A polarization imaging method for non-uniform fog scattering characteristics adaptation

Abstract

The application discloses a polarization imaging method for penetrating non-uniform fog with adaptive scattering characteristics, comprising the following steps: obtaining polarization images at different angles, calculating Stokes vectors, linear polarization degrees and double-channel polarization intensity images of the images; constructing non-uniform fog scattering characteristics, estimating double-channel non-uniform scattering intensity images; estimating background light at infinity, and calculating double-channel polarization intensity transmittance images; constructing an attenuation matrix of a polarization double-channel variable-scale degradation model; constructing a polarization double-channel variable-scale degradation imaging model, and solving a preliminary restoration of the double-channel non-uniform fog scene; iteratively optimizing the polarization variable-scale degradation matrix to obtain a final restoration image of the non-fog scene. The polarization imaging method for penetrating non-uniform fog with adaptive scattering characteristics can relieve problems such as loss of target polarization information and overexposure in a non-uniform fog scene, realize complete removal of the global non-uniform fog in the scene, and restore target scene information more clearly.

Description

Technical Field

[0001] This invention relates to the field of image data processing technology, and in particular to a polarization imaging method for penetrating non-uniform fog with adaptive scattering characteristics. Background Technology

[0002] In natural environments such as forests, changing seasonal climates and abundant surface water can easily lead to significant diurnal temperature variations and atmospheric humidity around dense vegetation, resulting in the formation of large amounts of non-uniform fog. The scattering and absorption of fog haze degrades the quality of scene imaging, while the significant differences in intensity caused by non-uniform scattering from fog posed an even greater challenge to the safety monitoring and clear imaging of industrial equipment submerged within it. Therefore, non-uniform fog scattering imaging is of great significance for human production operations in natural environments.

[0003] With the long-term development of image dehazing technology, single-image dehazing methods have been extensively studied. However, dehazing based on a single dimension of intensity or color is insufficient to meet the requirements of imaging through non-uniform fog, often leading to distortions such as overexposure and color cast. Furthermore, with the increase of scene depth, fog medium concentration, and the dispersion of fog distribution, the information of the target is gradually submerged in environmental scattering. In recent years, the rapid development of deep learning has significantly improved dehazing effects. However, training of learning-based methods heavily relies on datasets, and non-uniform fog is easily affected by natural factors and undergoes polymorphic changes. Therefore, a lack of suitable training samples usually leads to poor dehazing results, especially when dealing with scenes with dense fog and non-uniform fog features.

[0004] Unlike traditional single-image dehazing methods, polarization descattering methods use at least two polarimetric images to eliminate scattering effects and have been widely applied in atmospheric fog-penetrating imaging and underwater scattering imaging. However, they often perform poorly when applied to scenes with targets possessing high polarization. Specifically, for special scene areas such as metal buildings and glass windows, the strong polarization characteristics of the target can have a non-negligible impact on the overall polarization radiation of the scene, thus rendering the single polarization assumption invalid and leading to severe loss of scene information.

[0005] Therefore, the dual polarization assumption is not always valid in scenes with non-uniform fog distribution. In non-uniform fog distribution environments, the direct application of the dual polarization assumption may cause the detailed information of targets with high degree of linear polarization (DoLP) to be submerged by the scattering medium, resulting in overexposure and color shift. At the same time, due to the non-uniform scattering of polarized light of the target scene by the non-uniform fog medium, large field-of-view environments may exhibit incomplete dehazing and low-quality restoration due to the variable scale degradation of polarized light at discrete spatial positions. Summary of the Invention

[0006] The purpose of this invention is to provide a polarization imaging method for penetrating non-uniform fog with adaptive scattering characteristics. By jointly solving the polarization scaling degradation matrix through multi-dimensional information, the degradation process of the brightest and darkest polarization channels undergoing non-uniform scattering can be reconstructed. Under uniform scattering scenarios, it can adaptively regress to the traditional polarization imaging model. By combining the intensity domain scattering distribution characteristics and linear polarization degree (DoLP) information, a dynamic characterization mechanism for regions with significant scattering range is constructed to solve the estimation bias caused by the spatial discreteness of non-uniform scattering.

[0007] To achieve the above objectives, this invention provides a polarization imaging method for penetrating non-uniform fog with adaptive scattering characteristics, comprising the following steps:

[0008] Step S1: Obtain polarization images at different angles, and calculate the Stokes vector, linear polarization degree, and dual-channel polarization intensity image of the image;

[0009] Step S2: Construct non-uniform fog scattering features and estimate the dual-channel non-uniform scattering intensity image;

[0010] Step S3: Estimate the background light at infinity and calculate the dual-channel polarization intensity transmittance image;

[0011] Step S4: Construct the attenuation matrix of the polarization dual-channel variable-scale degradation model;

[0012] Step S5: Construct a polarization dual-channel variable-scale degradation imaging model to obtain a preliminary restoration of the dual-channel non-uniform fog scene;

[0013] Step S6: Iterate the optimal polarization scaling degradation matrix to obtain the final restored image of the fog-free scene.

[0014] Preferably, in step S1, polarization images at different angles are acquired, and the Stokes vector, linear polarization degree, and dual-channel polarization intensity image of the image are calculated. The specific process is as follows:

[0015] Step S11: Use a polarization camera to acquire images with different polarizations, and then calculate the Stokes vector of the image to describe the polarization state of light, as shown below:

[0016]

[0017] In the formula, I represents the total intensity of the incident light; Q and U represent the polarization information of the incident light, respectively; I p I is the fully polarized component of the total light intensity; up I0 and I are the completely unpolarized components of the total light intensity. 60 and I 120 These are the polarization image light intensity values ​​corresponding to incident light passing through polarizers with directions of 0°, 60°, and 120°, respectively.

