An image restoration method based on parameterized analytical modulation transfer function model of turbid atmosphere

Abstract

The present invention relates to the field of atmospheric image restoration technology, and specifically to an image restoration method based on a parametric analytical modulation transfer function model of a turbid atmosphere. The present invention first uses a radiation transfer numerical method based on a discrete coordinate DISORT algorithm to establish a data source library. Then, multivariate nonlinear fitting and linear interpolation methods are used to study the quantitative relationship between key atmospheric optical parameters, spatial frequency, and modulation transfer function (MTF) values, so as to establish a parametric analytical MTF model for a turbid atmosphere; then, the model is applied to the inverse filtering method to restore haze images, thereby effectively restoring the original image affected by haze; finally, combined with the Gamma correction technology, the brightness and contrast of the image are further improved to obtain a restored image with higher clarity and quality.

Description

Technical Field

[0001] The invention relates to the technical field of atmospheric image restoration, and in particular to an image restoration method based on a parameterized analytical modulation transfer function model of a turbid atmosphere. Background Art

[0002] Suspended particles such as haze in the turbid atmosphere will cause multiple scattering and absorption of light during propagation, making the captured image blurry and distorted in color, thereby reducing the image quality and affecting the visual effect and practical application of the image. The modulation transfer function (MTF) of an image is an important indicator that describes the impact of the imaging process on the signal transmission characteristics of different spatial frequencies. It reflects the resolution of the imaging process at different spatial frequencies and is of great significance for understanding and evaluating the performance of the imaging process. Accurately obtaining the MTF of the turbid atmosphere in haze weather with low visibility is crucial for high-quality real-time imaging and image restoration.

[0003] At present, the methods for obtaining the MTF of turbid atmosphere mainly include theoretical analysis, numerical simulation, controlled indoor experimental measurement and actual measurement in open atmosphere. Theoretical analysis obtains MTF by calculating the energy attenuation caused by the physical process of light scattering and absorption in turbid atmosphere, including using the small angle scattering approximation (SAA) and solving the radiation transfer equation to calculate MTF. Among them, the most commonly used is the modulation transfer function model based on small angle scattering approximation. This modulation transfer function model is effective within the appropriate parameter range, that is, when the optical thickness is small, the forward scattering pattern is strong, and the spatial frequency is low; in other cases, the model error is large. In the actual atmospheric environment, parameters such as optical thickness, forward scattering pattern, and spatial frequency are all changing in real time; especially in foggy weather, the above-mentioned modulation transfer function model has poor defogging effect, resulting in poor imaging quality.

[0004] It can be seen that there is an urgent need for an image processing method that can effectively improve the imaging quality in a foggy atmospheric environment to solve the problem of poor imaging quality caused by poor defogging effect of the MTF model. Summary of the invention

[0005] In order to avoid and overcome the technical problems existing in the prior art, the present invention provides an image restoration method based on a parameterized analytical modulation transfer function model of a turbid atmosphere. The present invention can effectively improve the clarity and color restoration of foggy images.

[0006] To achieve the above object, the present invention provides the following technical solutions:

[0007] An image restoration method based on a parameterized analytical modulation transfer function model of a turbid atmosphere includes the following restoration steps:

[0008] S1. Use the DISORT algorithm to calculate the MTF values ​​corresponding to each group of key atmospheric optical parameters, and store all the calculated MTF values ​​in the source database;

[0009] S2. Based on the MTF values ​​in the source database, the spatial frequency critical values ​​corresponding to each group of key atmospheric optical parameters are calculated, and the complete spatial frequency interval corresponding to the current group of key atmospheric optical parameters is divided into multiple spatial frequency sub-intervals according to the spatial frequency critical values;

[0010] S3. Based on the MTF values ​​in the source database, the parametric analytical modulation transfer function model of the turbid atmosphere in each spatial frequency sub-interval of each group of key atmospheric optical parameters is derived;

[0011] S4. Combined with the parametric analytical modulation transfer function model of turbid atmosphere, the apparent modulation transfer function of turbid medium is constructed to characterize the influence of turbid atmospheric medium on the image spatial spectrum under the background of skylight;

[0012] S5. Taking the apparent modulation transfer function of the turbid medium as a degradation function, assigning the degradation function to an inverse filtering method, and restoring the image using the inverse filtering method.

[0013] As a further solution of the present invention: key atmospheric optical parameters include optical thickness τ, single scattering albedo ω, and asymmetry factor g.

