Polarization image restoration method and system for scattering environment based on manifold constraint transmittance refinement

Abstract

This invention discloses a method and system for restoring polarized images of scattering environments based on manifold-constrained transmittance refinement. First, polarized images are acquired using a focal plane camera and channel compensation is performed to calculate Stokes parameters. Then, background polarization characteristics and background radiation are adaptively estimated. Next, an optical thickness proxy is constructed using polarization contrast, and an initial transmittance field is generated through a parameterized attenuation law with confidence weighting. Then, pixels are mapped to a five-dimensional polarization feature space to construct a data-adaptive manifold, and a Charbonnier penalty term is used to regularize and optimize the transmittance, resulting in a refined result that preserves the boundaries. Finally, scene radiation is inverted based on a physical model, and a closed-loop optimization of global parameters is performed using an unsupervised particle swarm optimization algorithm to improve the restoration quality. Compared with existing technologies, this invention can stably and accurately estimate transmittance, effectively suppress noise and artifacts, and is suitable for strong scattering environments such as underwater and foggy conditions.

Description

Technical Field

[0001] This invention relates to the field of polarization imaging and image restoration technology, and in particular to a method and system for restoring scattering environment polarization images based on manifold-constrained transmittance refinement. Background Technology

[0002] Light attenuation and backscattering caused by complex scattering media are the root causes of deteriorated image quality, resulting in decreased image contrast and loss of detail, which directly affects the reliability of subsequent visual tasks.

[0003] To improve imaging quality in complex scattering environments, existing methods can be broadly categorized into three types: visual enhancement methods, model-driven restoration methods, and polarization-based descattering methods. While methods based on physical models and polarization information have a clear direction, their common bottleneck lies in their sensitivity to estimation errors of scattering parameters (especially transmittance). In real-world complex scattering environments, due to the spatial non-uniformity of scattering distribution, multiple scattering effects, and sensor noise, the parameter estimation process is highly susceptible to interference, and errors are easily amplified during inversion, resulting in unwanted imaging artifacts such as false textures and dark boundaries. Furthermore, existing methods typically rely on empirical or scene-dependent parameter settings, making it difficult to maintain consistent restoration results under different medium properties, scattering intensities, and illumination conditions. Therefore, achieving stable and accurate estimation of scattering medium imaging parameters while minimizing reliance on external prior information or manual parameter adjustments has become a critical technical problem urgently needing to be solved in the field of polarization image descattering. Summary of the Invention

[0004] The purpose of this invention is to propose a method and system for restoring polarized images in scattering environments based on manifold-constrained transmittance refinement. By introducing physically interpretable compact parameters to construct polarization-based transmittance and combining it with graph manifold regularization, a stable estimate of transmittance in scattering environments is achieved, and non-physical fluctuations caused by noise are suppressed. Furthermore, an unsupervised parameter optimization strategy is adopted to perform adaptive parameter optimization solely based on observed image data, thereby improving the visual quality of polarized images without increasing imaging conditions, enabling them to work stably under different scattering conditions and imaging scenarios.

[0005] In order to achieve the above-mentioned objectives, the present invention proposes the following technical solution:

[0006] In a first aspect, a method for restoring scattering environment polarization images based on manifold-constrained transmittance refinement includes the following steps: S1. A single exposure using a split-focus plane camera is used to obtain multi-angle polarization information. To address the asymmetric energy characteristics of the channels in the scattering medium, the energy difference of the positive channels is physically compensated by the global parameter ρ to obtain an energy-balanced improved Stokes vector. S2. Based on the total light intensity and polarization information obtained from the Stokes vector analysis in S1, the background region dominated by scattering is dynamically screened through dual constraints of brightness and gradient, and the background polarization characteristics and background radiation intensity are estimated according to the selected region. S3. Based on the background polarization characteristics estimated in S2, calculate the polarization contrast of each pixel and map it to the optical thickness surrogate parameter. Combine the parameterized attenuation law to generate the initial transmittance field. At the same time, introduce a weighting mechanism based on polarization degree confidence to suppress error propagation in low signal-to-noise ratio regions. S4. Associate the polarization features obtained in S1 with the initial transmittance field obtained in S3, map each pixel to the five-dimensional polarization feature space, and construct an affinity map that integrates feature similarity and spatial proximity; using this map as a manifold constraint, use the Charbonnier penalty term to perform regularization optimization on the initial transmittance field, and output a smooth and boundary-preserving refined transmittance field. S5. Based on the background radiance estimated in S2 and the transmittance field optimized in S4, the preliminary restored scene radiance is obtained by inversion using the atmospheric scattering physics model; a multi-index evaluation function integrating image contrast, information entropy, and naturalness is constructed, and a particle swarm optimization algorithm is used to optimize the global parameter set. Unsupervised optimization is performed; the optimized parameter set is used to return and execute S1 to S5, thereby achieving a closed-loop improvement in parameter adaptation and restoration performance.