[0018] Step S12: Calculate the linear polarization degree DoLP of the image, as shown below:

[0019]

[0020] Step S13: Based on the Stokes vector of the image, calculate the dual-channel polarization intensity of the image, specifically including the polarization intensity I of the brightest channel of the image. max And the polarization intensity I of the darkest channel of the image min As shown below:

[0021]

[0022] Preferably, in step S2, non-uniform fog scattering features are constructed, and a dual-channel non-uniform scattering intensity image is estimated. The specific process is as follows:

[0023] Step S21: Calculate the mean and variance of intensity within each local window based on the intensity values ​​of image pixels, then filter out pixels with lower variance, i.e., locally uniform regions, and retain the pixels that pass the judgment as a locally uniform estimation set.

[0024] Step S22: By jointly utilizing the intensity information and corresponding polarization information of the scattered light in the original fog scene, joint constraint factors ω0(x,y), ω1(x,y) and ω2(x,y) are constructed, as shown below:

[0025]

[0026] In the formula, α is an empirical constant; I c (x,y) represents the pixel-by-pixel intensity value of the RGB channel corresponding to the total intensity image; c represents any one of the three RGB channels; DoLP(x,y) represents the pixel-by-pixel intensity value of the linear polarization image; V I V represents a locally uniform set of pixels in the total intensity image; P τ1 represents the set of locally uniform pixels in the linear polarization image; τ2 represents the mean global intensity; τ3 and τ4 are dynamic thresholds.

[0027] Step S23: The scattered light is estimated under the specification of the joint constraint factor using the guided filter GF method; wherein the joint constraint factor ω0(x,y) is used as the guiding map, and the scattered map B to be estimated is used as the guiding map. max With B min For the target image, the original fog scene I max (x,y) and I min A polarization joint guided filter (PGF) is obtained by performing guided filtering on (x,y), as shown below:

[0028]

[0029] In the formula, This represents the pixel-by-pixel scattered light intensity value of the RGB channel corresponding to the brightest polarization channel image; This represents the pixel-by-pixel scattered light intensity value of the RGB channel corresponding to the darkest polarization channel image; This represents the total light intensity value per pixel of the RGB channel corresponding to the brightest polarization channel image; This represents the total light intensity value per pixel of the RGB channel corresponding to the darkest polarization channel image; c represents any one of the three RGB channels.

[0030] Step S24: Calculate the brightest and darkest channels of fog scattering polarization intensity, as shown below:

[0031]

[0032] In the formula, B max This represents the intensity value of the scattered light from the brightest polarization channel image; The scattered light intensity value of each pixel in the R channel corresponding to the brightest polarization channel image; The scattered light intensity value of each pixel in the G channel corresponding to the brightest polarization channel image; This represents the pixel-by-pixel scattered light intensity value of the B channel corresponding to the brightest polarization channel image; B min This represents the intensity value of scattered light from the darkest polarization channel image. This represents the pixel-by-pixel scattered light intensity value of the R channel corresponding to the darkest polarization channel image; The scattered light intensity value of each pixel in the G channel corresponding to the darkest polarization channel image; This represents the pixel-by-pixel scattered light intensity value of the B channel corresponding to the darkest polarization channel image.

[0033] Preferably, in step S3, the background light at infinity is estimated, and the dual-channel polarization intensity transmittance image is calculated. The specific process is as follows:

[0034] Step S31: Map the distance to infinity to the pixels in the original fog image whose transmittance t(z) approaches 0, and estimate the background radiation B from infinity using the atmospheric scattering model. inf As shown below:

[0035] I = D + B = J·t + B inf ·(1-t);

[0036]

[0037] In the formula, I represents a real foggy image; D represents the direct transmitted light of the target scene; B represents atmospheric scattered light; J represents a fog-free image; B inf t represents the background radiation at infinity; z represents the transmittance; and z represents the scene depth.

[0038] Step S32: The transmittance of the brightest and darkest channels in the atmospheric polarization scattering imaging model are t, respectively. max and t min , used to describe the attenuation scattering state of polarized radiation;

[0039] The polarization dual-channel equations in the atmospheric scattering model are shown below:

[0040]

[0041] In the atmospheric polarization scattering imaging model, the transmittances of the brightest and darkest channels are t, respectively. max and t min As shown below:

[0042]

[0043]

[0044] Preferably, in step S4, the attenuation matrix of the polarization dual-channel variable-scale degradation model is constructed, and the specific process is as follows:

[0045] Step S41: Construct the attenuation matrix μ of the polarization dual-channel variable-scale degradation model, as shown below:

[0046]

[0047] In the formula, μ R This represents the component of the attenuation matrix μ in the R channel; μ G This represents the component of the attenuation matrix μ in the G channel; μ B This represents the component of the attenuation matrix μ in the B channel; DoLP is the linear polarization image; r, g, and b represent the RGB channels respectively, as shown below:

[0048]

[0049] In the formula, I R I G I B These are the normalized images of haze intensity image I in the RGB red, blue, and green channels, respectively. This represents the mean of the normalized image for the corresponding channel.