[0014] As a further solution of the present invention: the specific steps of step S2 are as follows:

[0015] S21. Calculate the spatial frequency critical value corresponding to the current group of key atmospheric optical parameters using the spatial frequency critical value calculation formula. The spatial frequency critical value calculation formula is as follows:

[0016]

[0017] In the formula, Ω c1 Indicates the critical value of the spatial frequency that divides the low spatial frequency sub-interval and the medium spatial frequency sub-interval corresponding to the current group of key atmospheric optical parameters; MTF n Indicates the MTF value of the nth spatial frequency corresponding to the current set of key atmospheric optical parameters; MTF max Indicates the MTF value of the current set of key atmospheric optical parameters at zero spatial frequency; MTF low MTF n and MTF max The absolute value of the difference between 1 Indicates the spatial frequency threshold for dividing the low spatial frequency subinterval and the medium spatial frequency subinterval corresponding to the current group of key atmospheric optical parameters; Ω c2Indicates the critical value of the spatial frequency sub-interval and the high spatial frequency sub-interval in the division corresponding to the current group of key atmospheric optical parameters; MTF min Indicates the MTF value of the current set of key atmospheric optical parameters at infinite spatial frequency; MTF high MTF n and MTF min The absolute value of the difference between 2 Indicates the spatial frequency thresholds of the middle spatial frequency subinterval and the high spatial frequency subinterval of the division corresponding to the current group of key atmospheric optical parameters;

[0018] S22, according to the corresponding spatial frequency critical value, the complete spatial frequency interval corresponding to the current group of key atmospheric optical parameters is divided into low spatial frequency sub-intervals [0,Ω c1 ), the mid-spatial frequency subinterval [Ω c1 ,Ω c2 ) and high spatial frequency subintervals [Ω c2 ,∞), where ∞ represents infinite spatial frequency.

[0019] As a further solution of the present invention: the specific steps of step S3 are as follows:

[0020] S31, all MTF values ​​corresponding to each key atmospheric optical parameter, each group of key atmospheric optical parameters, and the critical value Ω of the spatial frequency corresponding to each key atmospheric optical parameter c1 and the spatial frequency critical value Ω c2 All are stored in the training database;

[0021] S32. Based on the data in the training database, the spatial frequency critical value Ω corresponding to each group of key atmospheric optical parameters is obtained by multivariate nonlinear fitting. c1 Calculation function, spatial frequency critical value Ω c2 calculation function, an MTF value calculation function in a low spatial frequency subinterval, and an MTF value calculation function in a high spatial frequency subinterval;

[0022] S33. According to the fitted MTF value calculation function in the low spatial frequency sub-interval and the MTF value calculation function in the high spatial frequency sub-interval, a linear interpolation method is used to obtain the MTF value calculation function in the corresponding medium spatial frequency sub-interval; and the three MTF value calculation functions together constitute a parameterized analytical modulation transfer function model of the turbid atmosphere of the current group of key atmospheric optical parameters in the complete spatial frequency interval.

[0023] As a further solution of the present invention: the spatial frequency critical value Ω c1 The calculation function is expressed as follows:

[0024]

[0025] In the formula, exp represents the exponential function with the natural constant e as the base; a c1 Indicates the critical value of spatial frequency Ω c1 Calculate the constant term in the function; τ i+1 represents the optical thickness τ to the power of i+1, b c1,i Indicates the critical value of spatial frequency Ω c1 τ in the calculation function i+1 The coefficient of i+1 represents the single scattering albedo ω to the power of i+1, t c1,i Indicates the critical value of spatial frequency Ω c1 ω in the calculation function i+1 The coefficient of g i+1 represents the asymmetric factor g raised to the power i+1, d c1,i Indicates the critical value of spatial frequency Ω c1 Calculate the function g i+1 The coefficient of p c1 、f c1 、h c1 and j c1 Both represent the critical value of spatial frequency Ω c1 Calculate the coefficients of the corresponding single-degree polynomial in the function;

[0026] Spatial frequency threshold Ω c2 The calculation function is expressed as follows:

[0027]

[0028] In the formula, a c2 Indicates the critical value of spatial frequency Ω c2 Calculate the constant term in the function; b c2,i Indicates the critical value of spatial frequency Ω c2 τ in the calculation function i+1 The coefficient of t c2,i Indicates the critical value of spatial frequency Ω c2 ω in the calculation function i+1 The coefficient of d c2,i Indicates the critical value of spatial frequency Ω c2 Calculate the function g i+1 The coefficient of p c2 、f c2 、h c2 and j c2 Both represent the critical value of spatial frequency Ω c2 Compute the coefficients of the corresponding single degree polynomial in function.

[0029] As a further solution of the present invention: the MTF value calculation function in the low spatial frequency sub-interval is expressed as follows:

[0030]

[0031] In the formula, A represents the MTF value calculation function in the low spatial frequency subinterval about the spatial frequency Ω, where Ω represents the spatial frequency; c1 represents the constant term in the MTF value calculation function in the low spatial frequency sub-interval; B c1,i Indicates the MTF value calculation function in the low spatial frequency sub-interval τ i+1 The coefficient of T c1,i Indicates the MTF value calculation function in the low spatial frequency sub-interval ω i+1 The coefficient of D c1,i Indicates the MTF value calculation function in the low spatial frequency sub-interval g i+1 The coefficient of P c1 、F c1 , H c1 and J c1 They all represent the coefficients of the corresponding single-degree polynomial in the MTF value calculation function in the low spatial frequency sub-interval;