[0007] In some implementations, the Stokes vector is constructed using a positive channel asymmetric weighting mechanism, which adaptively compensates for channel energy unevenness caused by anisotropic scattering, target reflection, and residual polarization of illumination through a global parameter ρ.

[0008] In some implementations, the background representation area is determined by the total intensity map. The medium-intensity region intersects with the low-gradient region to reduce interference from target reflection and specular reflection, while retaining sufficient sample to counteract background radiation. A stability estimate is performed. The intermediate intensity region is the total intensity map. The set of pixels with medium grayscale values ​​between the 30th and 70th percentiles of the overall image pixel intensity; the low gradient region is the total intensity map. gradient magnitude The set of pixels below the 40th percentile of the gradient magnitude of the entire image; the background representative area is the intersection of the above two types of pixel sets. When the number of pixels in the intersection is insufficient, only the low gradient area is used as the background representative area. If it is still insufficient, the entire image pixels are used as the background representative area.

[0009] In some implementations, the transmittance field is constructed to satisfy a parameterized attenuation relationship:

[0010] in, It is based on polarization transmittance. It is an optical thickness proxy parameter constructed based on polarization contrast. This indicates the optical thickness scaling parameter. This represents the nonlinear sensitivity index, controlling the effect of transmittance on... The response intensity.

[0011] In some implementations, the data adaptive manifold constructs a reliable affinity relationship between polarization features and spatial coupling by treating each pixel as a node in a sparse graph and associating it with a five-dimensional polarization feature vector.

[0012] in, Represents the two-dimensional coordinates of node i. This represents the five-dimensional polarization eigenvector associated with node i. Controlling sensitivity to feature discontinuities enhances edge preservation capabilities at physical boundaries. Controlling spatial locality prevents the non-physical diffusion of smooth constraints in space.

[0013] In some implementations, the manifold regularization satisfies the following relationship:

[0014] in, This represents the refined transmittance. Indicates the initial transmittance. This represents the transmittance at node i. Indicates the regularization strength. This indicates a Charbonnier penalty.

[0015] In some implementations, the restored scene radiance satisfies the following relationship:

[0016] in, express Processing weight parameters The corrected total light intensity For the estimated background radiation, This represents the transmittance after manifold constraint refinement.

[0017] In some implementations, the unsupervised particle swarm optimization method constructs an optimization evaluation function by selecting multiple image quality evaluation indicators and weighting them together, thereby optimizing global parameters. .

[0018] Secondly, the present invention proposes a scattering medium polarization image restoration system based on manifold-constrained transmittance refinement for implementing the method according to any one of the above claims. This system achieves stable estimation of the transmittance field through a collaborative architecture of a polarization physics model and data adaptive manifold regularization, comprising the following modules that operate sequentially in a collaborative manner: The information acquisition and compensation module is configured to use a single exposure of a split-focus plane camera to acquire multi-angle polarization information. In view of the asymmetric characteristics of channel energy in the scattering medium, the energy difference of the positive channel is physically compensated by the global parameter ρ to obtain an improved Stokes vector with energy balance. The background characteristic estimation module is connected to the information acquisition and compensation module. It is configured to execute the total light intensity and polarization information based on the Stokes vector analysis, dynamically filter the background region dominated by scattering through dual constraints of brightness and gradient, and estimate the background polarization characteristics and background radiation intensity based on the selected region. The initial transmittance field construction module is connected to the background characteristic estimation module. It is configured to execute the calculation of polarization contrast of each pixel based on the estimated background polarization characteristics and map it to the optical thickness surrogate parameter. The initial transmittance field is generated by combining the parameterized attenuation law. At the same time, a weighting mechanism based on polarization degree confidence is introduced to suppress error propagation in low signal-to-noise ratio regions. The transmittance manifold optimization module is connected to the transmittance field initial construction module. It is configured to associate the polarization features with the initial transmittance field, map each pixel to a five-dimensional polarization feature space, and construct an affinity map that integrates feature similarity and spatial proximity. Using this map as a manifold constraint, the initial transmittance field is regularized and optimized using a Charbonnier penalty term to output a smooth and boundary-preserving refined transmittance field. The restoration and closed-loop optimization module, connected to the transmittance manifold optimization module, is configured to execute the preliminary restoration of scene radiance based on the estimated background radiance and optimized transmittance field, using an atmospheric scattering physics model. It constructs a multi-index evaluation function that integrates image contrast, information entropy, and naturalness, and employs a particle swarm optimization algorithm to optimize the global parameter set. Unsupervised optimization is performed; the optimized parameter set is returned for execution, achieving a closed-loop improvement in parameter adaptation and recovery performance.

