mtd> <mi>&omega;</mi> <mo>></mo> <mn>0.75</mn> </mtd> </mtr> <mtr> <mtd> <mfrac> <mi>A</mi> <mn>10</mn> </mfrac> </mtd> <mtd> <mi>&omega;</mi> <mo>&lt;</mo> <mn>0.75</mn> </mtd> </mtr> </mtable> </mfenced> </mrow> </math>

wherein ω is the area proportion of the sky part in the atmospheric light value selection area in the step C) in the area, τ is the area proportion of the sky part in the whole image, and the maximum value of τ is 0.35.

The tolerance is calculated by setting a threshold value for ω in this step, because when ω is larger, it indicates that the sky area occupies a larger proportion in the whole image, and it is necessary to increase the tolerance according to the sky area, and when ω is smaller, τ is taken as a fixed value.

22) From the tolerance K, a corrected transmission map t (x) is obtained by:

$t\left(x\right)=\left\{\begin{array}{cc}C\left(x\right)\tilde{t}\left(x\right)& C\left(x\right)>1\\ \tilde{t}\left(x\right)& C\left(x\right)<1\end{array}\right.$

wherein C (x) is a correction parameter, andI_w(x) Is a gray scale map of the pre-processed image. Fig. 5 shows the result of the transmission chart correction of the present embodiment.

E) And recovering a fog-free image:

according to the atmospheric light value A and the transmission graph t, a fog-free image J (x) is obtained by the following method:

$J\left(x\right)=\frac{I_w\left(x\right)-A}{\max (t\left(x\right),t_0)}+A$

wherein I_w(x) For the pre-processed image, t (x) is the intensity value of the transmission map t, t₀The threshold value set to avoid noise generation is 0.1 in the present embodiment.

F) A color tone adjusting step:

the method for adjusting the restored image by adopting the self-adaptive logarithm mapping operator comprises the following steps:

<math> <mrow> <msub> <mi>L</mi> <mi>d</mi> </msub> <mo>=</mo> <mfrac> <mrow> <msub> <mi>L</mi> <mrow> <mi>d</mi> <mi>max</mi> </mrow> </msub> <mo>&times;</mo> <mn>0.01</mn> </mrow> <mrow> <mi>lg</mi> <mrow> <mo>(</mo> <msub> <mi>L</mi> <mrow> <mi>w</mi> <mi>max</mi> </mrow> </msub> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>&CenterDot;</mo> <mfrac> <mrow> <mi>ln</mi> <mrow> <mo>(</mo> <msub> <mi>L</mi> <mi>w</mi> </msub> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> <mrow> <mi>ln</mi> <mo>{</mo> <mn>2</mn> <mo>+</mo> <mn>8</mn> <msup> <mrow> <mo>(</mo> <mfrac> <msub> <mi>L</mi> <mi>w</mi> </msub> <msub> <mi>L</mi> <mrow> <mi>w</mi> <mi>max</mi> </mrow> </msub> </mfrac> <mo>)</mo> </mrow> <mfrac> <mrow> <mi>ln</mi> <mi>b</mi> </mrow> <mrow> <mi>ln</mi> <mn>0.5</mn> </mrow> </mfrac> </msup> <mo>}</mo> </mrow> </mfrac> </mrow> </math>

wherein L is_dTo output luminance, L_dmaxIn this embodiment, the value is 100, L, for the maximum allowable output brightness value_wFor input luminance, L_wmaxB is the bias parameter, which is the maximum value in the input luminance, and is 0.85 in this embodiment. Fig. 6(a) shows the restoration result of the present example, and fig. 6(b) shows the restoration adjustment result of the present example.

Claims (4)

1. A foggy day image fast restoration method based on feedback mean filtering is characterized by comprising the following steps:

A) carrying out image preprocessing (2) on the input image (1) to eliminate fog color cast;

B) establishing a weight map (4) Q, comprising the steps of:

b1) establishing a brightness graph L and a smooth intensity graph P, wherein the specific method comprises the following steps:

$\left\{\begin{array}{c}L\left(x\right)=\frac{1}{3}(I_r\left(x\right)+I_g\left(x\right)+I_b\left(x\right))\\ P\left(x\right)=\exp (-E\left(x\right))\end{array}\right.$

wherein I_，(x)、I_g(x)、I_b(x) Respectively representing the intensity values of three channels of the preprocessed image, E (x) representing the intensity value obtained by extracting the image edge (3) of the preprocessed image through a Sobel operator, L (x) representing the intensity value of a brightness image, and P (x) representing the intensity value of a smooth intensity image;

b2) obtaining a weight map Q according to the obtained brightness map and the smooth intensity map:

Q(x)＝0.5L(x)+0.5P(x)

wherein Q (x) is the intensity value of the weight map;

C) estimating an atmospheric light value (7) A from the preprocessed image obtained in step A);

D) estimating a transmission map (12) t from the preprocessed image obtained in step A);

E) obtaining a restored image (13) through an atmospheric scattering model according to the atmospheric light value A and the transmission map t which are obtained through estimation;

F) and carrying out tone adjustment (14) on the restored image by adopting an adaptive logarithm mapping operator to obtain an output image (15).

2. The foggy day image fast restoration method based on the feedback mean value filtering as claimed in claim 1, wherein the image preprocessing (2) method in the step A) is white balance.