[0032] The MTF value calculation function in the high spatial frequency sub-interval is expressed as follows:

[0033]

[0034] In the formula, A represents the MTF value calculation function in the high spatial frequency subinterval of the spatial frequency Ω; c2 represents the constant term in the MTF value calculation function within the high spatial frequency sub-interval; B c2,i Indicates the MTF value calculation function in the high spatial frequency sub-interval τ i+1 The coefficient of T c2,i Indicates the MTF value calculation function in the high spatial frequency sub-interval ω i+1 The coefficient of D c2,i Indicates the MTF value calculation function in the high spatial frequency sub-interval g i+1 The coefficient of P c2 、F c2 , H c2 and J c2 They all represent the coefficients of the corresponding single-order polynomial in the MTF value calculation function within the high spatial frequency sub-interval;

[0035] The MTF value calculation function in the medium spatial frequency sub-interval is expressed as follows:

[0036]

[0037] In the formula, represents the MTF value calculation function in the mid-spatial frequency subinterval about the spatial frequency Ω; Ωc1-c2 Represents any spatial frequency within the medium spatial frequency subinterval of the current set of key atmospheric optical parameters;

[0038]

[0039] Where MTF(Ω) represents the parameterized analytical modulation transfer function model of the turbid atmosphere with respect to the spatial frequency Ω in the complete spatial frequency range of the current set of key atmospheric optical parameters.

[0040] As a further solution of the present invention: the apparent modulation transfer function of the turbid medium is expressed as follows:

[0041]

[0042] Where MTF′(Ω,λ) represents the apparent modulation transfer function of the turbid medium with respect to the spatial frequency Ω and the ambient light wavelength λ; MTF(Ω,λ) represents the parameterized analytical modulation transfer function model of the turbid atmosphere with respect to the spatial frequency Ω and the ambient light wavelength λ; I P (λ) represents the background light intensity after the ambient light is scattered by the turbid medium in the atmosphere; F o (Ω,λ) represents the background light intensity I P (λ) represents the Fourier transform of the spatial frequency Ω; δ(Ω) represents the Dirac function with respect to the spatial frequency Ω.

[0043] As a further solution of the present invention: MTF (Ω, λ) is expressed as follows:

[0044]

[0045] Wherein, τ(λ) represents the calculation formula of optical thickness with respect to ambient light wavelength λ, that is, the current optical thickness τ is calculated by ambient light wavelength λ; represents the MTF value calculation function in the low spatial frequency sub-interval with respect to the spatial frequency Ω and the ambient light wavelength λ; represents the MTF value calculation function in the high spatial frequency sub-interval with respect to the spatial frequency Ω and the ambient light wavelength λ; represents the MTF value calculation function in the mid-spatial frequency sub-interval with respect to the spatial frequency Ω and the ambient light wavelength λ;

[0046]

[0047] Wherein, L represents the transmission distance of ambient light; V represents the ambient visibility; and q represents the ambient light transmission distance coefficient.

[0048] As a further solution of the present invention: the background light intensity calculation formula is expressed as follows:

[0049]

[0050] Wherein, k(Ω,λ) represents the parameter calculation function about the spatial frequency Ω and the ambient light wavelength λ.

[0051] As a further solution of the present invention: after restoring the image using the inverse filtering method in step S5, the image is then processed using the Gamma function to obtain a restored image with high definition.

[0052] Compared with the prior art, the present invention has the following beneficial effects:

[0053] 1. The present invention significantly improves the clarity and color restoration of foggy images by constructing a parameterized analytical MTF model for turbid atmosphere and its application in image restoration, solving the problem of poor image defogging effect in traditional methods.

[0054] 2. In the process of image restoration, the present invention comprehensively considers the influence of atmospheric attenuation, multiple scattering and ambient light background, and fully describes the changes in image transmission under a complex atmospheric environment, ensuring that the restored image achieves the best effect in contrast and color reproduction.

[0055] 3. By combining the inverse filtering method with the Gamma correction technology, the present invention can handle the image blur problem caused by different visibility conditions. The restored image has natural color and high contrast, and is suitable for a variety of application scenarios.

[0056] 4. The average relative error of the parametric analytical MTF model of turbid atmosphere of the present invention does not exceed 8%, and the root mean square error is less than 0.05. It can accurately calculate the MTF under turbid atmospheric conditions and apply it to image restoration, ensuring that the restored image has significant improvements in details and overall quality. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] Figure 1 It is a flow chart of the recovery steps of the present invention.

[0058] Figure 2 This is an original photo taken in light foggy weather conditions.

[0059] Figure 3 This is an original photo taken in moderate foggy weather conditions.

[0060] Figure 4 This is an original photo taken in foggy weather conditions.

[0061] Figure 5 This is a restored photo using the He method under light fog conditions.

[0062] Figure 6 This is a restored photo using the He method under moderate foggy weather conditions.

[0063] Figure 7 This is a restored photo using the He method under dense fog conditions.