[0019] In some implementations, the scene radiation restoration and unsupervised parameter closed-loop optimization module integrates a particle swarm optimization algorithm unit, used to automatically optimize the global parameter set based on a multi-index evaluation function. The system then feeds back to control the aforementioned modules to re-run with optimized parameters, forming a closed-loop optimization system.

[0020] Compared with the prior art, the technical solution of the present invention brings unexpected technical effects and has a qualitative improvement over the prior art, specifically including: 1) The stability and accuracy of transmittance estimation are greatly improved: Through the regularization optimization of manifold constraints and Charbonnier penalty terms, non-physical fluctuations caused by noise are effectively suppressed, while maintaining the clarity of the target boundary, thus solving the core problem of unstable transmittance estimation in traditional methods. 2) The robustness of the restoration effect is significantly enhanced: The closed-loop parameter adaptive mechanism of unsupervised particle swarm optimization enables the method to maintain a stable restoration effect in different scattering intensities, lighting conditions and material conditions such as underwater and haze, without the need for manual adjustment, thus breaking through the scene limitations of existing methods. 3) Comprehensive improvement in image restoration quality: Experimental verification shows that the present invention is significantly superior to traditional polarization methods (Liang, Chen), visual enhancement methods (DCP, Retinex) and some learning-based methods in terms of multiple indicators such as contrast, information entropy, sharpness and local structure preservation. It can still clearly restore fine textures (such as coin relief and printed text) under strong scattering conditions, without obvious artifacts or uneven brightness. 4) Improved practicality of the system: The use of a split-focus plane camera to acquire multi-angle polarization information in a single exposure eliminates the need for complex multi-exposure or multi-device coordination. Combined with closed-loop optimization of the algorithm, the operational difficulty and hardware cost of practical applications are reduced. Attached Figure Description

[0021] Figure 1 This is a flowchart of the overall process for restoring the polarization image of the scattering environment based on manifold-constrained transmittance refinement according to the present invention.

[0022] Figure 2 This is a block diagram of the scattering environment polarization image restoration system based on manifold constraint transmittance refinement according to the present invention.

[0023] Figure 3 This is the original light intensity diagram corresponding to a turbid scattering water environment.

[0024] Figure 4 Comparison of reconstruction results between the method of this invention and the comparative method under milk water experimental conditions.

[0025] Figure 5 Comparison of visual restoration results between the method of the present invention and the comparative method under different degradation levels.

[0026] Figure 6 This image shows a quantitative comparison of various image quality evaluation indicators under different degradation levels.

[0027] Figure 7 This is a comparison chart showing the restoration effects of the method of this invention and several representative methods under different turbidity conditions.

[0028] Figure 8 This is an example diagram showing the restoration effect of the method of the present invention on targets of different materials in a high turbidity scattering environment. Detailed Implementation

[0029] To enable those skilled in the art to clearly understand and implement the present invention, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are only for explaining the present invention and are not intended to limit the scope of protection of the present invention.

[0030] Example 1: As Figure 1 As shown, the scattering environment polarization image restoration method based on manifold-constrained transmittance refinement according to the present invention specifically includes the following steps: Step 1: A single exposure using a split-focus plane camera acquires multi-angle polarization information. Addressing the energy asymmetry in the scattering medium, a physical compensation is performed on the energy difference between the orthogonal channels using a global parameter ρ to obtain an energy-balanced improved Stokes vector. Specifically, multi-angle polarization information is captured in a single exposure, and demultiplexed to obtain sub-images of the four analyzer channels. ) .