[0050] Preferably, in step S5, a polarization dual-channel variable-scale degradation imaging model is constructed to obtain a preliminary restoration of the dual-channel non-uniform fog scene. The specific process is as follows:

[0051] Step S51: For the brightest and darkest polarization channels of the foggy image, the scattered light intensity value B max (μ) and B min (μ), without considering its attenuation after scattering, the polarization-variable scale degradation model is as follows:

[0052] B max (μ)=B max ;

[0053] B min (μ)=B min ;

[0054] In the formula, B max (μ) and B min (μ) Intensity values ​​of scattered light from the brightest and darkest polarization channels;

[0055] Step S52: Decompose the reflected light of the target scene in the polarization dual-channel into two parts according to the presence or absence of polarization information, namely the polarization part. and and the non-polarized part and As shown below:

[0056]

[0057] In the formula, D max D represents the target light intensity value of the brightest polarization channel image. min This represents the target light intensity value of the darkest polarization channel image.

[0058] For the target light intensity values ​​D of the brightest and darkest polarization channels in a foggy image after non-uniform scattering attenuation, max (μ) and D min (μ), which can be represented as the foggy dual-channel polarization image D after uniform scattering attenuation. max and D min The product with the polarization-variable scale degradation matrix μ is as follows:

[0059]

[0060] Step S53: The brightest and darkest channels of the foggy polarization image contain all the polarization and non-polarization characteristics of the target in the foggy weather, i.e., the polarization-scale degradation model, as shown below:

[0061] I max (μ)=D max (μ)+B max (μ);

[0062] Imin (μ)=D min (μ)+B min (μ);

[0063] Based on the constructed polarization-variable scale degradation model and the direct optical decomposition method of the target, the physical model of traditional atmospheric polarization imaging is preserved, as shown below:

[0064] I max (μ)+I min (μ)=I max +I min =D+B;

[0065]

[0066] According to Malus's law, due to its uniformly distributed unbiased equilibrium state, completely unpolarized light, when transmitted through a linear polarizer with any bias angle, will always have a transmitted light intensity that is half the incident intensity, regardless of the polarization channel type (brightest maximum and darkest minimum), as shown below:

[0067]

[0068] Then, the target direct light intensity values ​​D of the brightest and darkest polarization channels can be obtained. max (μ) and D min (μ), as shown below:

[0069]

[0070] The reconstructed D max (μ) and D min (μ) and B max (μ) and B min Substituting (μ) into the brightest and darkest polarization channels that satisfy the physical model of atmospheric polarization imaging, we obtain the total intensity value I of the two channels. max (μ) and I min (μ), as shown below:

[0071]

[0072] The target direct light intensity value D of the polarization dual-channel max With D min As shown below:

[0073]

[0074] Step S54: Based on the atmospheric scattering imaging model and the polarization-variable scale degradation model, the restored dual-channel fog-free scene J is reconstructed. max (μ) and J min (μ), as shown below:

[0075]

[0076] In the formula, ξ is a very small positive number used to suppress image overexposure caused by pixels with 0 transmittance, and is set to 0.1.

[0077] Preferably, in step S6, the optimal polarization-variable scale degradation matrix is ​​iterated to obtain the final restored image of the fog-free scene. The specific process is as follows:

[0078] Based on the atmospheric scattering imaging model and the polarization-variable scale degradation model, the restored fog-free scene J(μ) is obtained, as shown below:

[0079]

[0080] The variable-scale degradation rate is obtained by reconstructing the initial univariate μ through multiple iterations. To obtain a fog-free restored image Therefore, the objective function is established as follows:

[0081]

[0082] In the formula, η1 and η2 are regularization parameters; ε(μ) is a defined loss function used to measure the quality of the current μ estimate, and the model solves for the optimal value by minimizing it. denoted by Frobenius norm; W is the weighting function; ω0 is the joint constraint factor for the scattered light estimation; ▽ is the gradient operator; γ is the coefficient of the weighting function; n is the number of iterations;

[0083] The variable-scale degenerate matrix μ is iterated multiple times, with the following conditional parameters for each iteration:

[0084]

[0085] In the formula, R and N are both empirical values; if the current iteration satisfies the above condition parameters, the iteration continues; otherwise, the iteration stops, and the final iteration result is recorded.

[0086] Therefore, the present invention employs the above-mentioned polarization imaging method for penetrating non-uniform fog based on adaptive scattering characteristics, and the beneficial effects are as follows:

[0087] (1) This invention solves the multidimensional information of the polarization-scale degradation matrix by jointly solving the matrix. It deconstructs the higher target polarization component that is submerged in the lower polarization scattering in the brightest and darkest polarization dual channels, so as to achieve effective compensation of target polarization information in non-uniform degradation path. In the uniform scattering scenario, it adaptively regresses to the traditional atmospheric polarization imaging model.

[0088] (2) This invention characterizes and acquires the non-uniform scattering of the environment in the intensity domain of the original fog scene, and introduces the linear polarization degree (DoLP) information of the scene to provide adaptive guidance constraints for the estimation of the environmental scattered light, which has good environmental scattering adaptability and target scene fidelity.

[0089] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0090] Figure 1 This is a schematic diagram of the imaging model of a polarization imaging method for penetrating non-uniform fog with adaptive scattering characteristics according to the present invention.

[0091] Figure 2 This is a flowchart illustrating the technique of a polarization imaging method for penetrating non-uniform fog with adaptive scattering characteristics according to the present invention.

[0092] Figure 3 This is a block diagram illustrating a specific implementation example of the polarization imaging penetration method for non-uniform fog with adaptive scattering characteristics according to the present invention.