[0064] Figure 8 This is a restored photo restored using the equivalent principle method under light fog conditions.

[0065] Fig. 9 This is a restored photo using the equivalent principle method under moderate foggy weather conditions.

[0066] Fig.10 This is a restored photo using the equivalent principle method under dense fog conditions.

[0067] Fig.11 This is a restored photo taken under light foggy weather conditions after restoration using the method of the present invention.

[0068] Fig.12 This is a restored photo after restoration using the method of the present invention under moderate foggy weather conditions.

[0069] Fig.13 This is a restored photo after restoration using the method of the present invention under dense fog weather conditions. DETAILED DESCRIPTION

[0070] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0071] See also Figures 1 to 13 In an embodiment of the present invention, an image restoration method based on a parameterized analytical MTF model of a turbid atmosphere includes the following contents.

[0072] 1. Parameterized analytical MTF model for turbid atmosphere.

[0073] 1) Establish a data source library:

[0074] The present invention first analyzes the MTF of turbid media based on the equivalent principle of modulation transfer function of turbid media, and then uses the discrete coordinate DISORT algorithm based on the numerical method of radiation transfer to calculate the MTF under different key atmospheric optical parameters. The equivalent principle of MTF of turbid media is an important method to describe the influence of turbid media (such as atmosphere) on image quality. MTF is a quantitative index of the ability of optical system to transmit contrast. It comprehensively considers the two factors of resolution and contrast, and can comprehensively describe the attenuation of image brightness by turbid media and the image blur caused by adjacent edge effect.

[0075] The DISORT algorithm uses a double Gaussian numerical integration method, and the integration nodes are large enough to obtain accurate results. The present invention uses 256 integration nodes in the process of DISORT algorithm calculation, and uses the Henyey-Greenstein (H-G) scattering phase function that adjusts the asymmetric factor g to represent the forward scattering characteristics of different intensities. It is established in the key atmospheric optical parameter range of optical thickness τ with a value range of [0,2.0], single scattering albedo ω with a value range of [0.1,1.0], and asymmetric factor g with a value range of [0.05,0.95], and contains a source database of 56,200 sample points. At the same time, in order to more carefully describe the impact of changes in key atmospheric optical parameters on MTF, the change step size of optical thickness τ is set to 0.05, the change step size of single scattering albedo ω is set to 0.03, and the change step size of asymmetric factor g is set to 0.02.

[0076] 2) Determine the critical spatial frequency:

[0077] When the key atmospheric optical parameters are specified, the MTF of the turbid medium is basically unchanged in the low spatial frequency sub-interval and the high spatial frequency sub-interval. In the medium spatial frequency sub-interval, the MTF is linearly related to the spatial frequency in logarithmic form. Therefore, it is assumed that the MTF is only related to the key atmospheric optical parameters in the low spatial frequency sub-interval and the high spatial frequency sub-interval; in the medium spatial frequency sub-interval, the MTF has a certain functional relationship with the key atmospheric optics and spatial frequency.

[0078] The present invention regards the corresponding spatial frequency as the critical value of the spatial frequency when the MTF under the specified key atmospheric optical parameters changes significantly, that is, the turning point of the MTF curve.

[0079] According to the data in the source database, the difference method is used to obtain the spatial frequency critical value calculation formulas of formula (1) and formula (2).

[0080]

[0081] According to the corresponding spatial frequency critical value, the complete spatial frequency interval corresponding to the current group of key atmospheric optical parameters is divided into low spatial frequency sub-intervals [0,Ω c1 ), the mid-spatial frequency subinterval [Ω c1 ,Ω c2 ) and high spatial frequency subintervals [Ω c2 ,∞).

[0082] Since MTF is affected by many factors, in order to ensure the reliability and accuracy of the established model, the present invention divides the key atmospheric optical parameters into 12 groups according to the source database, as shown in Table 1.

[0083] Table 1 Classification of key atmospheric optical parameters

[0084]

[0085] 3) Establishment of parameterized analytical MTF model for turbid atmosphere:

[0086] According to the critical value of spatial frequency, the relationship between key atmospheric optical parameters and MTF value is qualitatively analyzed, and according to the 12 groups of key atmospheric optical parameters divided in Table 1, the parametric analytical MTF model of turbid atmosphere is established.

[0087] First, the MTF average values ​​of the low and high spatial frequency sub-intervals corresponding to each key atmospheric optical parameter, each group of key atmospheric optical parameters, and the critical value of the spatial frequency corresponding to each key atmospheric optical parameter Ω are calculated. c1 and the spatial frequency critical value Ω c2 are stored in the training database.

[0088] Then, based on the data in the training database, the spatial frequency critical value Ω corresponding to each group of key atmospheric optical parameters was obtained by multivariate nonlinear fitting. c1 Calculation function, spatial frequency critical value Ω c2 The calculation function, the MTF value calculation function in the low spatial frequency sub-interval, and the MTF value calculation function in the high spatial frequency sub-interval are shown in formulas (3) to (6).