[0031] Step 2: Based on the total light intensity and polarization information obtained from the Stokes vector analysis in S1, the background region dominated by scattering is dynamically screened through dual constraints of brightness and gradient, and the background polarization characteristics and background radiation intensity are estimated according to the selected region. To compensate for the imbalance in the orthogonal channel response caused by inconsistencies in the micro-polarizer array and differences in system response during actual imaging, a global compensation parameter is introduced. The energy of the 0° and 90° channels is rebalanced, and the global compensation parameters are... The scaling factor is used to correct the gain of a specific polarization channel response. Its value is preferably in the range of 0.9–1.1, and can be extended to 0.8–1.2 when there are large differences in channel response. Based on the compensated sub-image, a linear Stokes vector is reconstructed, and the linear polarization degree and polarization angle of each pixel are calculated. Specifically, this includes the following sub-steps: Step 2.1: Construct the improved Stokes vector Its components are shown in the following formula: (1) in, This represents a sub-image of the four analyzer channels. This represents the channel imbalance compensation parameter, used to reduce deviations caused by micro-polarizer inconsistencies and differences in imaging system response; Step 2.2: Based on the linear Stokes parameters mentioned above, calculate the linear polarization degree and polarization angle of each pixel, as shown in the following formula: (2) in, This represents the degree of linear polarization for each pixel. Indicates the polarization angle.

[0032] Step 3: Based on the background polarization characteristics estimated in Step 2, calculate the polarization contrast of each pixel and map it to an optical thickness surrogate parameter. Combine this with the parameterized attenuation law to generate an initial transmittance field. Simultaneously, introduce a weighting mechanism based on polarization degree reliability to suppress error propagation in low signal-to-noise ratio regions. To accurately estimate the background polarization characteristics of the scene, a reliable representative background region must first be selected, such as a region with weak structural content and the fewest object edges. Then, the background linear polarization degree, polarization angle, and background radiation are calculated. Specifically, this includes the following sub-steps: Step 3.1: First, analyze the total light intensity diagram. Preprocessing is performed to remove outliers and determine their low and high quantile thresholds. These thresholds are then used to construct a brightness range mask, retaining pixels with intensity in the middle range. Simultaneously, calculations are performed... The gradient magnitude is calculated, and pixels with gradient quantile values ​​below a set threshold are retained to construct a low-gradient mask. The intersection of the brightness range mask and the low-gradient mask is then used to obtain the final background representation region for estimation. This method aims to eliminate the influence of strong target reflections and edge structures, ensuring that the selected area is primarily dominated by scattered light.

[0033] Step 3.2: To facilitate subsequent calculations, the Stokes parameters are normalized as shown in the following formula: (3) in, Represents the normalized result Quantity, Represents the normalized result Quantity, It represents a very small positive number, used to avoid calculation instability caused by a denominator of zero; Step 3.3, in the background area Inside, calculate the average value of the normalized parameters: (4) Then estimate the linear polarization degree of the background. and principal polarization direction : (5) Step 3.4, based on the same background area Background radiation was estimated using quantile statistics. : (6) in, This indicates a set high quantile (usually between 80% and 95%). This represents the quantile calculus. This represents a conservative scaling factor used to obtain stable and reliable estimates of background radiation.

[0034] Step 4: Associate the polarization features obtained in Step 1 with the initial transmittance field obtained in S3, mapping each pixel to a five-dimensional polarization feature space to construct an affinity map that fuses feature similarity and spatial proximity. Using this map as a manifold constraint, the initial transmittance field is regularized and optimized using a Charbonnier penalty term, outputting a smooth and boundary-preserving refined transmittance field. This step aims to construct the initial transmittance field based on polarization information. Its core is to define a polarization contrast to estimate the optical thickness, and then map it to polarization-based transmittance using a parameterized attenuation law. Finally, weighted fusion is performed using the reliability of polarization direction and degree of polarization to form a robust initial estimate. Specifically, it includes the following sub-steps: Step 4.1: Based on the estimated background polarization angle ,Will and Projected onto the background polarization direction, calculate the polarization components related to background scattering. As shown in the following formula: (7) Step 4.2: Polarization components obtained from projection Constructing polarization contrast This parameter can be physically represented as a proxy for optical thickness: (8) in, This represents the expected polarization amplitude caused by background scattering under the current light intensity. It represents a very small positive number to ensure computational stability.

[0035] Step 4.3: By introducing the attenuation law of two global parameters, the polarization contrast is increased. Mapped to polarization-driven transmittance As shown in the following formula: (9) in, This represents the optical thickness scaling factor. This represents the nonlinear sensitivity index, used to control the effect of transmittance on... The response intensity This indicates the set minimum transmittance limit.