[0093] Figure 4 Image of a non-uniform fog scene with 0° polarization;

[0094] Figure 5 Image of a non-uniform fog scene with 60° polarization;

[0095] Figure 6 Image of a non-uniform fog scene with 120° polarization;

[0096] Figure 7 Remove non-uniform fog from the scene to restore the image. Detailed Implementation

[0097] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0098] Example

[0099] As shown by the atmospheric scattering model, the total light intensity I of the image captured by the imaging detection system mainly consists of two parts: the direct transmitted light D from the target scene and the atmospheric scattered light B. The total light intensity I reaching the imaging system is as follows:

[0100] I = D + B = J·t + B inf ·(1-t)(1);

[0101] In the formula, I represents a real foggy image; J represents a fog-free image; B inf t represents the atmospheric light value at infinity, and t represents the transmittance.

[0102] Assuming that the distribution of haze suspended particles in the atmosphere is spatially uniform, the transmittance t is as follows:

[0103] t=t(z)=exp(-β·z) (2);

[0104] In the formula, z is the scene depth; β is the atmospheric scattering coefficient.

[0105] In reality, both the directly transmitted light D from the target and the atmospheric scattered light B are partially polarized with different vibrational directions. Based on the orthogonal polarization decomposition model, the original fog map I can be obtained from the brightest polarization channel and the darkest polarization channel. max and I min The polarization dual-channel equation, i.e., the traditional dual-polarization imaging model, is obtained as follows:

[0106] I max =D max +B max (3);

[0107] I min =D min +B min (4);

[0108] In the formula, the subscript max = θ || The intensity image represented is the brightest intensity image corresponding to one cycle of rotation of the polarizer with a step size Δθ = 1°; it is related to the subscript min = θ. ⊥ The images representing the darkest intensities are orthogonal to each other, with θ || =θ ⊥ ±90°.

[0109] In this invention, the direction of the principal optical axis of the polarizer is selected as θ. || The corresponding direction, therefore we get I. max =I0 and I min =I 90 Given a set of orthogonal dual channels, the polarization dual-channel equations in the atmospheric scattering model are as follows:

[0110]

[0111]

[0112] Therefore, from formulas (1)-(6), the restoration of the fog-free scene J can be obtained as follows:

[0113]

[0114] In hazy weather, the total light intensity I of a foggy scene is partially polarized light and can be described by a Stokes vector. When a beam of Stokes vector is S = (I, Q, U)... TWhen linearly polarized light passes through a polarizer with a bias angle of θ, the polarization image intensity I, expressed in terms of the Stokes vector, can be obtained based on the relationship between the Stokes vector and the Muller matrix. θ As shown below:

[0115]

[0116] When an incident beam of light passes through polarizers with orientations of 0°, 60°, and 120°, the corresponding polarization image light intensity values ​​are I0, I1, I2, and I3, respectively. 60 and I 120 Substituting this into formula (8), the Stokes vector can be calculated as follows:

[0117]

[0118] In the formula, I represents the total intensity of the incident light; Q and U represent the polarization information of the incident light, respectively.

[0119] Linear polarization degree DoLP and polarization angle AoP are shown below:

[0120]

[0121]

[0122] In the formula, I p I represents the fully polarized component of the total light intensity. up This represents the completely unpolarized component of the total light intensity.

[0123] Based on the above principles, this invention proposes a polarization imaging method for penetrating non-uniform fog with adaptive scattering characteristics. The method analyzes the Stocks vector and solves for the degree of linear polarization (DoLP). It then reconstructs the polarization intensity of the brightest and darkest polarization channels, utilizes the non-uniform characteristics of the discrete distribution of fog to obtain scattered light, and combines polarization parameters to construct a target polarization variable-scale degradation matrix under non-uniform scattering. This effectively restores fog-free scenes and achieves overexposure suppression.

[0124] For example Figure 1-3 As shown, the present invention provides a polarization imaging method for penetrating non-uniform fog with adaptive scattering characteristics, comprising the following steps:

[0125] Step S1: Obtain polarization images at different angles, and calculate the Stokes vector, linear polarization degree, and dual-channel polarization intensity image of the image.

[0126] Step S11: Use a polarization camera to acquire polarization images at 0°, 60°, and 120°, as shown below. Figures 4-6 As shown, the Stokes vector of the image is then calculated according to formula (9) to describe the polarization state of the light.

[0127] Step S12: Calculate the linear polarization degree DoLP of the image according to formula (10).

[0128] Step S13: Calculate the dual-channel polarization intensity of the image according to formula (8), specifically including the polarization intensity I of the brightest channel of the image. max And the polarization intensity I of the darkest channel of the image min As shown below:

[0129]

[0130] Step S2: Construct the non-uniform fog scattering feature ω0(x,y) and estimate the dual-channel non-uniform scattering intensity image, specifically including the non-uniform scattered light B of the brightest and darkest polarization channels. max (x,y) and B min (x,y).

[0131] Step S21: Identify local uniform regions in the image and retain the identified pixels as a local uniform estimation set.

[0132] Based on the distribution of non-uniform scattering of polarized light in a global haze scene, and combined with the RGB three channels and their degree of linear polarization of the hazy image, it is determined whether the intensity value of each pixel in the image is locally uniform.

[0133] The discrimination strategy is to calculate the mean and variance of the intensity within each local window based on the intensity value of each pixel, and then filter out pixels with low variance, i.e., locally uniform regions, as shown below:

[0134]

[0135] In the formula, and This represents the intensity variance of the channel c∈(R,G,B) within a local window at pixel position (x,y), used to evaluate the intensity variation within the local region. A smaller variance indicates less intensity variation in the region, i.e., local uniformity. n is the total number of pixels within the window; here, the window size is assumed to be n = 3 × 3. W(x,y) is a rectangular window region centered at pixel position (x,y); I c (i,j) represents the pixel-by-pixel intensity value of the total light intensity image in channel c∈(R,G,B); DoLP(i,j) represents the average intensity value of all pixels within the window in channel c∈(R,G,B); DoLP(i,j) represents the intensity value of each pixel in the linear polarization image. This represents the average intensity value of all pixels within the window in channel c∈(R,G,B) for the degree of linear polarization.