[0089] Spatial frequency threshold Ω c1 The calculation function is expressed as follows:

[0090]

[0091] Spatial frequency threshold Ω c2 The calculation function is expressed as follows:

[0092]

[0093] The MTF value calculation function in the low spatial frequency sub-interval is expressed as follows:

[0094]

[0095] The MTF value calculation function in the high spatial frequency sub-interval is expressed as follows:

[0096]

[0097] Finally, according to the MTF value calculation function in the low spatial frequency sub-interval and the MTF value calculation function in the high spatial frequency sub-interval obtained by fitting, the linear interpolation method is used to obtain the MTF value calculation function in the corresponding medium spatial frequency sub-interval, as shown in formula (7). And the three MTF value calculation functions together constitute the parametric analytical MTF model of the turbid atmosphere of the current group of key atmospheric optical parameters in the complete spatial frequency interval, as shown in formula (8). The idea of ​​using the interpolation method in the present invention is mainly as follows:

[0098] (1)MTF is affected by optical thickness τ, single scattering albedo ω, asymmetry factor g, and spatial frequency Ω.

[0099] (2) Since the MTF of the low spatial frequency subinterval and the MTF of the high spatial frequency subinterval remain substantially unchanged during the experiment, the present invention first assumes that the MTF of the low spatial frequency subinterval and the MTF of the high spatial frequency subinterval do not change with the change of the spatial frequency Ω, while the MTF of the medium spatial frequency subinterval changes with the change of the spatial frequency Ω.

[0100] (3) Based on the above two points, we first calculate the MTF of the corresponding group of key atmospheric optical parameters: min and MTF max , then let the MTF min is the value of all spatial frequencies of this set of key atmospheric optical parameters in the low spatial frequency sub-interval, let the MTF max is the value of all spatial frequencies of this group of key atmospheric optical parameters in the high spatial frequency sub-interval, and finally the interpolation method is used to solve the MTF of this group of key atmospheric optical parameters in the medium spatial frequency sub-interval.

[0101] The MTF value calculation function in the medium spatial frequency sub-interval is expressed as follows:

[0102]

[0103] The parameterized analytical MTF model of turbid atmosphere is expressed as follows:

[0104]

[0105] 2. Image restoration.

[0106] The parametric analytical MTF model of turbid atmosphere is applied to the field of image restoration, and the image is restored using the inverse filtering method. Then, under different foggy weather conditions, the peak signal-to-noise ratio (PSNR) and structural similarity (SSIM) are calculated simultaneously using the method of the present invention, the equivalent principle method and the He Kaiming method (He), and the peak signal-to-noise ratio (PSNR) and structural similarity (SSIM) of the three are compared, and the effectiveness of the parametric analytical MTF model of turbid atmosphere is evaluated based on the comparison results.

[0107] 1) Construct the apparent MTF of turbid media:

[0108] In order to comprehensively consider the influence of turbid atmospheric medium on the spatial spectral components of the image under the background of natural light, the background light influence after the ambient light is scattered by the turbid medium is included in an overall expression, and it is called the apparent MTF of the turbid medium, denoted as MTF′(Ω,λ), as shown in formula (9). Formula (9) can characterize the comprehensive influence of the turbid medium when the image is transmitted in the turbid atmosphere.

[0109]

[0110] Among them, δ(Ω=0)=1 and δ(Ω≠0)=0.

[0111] MTF′(Ω,λ) comprehensively considers the influence of turbid atmospheric attenuation, multiple scattering and background light after ambient light scattering on the image, and fully describes the influence of turbid media on the spatial spectral components of the target image when it is transmitted through the atmosphere against the background of sky light.

[0112] It can be seen from formula (9) that the first factor affecting the image spatial spectrum is the turbid medium MTF (Ω, λ), which represents the attenuation and multiple scattering effects of the turbid atmosphere. According to the equivalent principle, the MTF (Ω, λ) is the same as the value of the output light intensity distribution. According to the parameterized analytical MTF model of the turbid atmosphere, the MTF (Ω, λ) with the ambient light wavelength λ added can be calculated, as shown in formulas (10) to (13). The average relative error of the parameterized analytical MTF model of the turbid atmosphere is less than 8%, and the single calculation speed using this model is faster than that using the DISORT algorithm. The code has strong portability and can be coupled in large codes for application in the field of real-time image processing.