[0036] Step 4.4: To evaluate the reliability of the polarization estimation for each pixel, construct polarization confidence weights. This weight is determined by the angle consistency weight. Polarization-dependent weights Multiplying them together gives: (10) Angle Consistency Weight By comparing pixel polarization angles polarization angle with background The difference is calculated based on the difference. Function mapping to The interval is consistent with the polarization angle. Periodicity: (11) Among them, scale parameter This represents the expected angular dispersion caused by underwater multiple scattering and measurement noise, with a preferred value range of 10° to 20°.

[0037] Polarization degree dependent weight Then, based on the degree of polarization of the pixel calculate: (12) in, This represents the transition threshold between the set low-confidence and high-confidence polarization degrees, in terms of polarization degree. When normalized to the range of 0 to 1, its preferred value range is 0.05 to 0.15, which aims to suppress unstable polarization estimation in the weak polarization region and prevent overconfidence under high polarization degree.

[0038] Step 4.5: Finally, through polarization estimation... and auxiliary reserve estimates (Used when polarization is unreliable, usually set to 1) Interpolation based on confidence weights is performed between these values ​​to form the initial transmittance field. : (13) When the polarization cues are unreliable (e.g., low polarization degree, rapidly changing polarization angle, or sensor noise), this design ensures that the algorithm smoothly reverts to the identity condition when the polarization cues are unreliable (e.g., low polarization degree, rapidly changing polarization angle, or high noise). t 1), thereby avoiding unstable inversion and spurious enhancement.

[0039] Step 5: Based on the background radiance estimated by S2 and the transmittance field optimized by S4, the preliminary restored scene radiance is obtained by inversion according to the atmospheric scattering physics model; a multi-index evaluation function integrating image contrast, information entropy, and naturalness is constructed, and the particle swarm optimization algorithm is used to optimize the global parameter set. Unsupervised optimization is performed; the optimized parameter set is then used to return and execute steps 1 to 5, achieving a closed-loop improvement in parameter adaptation and restoration performance. In this step, each pixel is treated as a node in an undirected sparse graph and associated with a five-dimensional polarization feature vector. By defining the affinity between features and space, a data-adaptive manifold is constructed, and a Charbonnier penalty term is introduced for manifold regularization. This is combined with iterative weighted least squares optimization to finally solve for the refined transmittance. Using this transmittance, the scene radiance is restored through an inversion algorithm. Specifically, the following sub-steps are included: Step 5.1: First, downsample the relevant fields to reduce the image size and computational cost. For each pixel... i Consider a node in an undirected sparse graph as an edge between nodes. It is formed by their spatial adjacency relationships. Each node i Associate a five-dimensional polarization eigenvector: (14) Each feature channel is normalized to the [0,1] interval to balance the scale of different features.

[0040] Step 5.2: Calculate the affinity between nodes, as shown in the following formula: (15) in, Represents a node i Two-dimensional coordinates on the sampled grid. Controlling sensitivity to feature discontinuities enhances edge preservation capabilities at physical boundaries. By controlling spatial locality, the non-physical diffusion of smoothing constraints in space is prevented. This construction induces a data-adaptive manifold: nodes are strongly connected only when they are spatially close and have similar polarization characteristics, thus encouraging smoothing in uniformly scattering regions while respecting the structural boundaries of objects.

[0041] Step 5.3: Introduce the Charbonnier penalty term. Construct a manifold regularization optimization problem with the following objective function: (16) in, This represents the refined transmittance field to be determined. This represents the estimated initial transmittance. This represents the regularization strength parameter. The Charbonnier penalty term is defined as: (17) Among them, parameters It is a minimum value, and the preferred value range is... The value can be adaptively set according to the noise level or scattering intensity. A smaller value is used for low-noise water bodies and a larger value is used for strong scattering water bodies to control the smooth transition between quadratic behavior and absolute behavior.

[0042] Step 5.4: The optimization problem is a convex optimization problem, and the global optimal solution can be obtained through iterative reweighted least squares method. In the... k In the next iteration, based on the current transmittance estimate For each edge Update the corresponding reweighting factor : (18) And thus obtain effective edge weights : (19) Construct a reweighted adjacency matrix based on effective edge weights. and its corresponding degree matrix (in Thus, the reweighted graph Laplace operator is obtained: (20) At this point, the transmittance update process is transformed into solving the following sparse symmetric positive definite linear system: (twenty one) By iteratively solving the linear system and dynamically updating the weights, the transmittance is progressively refined. The optimized transmittance is then mapped back to the original resolution using standard interpolation, and then... Optional lightweight edge alignment refinement is performed as a guide to address slight blockiness or boundary misalignment that may be introduced by downsampling, resulting in the final refined transmittance field. This reweighting mechanism can automatically reduce the cross-boundary smoothing intensity at locations with significant transmittance changes, effectively suppressing blurring and halo artifacts, while enhancing consistency constraints in uniform scattering regions to suppress noise.