[0136] The pixels that pass the discrimination are retained and recorded as a local uniform estimation set V. I and V P As shown below:

[0137]

[0138] In the formula, V I V represents a locally uniform set of pixels in the total light intensity image; P It represents a locally uniform set of pixels in a linearly polarized image.

[0139] The mean of the global intensity is represented by M, where M is the length of the image and N is the width of the image. The scattering intensity is at least higher than the mean of the global intensity τ1, because the source of scattering is mainly haze, which is often grayish-white and should have a higher intensity value.

[0140] This represents the mean of the global polarization degree; the polarization degree of the scattered scattering should at most not exceed the mean of the global polarization degree τ2, because the polarization degree of the polarization scattering caused by haze is relatively low compared to the polarization degree of the scene target itself.

[0141] and The threshold is dynamically determined based on the range of the overall variance; where... and This represents the intensity variance within a local window at a pixel location, used to evaluate intensity variations within a local area. A smaller variance indicates less intensity variation in that area, meaning it is locally uniform; k is a weighting coefficient, taken as an empirical value of 0.5; σ I and σ P This represents the standard deviation corresponding to the intensity variance within a local window at the pixel location.

[0142] Step S22: By jointly utilizing the intensity information and corresponding polarization information of the scattered light in the original fog scene, joint constraint factors ω0(x,y), ω1(x,y) and ω2(x,y) are constructed, as shown below:

[0143]

[0144] In the formula, α is taken as an empirical constant of 0.5; I c (x,y) represents the intensity value of each pixel in the RGB channel of the total intensity image, where c represents any one of the three RGB channels; DoLP(x,y) represents the intensity value of each pixel in the linear polarization image.

[0145] Step S23: Use guided filtering (GF) to reasonably estimate the scattered light under the specification of the joint constraint factor.

[0146] Guided filtering has the core advantage of edge smoothing, which can weaken redundant details in the image and accurately preserve key edge structures and other features of non-uniform scattering while suppressing noise interference.

[0147] Using the joint constraint factor ω0(x,y) as the guiding graph, and the scattering graph B to be estimated... max (x,y) and B min (x,y) represents the target image, representing the original fog scene I. max (x,y) and I min A polarization joint steering filter (PGF) is obtained by performing a steering filter on (x,y), as shown below:

[0148]

[0149] In the formula, This represents the pixel-by-pixel scattered light intensity value of the RGB channel corresponding to the brightest polarization channel image; This represents the pixel-by-pixel scattered light intensity value of the RGB channel corresponding to the darkest polarization channel image; This represents the total light intensity value per pixel of the RGB channel corresponding to the brightest polarization channel image; is the total light intensity value of each pixel in the RGB channel corresponding to the darkest polarization channel image; c represents any one of the three RGB channels.

[0150] Step S24: Calculate the brightest channel B of the fog scattering polarization intensity. max (x,y) and the darkest channel B min (x,y).

[0151] According to formula (8), the three-channel polarization images I0(x,y) and I2C(x,y) captured by the polarization camera are obtained. 60 (x,y) and I 120 (x,y) represents the brightest value of the polarization intensity in the composite foggy image. max (x,y) and the darkest value I min (x,y), apply the above method to both and merge the RGB channels to obtain the brightest channel B of the fog scattering polarization intensity. max (x,y) and the darkest channel B min (x,y), as shown below:

[0152]

[0153] Step S3: Estimate the background light at infinity and calculate the dual-channel polarization intensity transmittance image.

[0154] The background light at infinity can be considered as natural radiation from a sufficiently distant light source, such as the sun, while the transmittance t(z) can be considered as an exponential decay function that varies with the distance parameter z. When the target position is sufficiently far from the image receiving position, i.e., z→∞, the transmittance t(z) approaches 0. Therefore, the distance at infinity can be mapped from the pixels in the original fog image where the transmittance t(z) approaches 0, and the background radiation B from infinity can be estimated using formula (1). inf As shown below:

[0155]

[0156] In the formula, I represents a real foggy image; D represents the direct transmitted light of the target scene; B represents atmospheric scattered light; J represents a fog-free image; B inf Let t be the background radiation at infinity, and t be the transmittance.

[0157] Therefore, if a pixel value in I has a similar intensity to a pixel value at the same coordinates in B, then that pixel can be included in the set V of background light at infinity. Binf In this context, the mean value is used as an estimate of the background light at infinity, as shown below:

[0158] V Binf ={I|abs[B max +B min -I]→0} (25);

[0159]

[0160] In the atmospheric polarization scattering imaging model, the transmittances of the brightest and darkest channels are t, respectively. max and t min The attenuation scattering state of polarized radiation is described by equations (1) and (6), as shown below:

[0161]

[0162] Step S4: Construct the attenuation matrix of the polarization dual-channel variable-scale degradation model.

[0163] By mapping the red, blue, and green components of the target transmitted light using an RGB three-channel color model for polarization imaging in foggy weather, the red channel components typically retain more information and offer relatively better visual quality. The blue and green channel components, however, may appear weaker due to stronger scattering. The transmittance parameter in the atmospheric scattering imaging model reflects the scattering characteristics of each channel. Therefore, in the transmittance maps of the brightest and darkest polarization channels, the polarization components of the blue and green channels are enhanced based on the red channel polarization component to recover richer color details.