[0113]

[0114]

[0115] Among them, τ(λ) represents the calculation formula of optical thickness about ambient light wavelength λ, that is, the current optical thickness τ is calculated by ambient light wavelength λ, and the red, green and blue wavelengths correspond to 700nm, 520nm and 440nm respectively. The calculation process of τ(λ) is as follows:

[0116] First, the extinction coefficient β of the three channels of the image RGB is calculated using the empirical relationship between the ambient visibility V and the ambient light wavelength λ. ext (λ), as shown in formula (14):

[0117]

[0118] Among them, the ambient light transmission distance coefficient q and the ambient visibility V are shown in formula (15):

[0119]

[0120] When the ambient light is transmitted uniformly, according to the transmission distance L and the extinction coefficient β ext (λ), the optical thickness τ of the RGB three channels during image formation is calculated, as shown in formula (16):

[0121] τ(t)=β ext (λ)×L (16)

[0122] It can be seen that the overall absorption of the light band is small, and the single scattering albedo ω can be approximately taken as 1.0. Therefore, when restoring the image, the invention takes the single scattering albedo ω as 1.0, and the asymmetry factor g is taken according to the weather type in Table 3. Then, the specific values ​​of the optical thickness τ, the single scattering albedo ω, and the asymmetry factor g are input into the turbid atmosphere parameterized analytical MTF model to obtain the MTF of the turbid atmosphere attenuation and multiple scattering effect of the RGB three channels.

[0123] It can be seen from formula (9) that the second item in the image spatial spectrum influencing factors is the influence of the background light after ambient light scattering on the zero-frequency component of the image, which is mainly reflected in that increasing the zero-frequency component will reduce the overall contrast of the image, significantly affecting the contrast of the target image. The imaging of the present invention is skylight background imaging under natural light illumination. Under normal circumstances, that is, backlight or front light far away from the direction of sunlight, the influence of the background light after ambient light is scattered by the turbid atmosphere on the zero-frequency component of the image is expressed as shown in formula (17):

[0124]

[0125] In formula (17), F o The value of Ω in (Ω,λ) and k(Ω,λ) is 0, and k(Ω,λ) is a parameter related to the target zero-frequency component, which can be obtained by calculating the average brightness of a single channel.

[0126] Among them, the relationship between transmittance T(λ) and τ(λ) is shown in formula (18):

[0127] T(λ)=exp(-τ(λ)) (18)

[0128] 2) Use inverse filtering method to restore the image:

[0129] In summary, the MTF of the turbid medium calculated by the parameterized analytical MTF model of the turbid atmosphere and the influence of the background light on the zero-frequency component of the image are superimposed on each other to obtain the apparent MTF of the turbid medium, and the image is corrected using the inverse filtering method to obtain the restored image.

[0130] The basic principle of the inverse filtering method is to restore the original image through a known degradation function. In the present invention, the apparent MTF of the turbid medium is used as the degradation function, and the image affected by haze is inversely filtered. Finally, the Gamma function is used to improve the overall brightness of the image. The Gamma value is 0.6 to obtain a clear image after restoration.

[0131] Table 2 shows the camera parameters for taking the image to be restored. Table 3 shows the specific values ​​of various input parameters of the apparent MTF of the turbid medium in the embodiment of the present invention when restoring the image.

[0132] Table 2 Camera parameters

[0133]

[0134] Table 3 Input parameters of apparent MTF of turbid media

[0135]

[0136] The specific values ​​of the input parameters in Tables 2 and 3 are sequentially input into the apparent MTF of the turbid medium for image restoration.

[0137] Figure 2 to Figure 13 The comparison results of image restoration are given. Figure 2 This is an original photo taken in light foggy weather conditions. Figure 3 This is an original photo taken in moderate foggy weather conditions. Figure 4 This is an original photo taken in foggy weather conditions. Figure 5 This is a restored photo using the He method under light fog conditions. Figure 6 This is a restored photo using the He method under moderate foggy weather conditions. Figure 7 This is a restored photo using the He method under dense fog conditions. Figure 8 This is a restored photo using the equivalent principle method under light fog conditions. Fig. 9 This is a restored photo using the equivalent principle method under moderate foggy weather conditions. Fig.10 This is a restored photo using the equivalent principle method under dense fog conditions. Fig.11 This is a restored photo after restoration using the method of the present invention under light foggy weather conditions. Fig.12 This is a restored photo after restoration using the method of the present invention under moderate foggy weather conditions. Fig.13 This is a restored photo after restoration using the method of the present invention under dense fog weather conditions.

[0138] from Figure 2 to Figure 13 It can be seen that compared with the other two methods, the image restored by He's method has a high contrast, but the color distortion is more serious and the tone is warmer. The color of the image restored by the equivalent principle method and the method of the present invention is natural.

[0139] In order to objectively describe the image quality restored by the three methods, the peak signal-to-noise ratio (PSNR) and structural similarity (SSIM) are used to measure the restored image effect. Among them, the larger the PSNR value, the better the image quality. The SSIM value is between 0 and 1. The closer the value is to 1, the better the image quality, indicating that the structures of the two images are more similar. Tables 4 and 5 list the PSNR and SSIM values ​​restored by different methods in three weather conditions: light fog, moderate fog, and dense fog.

[0140] Table 4 PSNR value comparison

[0141]

[0142] Table 5 Comparison of SSIM values

[0143]

[0144] It can be seen from Tables 4 and 5 that the constructed MTF model based on the parameterized analytical turbid atmosphere achieves higher PSNR and SSIM values ​​when processing haze and light fog weather. He's method has a slight advantage in processing foggy weather, but the color distortion is more serious. From the perspective of PSNR and SSIM values, when the method of the present invention is used to restore the image, both PSNR and SSIM are slightly higher than the equivalent principle method, which further verifies the effectiveness of the MTF model based on the parameterized analytical turbid atmosphere.