[0043] Step 5.5: Inverse the standard single-scattering imaging model to recover the potential scene radiance. : (twenty two) in, This represents the total light intensity after channel compensation. This represents the estimated background radiation. This represents the refined transmittance obtained after manifold regularization. After inverse reconstruction, for display purposes, contrast-limited adaptive histogram equalization can be applied for post-processing. This step is not part of the physics estimator and does not change the recovered radiation structure.

[0044] Further, in step 5.6, unsupervised parameter closed-loop optimization and image restoration are performed; This step employs an unsupervised particle swarm optimization algorithm. By constructing a multi-index evaluation function, it automatically optimizes the global parameters within a preset parameter space and re-executes the aforementioned restoration process using the optimal parameters, ultimately obtaining a restored image with improved quality.

[0045] Step 5.6.1: Define the optimization evaluation function Used for quantitative evaluation of restored images L The overall quality. This function is a weighted linear combination of multiple no-reference image quality metrics: (twenty three) in, This represents a measure of normalized contrast between automatically constructed foreground / background masks. This indicates a measure of local enhancement effect (such as the average enhancement energy within the mask). This represents a measure of the information entropy of an image. This indicates that the high-frequency residuals in the background region are penalized (to suppress noise amplification). This indicates background variance that is being over-punished (suppressing inhomogeneity). , , , , This represents the weighting coefficient for each indicator.

[0046] Step 5.6.2: Represent the global parameters to be optimized as follows: The optimal combination of parameters that maximizes the evaluation function is searched within a finite set of feasible parameters Ω using an unsupervised particle swarm optimization algorithm. : (twenty four) in, This represents the scene radiance reconstructed using parameter θ through polarization transmittance estimation and physical inversion formulas (i.e., the steps mentioned above).

[0047] After optimization and convergence, the optimal parameter set is obtained. Using this parameter set, re-execute all calculations from steps S2 to S5, ultimately outputting a high-quality restored image after global optimization. L .

[0048] By introducing physically interpretable compact parameters to construct polarization-based transmittance and combining it with graph manifold regularization, stable estimates of transmittance under scattering environments are achieved, while suppressing non-physical fluctuations caused by noise. Furthermore, an unsupervised particle swarm optimization algorithm is employed to adaptively optimize parameters based solely on observed image data, improving the visual quality of polarization images without increasing imaging conditions. This enables stable operation under various scattering conditions and imaging scenarios, making it suitable for strong scattering environments such as underwater and atmospheric haze.

[0049] Example 2: Figure 2 As shown, this is the scattering environment polarization image restoration system based on manifold-constrained transmittance refinement according to the present invention. The system includes the following modules that operate in sequence and in coordination: The information acquisition and compensation module 100 is configured to use a single exposure of a split-focus plane camera to acquire multi-angle polarization information. In view of the asymmetric characteristics of channel energy in the scattering medium, the energy difference of the positive channel is physically compensated by the global parameter ρ to obtain an improved Stokes vector with energy balance. Background characteristic estimation module 200 is connected to information acquisition and compensation module 100. It is configured to execute total light intensity and polarization information based on Stokes vector analysis, dynamically filter background regions dominated by scattering through dual constraints of brightness and gradient, and estimate background polarization characteristics and background radiation intensity based on the selected regions. The initial transmittance field construction module 300 is connected to the background characteristic estimation module 200. It is configured to execute the calculation of polarization contrast of each pixel based on the estimated background polarization characteristics and map it to the optical thickness surrogate parameter. The initial transmittance field is generated by combining the parameterized attenuation law. At the same time, a weighting mechanism based on polarization degree confidence is introduced to suppress error propagation in low signal-to-noise ratio regions. The transmittance manifold optimization module 400 is connected to the transmittance field initial construction module 300. It is configured to associate the polarization features with the initial transmittance field, map each pixel to a five-dimensional polarization feature space, and construct an affinity map that integrates feature similarity and spatial proximity. Using this map as a manifold constraint, the initial transmittance field is regularized and optimized using a Charbonnier penalty term to output a smooth and boundary-preserving refined transmittance field. The restoration and closed-loop optimization module 500, connected to the transmittance manifold optimization module 400, is configured to execute the preliminary restoration of scene radiance based on the estimated background radiance intensity and the optimized transmittance field, and invert the radiance of the scene according to the atmospheric scattering physics model; it constructs a multi-index evaluation function that integrates image contrast, information entropy, and naturalness, and uses a particle swarm optimization algorithm to optimize the global parameter set. Unsupervised optimization is performed; the optimized parameter set is returned for execution, achieving a closed-loop improvement in parameter adaptation and recovery performance.