[0164] In summary, the attenuation matrix μ for the polarization dual-channel variable-scale degradation model is constructed as follows:

[0165]

[0166]

[0167] In the formula, μ R This represents the component of the attenuation matrix μ in the R channel; μ G This represents the component of the attenuation matrix μ in the G channel; μ B This represents the component of the attenuation matrix μ in the B channel; DoLP is the linear polarization image; r, g, and b represent the RGB channels respectively, as shown below:

[0168]

[0169] In the formula, I R I G I B These are the normalized images of haze intensity image I in the RGB three channels; This represents the mean of the normalized image for the corresponding channel.

[0170] Step S5: Construct a polarization dual-channel variable-scale degradation imaging model to obtain the preliminary reconstruction of the dual-channel non-uniform fog scene, i.e., the preliminary reconstruction scene J of the brightest and darkest polarization dual channels. max (μ) and J min (μ).

[0171] For the scattered light intensity values ​​B of the brightest and darkest polarization channels in a foggy image max (μ) and B min (μ), traditional polarization imaging modes usually treat it as scattering that does not contain target information and remove it. Since the ambient scattered light itself is the scattering source, there is no need to consider its attenuation after scattering.

[0172] Therefore, the polarization-variable scale degradation model of this invention is as follows:

[0173] B max (μ)=B max (33);

[0174] B min (μ)=B min (34);

[0175] The reflected light from the target scene in the polarization dual-channel is decomposed into two parts based on the presence or absence of polarization information: the polarization part and the polarization part. and and the non-polarized part and As shown below:

[0176]

[0177] In the formula, D max D represents the target light intensity corresponding to the brightest polarization channel. min This represents the target light intensity corresponding to the darkest polarization channel.

[0178] For the target light intensity values ​​D of the brightest and darkest polarization channels in a foggy image after non-uniform scattering attenuation, max (μ) and D min (μ), which can be represented as the foggy dual-channel polarization image D after uniform scattering attenuation. max and D min The product with the polarization-scaled degradation matrix μ aims to characterize non-uniform scattering by superimposing a non-uniform attenuation with varying scale on top of uniform scattering of the target polarized light. The polarization-scaled degradation model is expressed as follows:

[0179]

[0180] To solve and Considering that the brightest and darkest channels of the foggy polarization image contain all the polarization and non-polarization characteristics of the target in the foggy sky, they can be expressed as follows according to formulas (3) and (4):

[0181] I max (μ)=D max (μ)+B max (μ) (39);

[0182] I min (μ)=D min (μ)+B min (μ) (40);

[0183] Based on the constructed polarization-variable scale degradation model and the direct light decomposition method of the target, the traditional atmospheric polarization imaging physical model expressed by equations (3) and (4) should be conserved, as shown below:

[0184] I max (μ)+I min (μ)=I max +I min =D+B (41);

[0185]

[0186] Furthermore, according to Malus's Law, due to its uniformly distributed unbiased equilibrium state, completely unpolarized light, when transmitted through a linear polarizer with any bias angle, will always have a transmitted light intensity that is half the incident intensity, regardless of the polarization channel type (max or min), as shown below:

[0187]

[0188] Combining formulas (41) and (43), we obtain the reconstructed... and As shown below:

[0189]

[0190] Then, the target direct light intensity values ​​D of the brightest and darkest polarization channels can be obtained. max (μ) and D min (μ), as shown below:

[0191]

[0192] The reconstructed D max (μ) and D min (μ) and B max (μ) and B min Substituting (μ) into the brightest and darkest polarization channels that satisfy the physical model of atmospheric polarization imaging, we obtain the total intensity value I of the two channels. max (μ) and I min (μ), as shown below:

[0193]

[0194] Combining formulas (47) and (48), the target direct light intensity value D of the polarization dual-channel is obtained. max With D min As shown below:

[0195]

[0196] By combining equations (1), (5), (6), (47), and (48), the restored dual-channel fog-free scene J is obtained by reconstructing the atmospheric scattering imaging model and the polarization-variable scale degradation model. max (μ) and J min (μ), as shown below:

[0197]

[0198] Step S6: Iterate the optimal polarization scaling degradation matrix to obtain the final restored image of the fog-free scene.

[0199] Solve for the fog-free restoration J(μ) of a non-uniform fog scene, and obtain the restored scene with high-brightness overexposure suppression through optimal iteration. By combining equations (7), (50), and (51), and reconstructing the scene based on the atmospheric scattering imaging model and the polarization-variable scale degradation model, the restored fog-free scene J(μ) is obtained, as shown below:

[0200]

[0201] In the formula, μ can be obtained by formulas (30)-(32); ξ is a very small positive number used to suppress image overexposure caused by pixels with a transmittance of 0. In this invention, the value of ξ is set to 0.1.

[0202] To optimize the imaging effect of scene dehazing and restoration, considering that in the expression of J(μ), the solutions for I, B, and t do not depend on μ, while the solution for J(μ) does depend on μ, μ can be considered as a relatively single variable in J(μ). The optimal variable-scale degradation rate is obtained by reconstructing the initial single-variable μ through multiple iterations. To obtain a haze-free restored image with good imaging quality Therefore, the objective function is established as follows:

[0203]

[0204] In the formula, W and ω0, η1 and η2 are regularization parameters. The second L1 norm regularization controls the reciprocity of edges between the image and the scattering map. Since the original fog map contains unnecessary details other than scattering information, a weighting function W is introduced to distinguish between edges and uniform regions. μ0 can be estimated pixel-wise by formulas (30)-(32). The variable-scale degradation matrix μ is iterated multiple times according to formula (53), and the conditional parameters for the iteration are as follows:

[0205]

[0206] If the current iteration satisfies the parameters expressed by formula (54), the iteration continues; otherwise, the iteration stops. Set the empirical values ​​N = 10 and R = 5e. -4 Record the final iteration result as like Figure 7 As shown.