[0145] The above description is only a preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field can make equivalent replacements or changes according to the technical scheme and inventive concept of the present invention within the technical scope disclosed by the present invention, which should be covered by the protection scope of the present invention.

Claims

1. An image restoration method based on a parameterized analytical modulation transfer function model of turbid atmosphere, characterized in that: The recovery steps include: S1. Use the DISORT algorithm to calculate the MTF values ​​corresponding to each group of key atmospheric optical parameters, and store all the calculated MTF values ​​in the source database; Key atmospheric optical parameters include optical thickness τ, single scattering albedo ω, and asymmetry factor g; S2. Based on the MTF values ​​in the source database, the spatial frequency critical values ​​corresponding to each group of key atmospheric optical parameters are calculated, and the complete spatial frequency interval corresponding to the current group of key atmospheric optical parameters is divided into multiple spatial frequency sub-intervals according to the spatial frequency critical values; S3. Based on the MTF values ​​in the source database, the parametric analytical modulation transfer function model of the turbid atmosphere in each spatial frequency sub-interval of each group of key atmospheric optical parameters is derived; S4. Combined with the parametric analytical modulation transfer function model of turbid atmosphere, the apparent modulation transfer function of turbid medium is constructed to characterize the influence of turbid atmospheric medium on the image spatial spectrum under the background of skylight; S5, taking the apparent modulation transfer function of the turbid medium as a degradation function, assigning the degradation function to an inverse filtering method, and restoring the image using the inverse filtering method; The specific steps of step S2 are as follows: S21. Calculate the spatial frequency critical value corresponding to the current group of key atmospheric optical parameters using the spatial frequency critical value calculation formula. The spatial frequency critical value calculation formula is as follows: In the formula, Ω c1 Indicates the critical value of the spatial frequency that divides the low spatial frequency sub-interval and the medium spatial frequency sub-interval corresponding to the current group of key atmospheric optical parameters; MTF n Indicates the MTF value of the nth spatial frequency corresponding to the current set of key atmospheric optical parameters; MTF max Indicates the MTF value of the current set of key atmospheric optical parameters at zero spatial frequency; MTF low MTF n and MTF max The absolute value of the difference between Indicates the spatial frequency threshold for dividing the low spatial frequency subinterval and the medium spatial frequency subinterval corresponding to the current group of key atmospheric optical parameters; Ω c2 Indicates the critical value of the spatial frequency sub-interval and the high spatial frequency sub-interval in the division corresponding to the current group of key atmospheric optical parameters; MTF min Indicates the MTF value of the current set of key atmospheric optical parameters at infinite spatial frequency; MTF high MTF n and MTF min The absolute value of the difference between Indicates the spatial frequency thresholds of the middle spatial frequency subinterval and the high spatial frequency subinterval of the division corresponding to the current group of key atmospheric optical parameters; S22, according to the corresponding spatial frequency critical value, the complete spatial frequency interval corresponding to the current group of key atmospheric optical parameters is divided into low spatial frequency sub-intervals [0,Ω c1 ), the mid-spatial frequency subinterval [Ω c1 ,Ω c2 ) and high spatial frequency subintervals [Ω c2 ,∞), where ∞ represents infinite spatial frequency; The specific steps of step S3 are as follows: S31, all MTF values ​​corresponding to each key atmospheric optical parameter, each group of key atmospheric optical parameters, and the critical value Ω of the spatial frequency corresponding to each key atmospheric optical parameter c1 and the spatial frequency critical value Ω c2 All are stored in the training database; S32. Based on the data in the training database, the spatial frequency critical value Ω corresponding to each group of key atmospheric optical parameters is obtained by multivariate nonlinear fitting. c1 Calculation function, spatial frequency critical value Ω c2 calculation function, an MTF value calculation function in a low spatial frequency subinterval, and an MTF value calculation function in a high spatial frequency subinterval; S33, according to the MTF value calculation function in the low spatial frequency sub-interval and the MTF value calculation function in the high spatial frequency sub-interval obtained by fitting, a linear interpolation method is used to obtain the MTF value calculation function in the corresponding medium spatial frequency sub-interval; and the three MTF value calculation functions together constitute a parameterized analytical modulation transfer function model of the turbid atmosphere of the current group of key atmospheric optical parameters in the complete spatial frequency interval; Spatial frequency threshold Ω c1 The calculation function is expressed as follows: In the formula, exp represents the exponential function with the natural constant e as the base; a c1 Indicates the critical value of spatial frequency Ω c1 Calculate the constant term in the function; τ i+1 represents the optical thickness τ to the power of i+1, b c1,i Indicates the critical value of spatial frequency Ω c1 τ in the calculation function