[0050] The restoration and closed-loop optimization module 500 integrates a particle swarm optimization algorithm unit, used to automatically optimize the global parameter set based on a multi-index evaluation function. The system then feeds back to control the aforementioned modules to re-run with optimized parameters, forming a closed-loop optimization system.

[0051] like Figure 3 As shown, the method proposed in this invention is validated using this dataset. The dataset is obtained as follows: a controllable scattering environment is constructed using a transparent water tank. The target board (containing multiple material details such as metal coins, plastic coins, printed text / patterns, and mosaic pieces) is fixed at the far end of the water tank. An expanded laser light source is placed at the incident end. A polarizer is placed in front of the light source as a "polarization generator" (PSG). A rotatable polarizer is placed in front of the camera as a polarization analyzer (PSA). The imaging device is a CCD / CMOS industrial camera with a fixed focal length lens. Manual exposure and fixed gain settings are used. Since grayscale information is processed, white balance correction is not required to ensure that all experimental groups have consistent conditions. The experiment used pure water as a baseline, and then milk emulsion was added stepwise to the same volume of water, for example, 5 ml, 10 ml, 13 ml, 15 ml, 19 ml, and 21 ml. Each time, the mixture was thoroughly stirred and allowed to stand until the scattering was uniform before completing one acquisition. The acquisition sequence was to obtain polarimetric images at three analysis angles: 0°, 45°, and 90° (or obtain three channels at once using a spectrophotometer), and simultaneously record the exposure time and the distance from the target to the camera. After acquisition, dark-field and flat-field corrections were performed to eliminate fixed-mode noise and uneven illumination. Then, the Stokes components were calculated from the three sub-images, including... , , Verification of the method of this invention: Stokes parameters and polarization features are reconstructed through global channel compensation. Background polarization / radiance is estimated based on low-texture background regions. Initial transmittance is obtained by parametric attenuation and reliability weighting of polarization contrast. Then, Charbonnier robust regularization is introduced on the graph manifold induced by polarization features, and transmittance is refined iteratively using IRLS. Scene radiance is recovered by inversion according to the single scattering model. Finally, global parameters are optimized by unsupervised PSO to obtain the final restoration result. To verify the effect, in a 15ml milk experiment, the original intensity image, the image processed by the method of this invention, the image processed by the method based on the original Stokes formula (abbreviated as Liang), and the image processed by the underwater polarization descattering method based on scene adaptation and multi-parameter optimization (abbreviated as Chen) are compared in detail based on different material regions (e.g., ...). Figure 4 (As shown). To verify the applicability of the method of the present invention in scattering environments of different degrees, a comparative study was conducted by gradually increasing the degradation intensity from level 1 to level 5. The comparison images are the original image, the image processed by Chen's method, and the image processed by the method of the present invention. Figure 5 The three images were quantitatively evaluated using nine normalized image evaluation metrics at five levels of degradation intensity. Figure 6 To provide a comprehensive benchmark, the method of this invention is compared with representative enhancement-based methods (DCP, Retinex, and CLAHE), classical polarization pipelines (Liang method and its post-processing variants), five polarization-based recovery methods (Chen, Li, Shen, Schechner, and Dong), and three learning-based models (HCLR, TACL, and SAM). Figure 7 Finally, the recovery results of the method of the present invention on different material targets under two relatively high turbidity conditions are presented. Figure 8 ).