[0207] Therefore, this invention employs a polarization imaging method for penetrating non-uniform fog based on adaptive scattering characteristics. It focuses on highlighting the subtle polarization differences between the target and background in discretely distributed non-uniform fog patches and uniform fog layers. This allows for better identification of the polarization characteristics of the target scene even in scenes with large scattering differences. This invention performs excellently in handling complex target scenes with varying degrees of fog scattering dispersion and polarization characteristics, demonstrating good scene restoration capabilities and overexposure suppression effects in experiments.

[0208] Compared with existing technologies, this invention not only effectively alleviates problems such as overexposure due to loss of target polarization information in non-uniform fog scenes, but also basically achieves complete removal of global non-uniform fog in the scene. It can restore the hierarchical structure and texture information of the scene in a large field of view and long distance fog environment, and has excellent non-uniform fog scattering removal capability, and restores the target scene information more clearly.

[0209] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A polarization imaging method for penetrating non-uniform fog with adaptive scattering characteristics, characterized in that, Includes the following steps: Step S1: Obtain polarization images at different angles, and calculate the Stokes vector, linear polarization degree, and dual-channel polarization intensity image of the image; Step S2: Construct non-uniform fog scattering features and estimate the dual-channel non-uniform scattering intensity image; Step S3: Estimate the background light at infinity and calculate the dual-channel polarization intensity transmittance image; Step S4: Construct the attenuation matrix of the polarization dual-channel variable-scale degradation model; Step S5: Construct a polarization dual-channel variable-scale degradation imaging model to obtain a preliminary restoration of the dual-channel non-uniform fog scene; Step S6: Iterate the optimal polarization scaling degradation matrix to obtain the final restored image of the fog-free scene.

2. The polarization imaging method for penetrating non-uniform fog with adaptive scattering characteristics according to claim 1, characterized in that, In step S1, polarization images at different angles are acquired, and the Stokes vector, linear polarization degree, and dual-channel polarization intensity image of the image are calculated. The specific process is as follows: Step S11: Use a polarization camera to acquire images with different polarizations, and then calculate the Stokes vector of the image to describe the polarization state of light, as shown below: ； In the formula, This refers to the total intensity information of the incident light; and These are the polarization information of the incident light rays; This is the fully polarized component of the total light intensity; This is the completely unpolarized component of the total light intensity; , and These are the polarization image light intensity values ​​corresponding to incident light passing through polarizers with directions of 0°, 60°, and 120°, respectively. It is the polarization angle; Step S12: Calculate the linear polarization degree of the image. As shown below: ； Step S13: Based on the Stokes vector of the image, calculate the dual-channel polarization intensity of the image, specifically including the polarization intensity of the brightest channel of the image. and the polarization intensity of the darkest channel of the image As shown below: 。 3. The polarization imaging method for penetrating non-uniform fog with adaptive scattering characteristics according to claim 1, characterized in that, In step S2, non-uniform fog scattering features are constructed, and the intensity image of dual-channel non-uniform scattering is estimated. The specific process is as follows: Step S21: Calculate the mean and variance of intensity within each local window based on the intensity values ​​of image pixels, then filter out pixels with lower variance, i.e., locally uniform regions, and retain the pixels that pass the judgment as a locally uniform estimation set. Step S22: Construct a joint constraint factor by jointly utilizing the intensity information and corresponding polarization information of the scattered light in the original fog scene. , and As shown below: ； ； ； In the formula, These are empirical constants; This represents the intensity value of each pixel in the RGB channel corresponding to the total intensity image; It represents any one of the three RGB channels; This represents the intensity value of each pixel in the linear polarization image; This represents a set of pixels that are locally uniform in the total intensity image; It represents a locally uniform set of pixels in a linear polarization image; This represents the mean of the global intensity. This represents the mean of the global linear polarization degree; and For dynamic thresholds; Step S23: Estimate the scattered light under the specification of the joint constraint factor using the guided filter GF method; wherein, the joint constraint factor is used as the specification of the joint constraint factor. For the guiding map, the scattering map to be estimated and The target image is the original fog scene. and Perform guided filtering to obtain a polarization-coupled guided filter (PGF), as shown below: ； ； In the formula, This represents the pixel-by-pixel scattered light intensity value of the RGB channel corresponding to the brightest polarization channel image; This represents the pixel-by-pixel scattered light intensity value of the RGB channel corresponding to the darkest polarization channel image; This represents the total light intensity value per pixel of the RGB channel corresponding to the brightest polarization channel image; This represents the total light intensity value per pixel in the RGB channel corresponding to the darkest polarization channel image. It represents any one of the three RGB channels; Step S24: Calculate the brightest and darkest channels of fog scattering polarization intensity, as shown below: ； ； In the formula, This represents the intensity value of the scattered light from the brightest polarization channel image; The scattered light intensity value of each pixel in the R channel corresponding to the brightest polarization channel image; The scattered light intensity value of each pixel in the G channel corresponding to the brightest polarization channel image; This represents the pixel-by-pixel scattered light intensity value of the B channel corresponding to the brightest polarization channel image; This represents the intensity value of scattered light from the darkest polarization channel image. This represents the pixel-by-pixel scattered light intensity value of the R channel corresponding to the darkest polarization channel image; The scattered light intensity value of each pixel in the G channel corresponding to the darkest polarization channel image; This represents the pixel-by-pixel scattered light intensity value of the B channel corresponding to the darkest polarization channel image.