3. The foggy day image fast restoration method based on the feedback mean value filtering as claimed in claim 1, wherein the specific manner of estimating the atmospheric light value (7) a in the step C) is as follows: dividing the weight map Q into M multiplied by M areas with equal size, selecting the area with the maximum weight sum in the divided areas, finding the corresponding area in the preprocessed image, determining the area as an atmospheric light value selection area (5), and finally selecting the maximum value in the area as an atmospheric light value A.

4. The foggy day image fast restoration method based on the feedback mean filtering as claimed in claim 1, wherein the specific steps of obtaining the estimated transmission map (12) t in the step D) are as follows:

A) obtaining a mean filtering result, comprising:

a1) extracting a minimum channel map (8) from the preprocessed image, wherein the specific method comprises the following steps:

<math> <mrow> <mi>W</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <munder> <mi>min</mi> <mrow> <mi>c</mi> <mo>&Element;</mo> <mo>{</mo> <mi>r</mi> <mo>,</mo> <mi>g</mi> <mo>,</mo> <mi>b</mi> <mo>}</mo> </mrow> </munder> <mrow> <mo>(</mo> <msubsup> <mi>I</mi> <mi>w</mi> <mi>c</mi> </msubsup> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>)</mo> </mrow> </mrow> </math>

wherein,w (x) is the corresponding minimum channel map for the intensity value of a certain channel of the preprocessed image;

a2) and (9) performing average filtering on the minimum channel map, wherein the size of a filtering template is m multiplied by m, m is max (3, N/25000), N is the total pixel number of the image, and all elements in the filtering template are 1/lambda m²λ is an adjustment parameter, and the specific filtering method is as follows:

<math> <mrow> <mi>G</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>s</mi> <mo>=</mo> <mo>-</mo> <mi>a</mi> </mrow> <mi>a</mi> </munderover> <munderover> <mi>&Sigma;</mi> <mrow> <mi>t</mi> <mo>=</mo> <mo>-</mo> <mi>a</mi> </mrow> <mi>a</mi> </munderover> <mi>w</mi> <mrow> <mo>(</mo> <mi>s</mi> <mo>,</mo> <mi>t</mi> <mo>)</mo> </mrow> <mi>f</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>+</mo> <mi>s</mi> <mo>,</mo> <mi>y</mi> <mo>+</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </math>

where f (x, y) is the value of the minimum channel map at (x, y), w is the element in the filter template, G (x, y) is the mean filter result, and a is (m-1)/2;

a3) according to the minimum channel map and the filtering result, the feedback parameter gamma is obtained by the following method:

<math> <mrow> <mi>&gamma;</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <mi>W</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </mrow> <mi>&lambda;</mi> </mfrac> <mo>-</mo> <mi>G</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </mrow> </math>

wherein λ is the tuning parameter set in step a 2);

a4) according to the filtering result and the feedback parameter, the fuzzy edge (10) is repaired by the feedback parameter to obtain a corrected result I_edge：

<math> <mrow> <msub> <mi>I</mi> <mi>edge</mi> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfenced open='{' close=''> <mtable> <mtr> <mtd> <mi>G</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>+</mo> <mfrac> <mrow> <mi>&gamma;</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </mrow> <mi>&lambda;</mi> </mfrac> </mtd> <mtd> <mi>&gamma;</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>></mo> <mn>0.01</mn> </mtd> </mtr> <mtr> <mtd> <mi>G</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </mtd> <mtd> <mi>&gamma;</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>&lt;</mo> <mn>0.01</mn> </mtd> </mtr> </mtable> </mfenced> </mrow> </math>

Wherein λ is the adjustment parameter set in step a2), and γ (x) is the feedback parameter obtained in step a 3);

a5) obtaining an initial transmission map according to the filtering result after edge correction in the following way

<math> <mrow> <mover> <mi>t</mi> <mo>~</mo> </mover> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <mn>1</mn> <mo>-</mo> <mi>&omega;</mi> <msub> <mi>I</mi> <mi>dark</mi> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </mrow> </math>

Wherein omega is a regulating parameter, and the default value is 0.95;

B) -adaptively modifying the transmittance (11) in the highlight region, the steps comprising:

b1) determining the area (6) of the sky region in the preprocessed image, wherein the specific mode is as follows: a threshold μ is set in the weight map Q, defined as a sky region when Q (x) > μ, and a non-sky region otherwise.

b2) Setting a tolerance K according to the proportion of the sky area in the whole image to adaptively correct the transmissivity, and obtaining the tolerance K by the following method:

<math> <mrow> <mi>K</mi> <mo>=</mo> <mfenced open='{' close=''> <mtable> <mtr> <mtd> <mi>&tau;A</mi> </mtd> <mtd> <mi>&omega;</mi> <mo>></mo> <mn>0.75</mn> </mtd> </mtr> <mtr> <mtd> <mfrac> <mi>A</mi> <mn>10</mn> </mfrac> </mtd> <mtd> <mi>&omega;</mi> <mo>&lt;</mo> <mn>0.75</mn> </mtd> </mtr> </mtable> </mfenced> </mrow> </math>

wherein omega is the area proportion of the sky part in the area of the selected atmospheric light value in the area, tau is the area proportion of the sky part in the whole image, and the maximum value of tau is 0.35;

b3) from the tolerance K, a corrected transmission map t (x) is obtained by:

$t\left(x\right)=\left\{\begin{array}{cc}C\left(x\right)\tilde{t}\left(x\right)& C\left(x\right)>1\\ \tilde{t}\left(x\right)& C\left(x\right)<1\end{array}\right.$

wherein C (x) is a correction parameter, andwherein I_w(x) For the gray scale of the pre-processed image, t (x) is the final estimated transmission map (12) intensity value.