i+1 The coefficient of i+1 represents the single scattering albedo ω to the power of i+1, t c1,i Indicates the critical value of spatial frequency Ω c1 ω in the calculation function i+1 The coefficient of g i+1 represents the asymmetric factor g raised to the power i+1, d c1,i Indicates the critical value of spatial frequency Ω c1 Calculate the function g i+1 The coefficient of p c1 、f c1 、h c1 and j c1 Both represent the critical value of spatial frequency Ω c1 Calculate the coefficients of the corresponding single-degree polynomial in the function; Spatial frequency threshold Ω c2 The calculation function is expressed as follows: In the formula, a c2 Indicates the critical value of spatial frequency Ω c2 Calculate the constant term in the function; b c2,i Indicates the critical value of spatial frequency Ω c2 τ in the calculation function i+1 The coefficient of t c2,i Indicates the critical value of spatial frequency Ω c2 ω in the calculation function i+1 The coefficient of c2,i Indicates the critical value of spatial frequency Ω c2 Calculate the function g i+1 The coefficient of p c2 、f c2 、h c2 and j c2 Both represent the critical value of spatial frequency Ω c2 Calculate the coefficients of the corresponding single-degree polynomial in the function; The MTF value calculation function in the low spatial frequency sub-interval is expressed as follows: In the formula, A represents the MTF value calculation function in the low spatial frequency subinterval about the spatial frequency Ω, where Ω represents the spatial frequency; c1 represents the constant term in the MTF value calculation function in the low spatial frequency sub-interval; B c1,i Indicates the MTF value calculation function in the low spatial frequency sub-interval τ i+1 The coefficient of T c1,i Indicates the MTF value calculation function in the low spatial frequency sub-interval ω i+1 The coefficient of D c1,i Indicates the MTF value calculation function in the low spatial frequency sub-interval g i+1 The coefficient of P c1 、F c1 , H c1 and J c1 They all represent the coefficients of the corresponding single-degree polynomial in the MTF value calculation function in the low spatial frequency sub-interval; The MTF value calculation function in the high spatial frequency sub-interval is expressed as follows: In the formula, A represents the MTF value calculation function in the high spatial frequency subinterval of the spatial frequency Ω; c2 represents the constant term in the MTF value calculation function within the high spatial frequency sub-interval; B c2,i Indicates the MTF value calculation function in the high spatial frequency sub-interval τ i+1 The coefficient of T c2,i Indicates the MTF value calculation function in the high spatial frequency sub-interval ω i+1 The coefficient of D c2,i Indicates the MTF value calculation function in the high spatial frequency sub-interval g i+1 The coefficient of P c2 、F c2 , H c2 and J c2 They all represent the coefficients of the corresponding single-order polynomial in the MTF value calculation function within the high spatial frequency sub-interval; The MTF value calculation function in the medium spatial frequency sub-interval is expressed as follows: In the formula, represents the MTF value calculation function in the mid-spatial frequency subinterval about the spatial frequency Ω; Ω c1-c2 Represents any spatial frequency within the medium spatial frequency subinterval of the current set of key atmospheric optical parameters; Where MTF(Ω) represents the parameterized analytical modulation transfer function model of the turbid atmosphere with respect to the spatial frequency Ω in the complete spatial frequency range of the current set of key atmospheric optical parameters; The apparent modulation transfer function of turbid media is expressed as follows: Where MTF'(Ω,λ) represents the apparent modulation transfer function of the turbid medium with respect to the spatial frequency Ω and the ambient light wavelength λ; MTF(Ω,λ) represents the parameterized analytical modulation transfer function model of the turbid atmosphere with respect to the spatial frequency Ω and the ambient light wavelength λ; I P (λ) represents the background light intensity after the ambient light is scattered by the turbid medium in the atmosphere; F o (Ω,λ) represents the background light intensity I P (λ) represents the Fourier transform of; δ(Ω) represents the Dirac function with respect to the spatial frequency Ω; MTF(Ω,λ) is expressed as follows: Wherein, τ(λ) represents the calculation formula of optical thickness with respect to ambient light wavelength λ, that is, the current optical thickness τ is calculated by ambient light wavelength λ; represents the MTF value calculation function in the low spatial frequency sub-interval with respect to the spatial frequency Ω and the ambient light wavelength λ; represents the MTF value calculation function in the high spatial frequency sub-interval with respect to the spatial frequency Ω and the ambient light wavelength λ; represents the MTF value calculation function in the mid-spatial frequency sub-interval with respect to the spatial frequency Ω and the ambient light wavelength λ; Where, L represents the transmission distance of ambient light; V represents the ambient visibility; q represents the ambient light transmission distance coefficient; The background light intensity calculation formula is as follows: Wherein, k(Ω,λ) represents the parameter calculation function about the spatial frequency Ω and the ambient light wavelength λ.

2. The image restoration method based on the parameterized analytical modulation transfer function model of turbid atmosphere according to claim 1, characterized in that: After the image is restored using the inverse filtering method in step S5, the image is then processed using the Gamma function to obtain a restored image.

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