4. The polarization imaging method for penetrating non-uniform fog with adaptive scattering characteristics according to claim 1, characterized in that, In step S3, the background light at infinity is estimated, and the dual-channel polarization intensity transmittance image is calculated. The specific process is as follows: Step S31: From the transmittance in the original haze image Pixels approaching 0 are used to map the distance to infinity, and atmospheric scattering models are used to estimate the background radiation from infinity. As shown below: ； ； In the formula, Images are of real foggy weather; The direct transmitted light of the target scene; It is atmospheric scattered light; A fog-free image; Background radiation at infinity; Transmittance; For scene depth; Step S32: The transmittance of the brightest and darkest channels in the atmospheric polarization scattering imaging model are respectively... and , used to describe the attenuation scattering state of polarized radiation; The polarization dual-channel equations in the atmospheric scattering model are shown below: ； The transmittance of the brightest and darkest channels in the atmospheric polarization scattering imaging model are respectively... and As shown below: ； ； 。 5. The polarization imaging method for penetrating non-uniform fog with adaptive scattering characteristics according to claim 1, characterized in that, In step S4, the attenuation matrix of the polarization dual-channel variable-scale degradation model is constructed, and the specific process is as follows: Step S41: Construct the attenuation matrix of the polarization dual-channel variable-scale degradation model. As shown below: ； ； In the formula, Represents the attenuation matrix Components in the R channel; Represents the attenuation matrix Components in the G channel; Represents the attenuation matrix Components in channel B; This is a linear polarization degree image; , , These represent the three RGB channels, as shown below: ； In the formula, , , Images of smog intensity Normalized image with RGB red, blue and green channels; , , This represents the mean of the normalized image for the corresponding channel.

6. The polarization imaging method for penetrating non-uniform fog with adaptive scattering characteristics according to claim 1, characterized in that, In step S5, a polarization dual-channel variable-scale degradation imaging model is constructed to obtain a preliminary restoration of the dual-channel non-uniform fog scene. The specific process is as follows: Step S51: Calculate the scattered light intensity values ​​of the brightest and darkest polarization channels in the foggy image. and Ignoring the attenuation after scattering, the polarization-variable scale degradation model is as follows: ； ； In the formula, and These are the scattered light intensity values ​​of the brightest and darkest polarization channels; Step S52: Decompose the reflected light of the target scene in the polarization dual-channel into two parts according to the presence or absence of polarization information, namely the polarization part. and and the non-polarized part and As shown below: ； ； In the formula, This represents the target light intensity value of the brightest polarization channel image. This represents the target light intensity value of the darkest polarization channel image. For the target light intensity values ​​of the brightest and darkest polarization channels in a foggy image after non-uniform scattering attenuation. and It can be represented as a dual-channel polarization image of a foggy day after undergoing uniform scattering attenuation. and With polarization-variable scale degradation matrix The pixel-by-pixel product of the image on the corresponding RGB channels is shown below: ； ； Step S53: The brightest and darkest channels of the foggy polarization image contain all the polarization and non-polarization characteristics of the target in the foggy weather, i.e., the polarization-scale degradation model, as shown below: ； ； Based on the constructed polarization-variable scale degradation model and the direct optical decomposition method of the target, the physical model of traditional atmospheric polarization imaging is preserved, as shown below: ； ； According to Malus's law, completely unpolarized light, due to its uniformly distributed unbiased equilibrium state, will always have an intensity half that of the incident light when transmitted through a linear polarizer with any bias angle. This is consistent with the brightest polarization channel type. and the darkest It is irrelevant, as shown below: ； ； Then, the direct light intensity values ​​of the target in the brightest and darkest polarization channels can be obtained. and As shown below: ； ； Reconstruction and as well as and Substituting the values ​​into the brightest and darkest polarization channels that satisfy the physical model of atmospheric polarization imaging, we obtain the total intensity value of the two channels. and As shown below: ； ； The target direct light intensity value of the polarization dual channel and As shown below: ； Step S54: Based on the atmospheric scattering imaging model and the polarization-variable scale degradation model, the restored dual-channel fog-free scene is reconstructed. and As shown below: ； ； ； In the formula, It is a very small positive number used to suppress image overexposure caused by pixels with 0 transmittance, set to 0.

1.

7. The polarization imaging method for penetrating non-uniform fog with adaptive scattering characteristics according to claim 1, characterized in that, In step S6, the optimal polarization-variable scale degradation matrix is ​​iterated to obtain the final restored image of the fog-free scene. The specific process is as follows: The restored fog-free scene was obtained by reconstructing the scene using an atmospheric scattering imaging model and a polarization-variable scale degradation model. As shown below: ； The initial state of the single variable was reconstructed through multiple iterations. The variable-scale degradation rate is obtained by means of the method. To obtain a fog-free restored image Therefore, the objective function is established as follows: ； In the formula, and It is a regularization parameter; It is a defined loss function used to measure the current... The quality of the estimated value is determined by how the model minimizes it to find the optimal solution. , It is the Frobenius norm; For weighting functions; The joint constraint factor for estimating the scattered light; For gradient operators; These are the coefficients of the weighting function; This represents the number of iterations. Degenerate matrix of variable scale The process involves multiple iterations, with the following conditional parameters: ； In the formula, and These are all empirical values; if the current iteration meets the above conditions, the iteration continues; otherwise, the iteration stops, and the final iteration result is recorded. .

Images