[0052] like Figure 4 As shown, the comparative reconstruction results obtained under experimental conditions of 15ml milk are presented. The results are in the following order: original intensity image, method of this invention, Liang method, and Chen method. Figure 3 As shown in (a), the original observed image is severely affected by backscattering, exhibiting significant low-frequency intensity deviation and contrast attenuation, making it difficult to discern detailed structures such as the coin relief (D1) and pattern markings (D2). Figure 3 As shown in (b), the method of this invention achieves a relatively uniform restoration effect throughout the scene, significantly enhancing structural boundaries and fine textures. In region D1, coin engravings and edge details are clearly restored; in region D2, the readability of label characters is significantly improved; simultaneously, the brightness distribution in the background region D3 is more uniform, and residual haze and lighting gradients are effectively suppressed. In contrast, as... Figure 3 As shown in (c), Liang's AoP / DoLP-based method mitigated the impact of haze to some extent, but residual intensity gradients remained, resulting in limited detail recovery, especially in low-texture background areas. Figure 3 As shown in (d), the Chen method improves overall visibility and enhances the high-contrast pattern area (D2), but the relief details are not fully recovered in the coin area (D1), resulting in low prominence. Furthermore, the three-dimensional intensity profile results corresponding to D1 show that the method of this invention can recover stronger and more structural relief undulations, consistent with the actual embossed morphology on the coin surface; in contrast, the Liang method's profile is dominated by low-frequency deviations, while the relief undulation amplitude of the Chen method is relatively small.

[0053] like Figure 5As shown, the visual comparison results of the original input, the Chen method, and the method of this invention are presented under degradation intensity increasing from Level-1 to Level-5. It can be observed that as the degradation level increases, the original image is affected by both strong scattering and contrast decay, gradually exhibiting reduced overall brightness, edge diffusion, and severe loss of fine structure, resulting in a significant decrease in target readability. The Chen method can enhance the overall appearance and restore the main structure to some extent under mild degradation conditions, but its results are still limited in edge preservation and detail recovery. Furthermore, at high degradation levels, local contrast is further weakened, and fine stripes and characters become increasingly difficult to distinguish. In contrast, the method of this invention can effectively suppress scattering effects at all degradation levels, maintaining relatively clear target boundaries and continuous structural morphology. High-frequency details such as fine characters, stripes, and scribe lines still have good discernibility under strong degradation conditions, resulting in a more stable and balanced overall visual effect.

[0054] like Figure 6 As shown, the trends of various methods on multiple normalized image quality metrics are further presented under different degradation levels from Level-1 to Level-5. The quantification metrics used include: contrast ratio C, reflecting the overall brightness distribution and contrast relationship; RMS (Root Mean Square Contrast Ratio), measuring the degree of grayscale fluctuation in the image; EME (Enhancement Measurement Evaluation), describing the local contrast enhancement effect; Entropy, characterizing the amount of image information; LSM (Local Structure Measurement), reflecting the ability to preserve local structure; Brenner gradient, used to characterize image sharpness; SF (Spatial Frequency), measuring the content of high-frequency details; AG (Average Gradient), reflecting the sharpness of edges; and PSNR, comprehensively measuring the overall reconstruction quality. The metric trends show that as the degradation level increases, the Chen method exhibits a gradual decline in most metrics, especially in sharpness and detail-related metrics, indicating that its ability to preserve structure and detail is limited under strong degradation conditions. In contrast, the method of this invention maintains higher and more stable normalized values ​​across all metrics, especially at high degradation levels, where it retains good contrast, information content, and sharpness, demonstrating stronger resistance to degradation and overall robustness. Quantitative results and Figure 5 The visual observations were highly consistent, further verifying the stability and superiority of the method of the present invention in complex degradation scenarios.

[0055] As shown in Figure 7, the method of this invention was systematically compared with several representative underwater image enhancement and restoration methods, including traditional enhancement-based methods (DCP, Retinex, and CLAHE), classic polarization processing pipelines (Liang method and its post-processing variants), five polarization-based underwater restoration methods (Chen, Li, Shen, Schechner, and Dong), and three learning-based models (HCLR, TACL, and SAM). Comparative experiments were conducted under medium turbidity (15 ml) and high turbidity (19 ml) conditions.

[0056] The results show that although the above methods improve image visibility to varying degrees, they all exhibit their own performance limitations as turbidity increases. Specifically, DCP can suppress scattering blur to some extent, but often introduces problems such as overall brightness reduction and spatial brightness unevenness; CLAHE mainly enhances local contrast and has limited ability to suppress global backscattering; Retinex-based methods are prone to inconsistent tone reconstruction during brightness correction and are accompanied by residual haze.

[0057] When DCP or CLAHE are introduced into the Liang method as post-processing, the improvement under strong scattering conditions is limited, and noise or structural artifacts are further amplified in some areas. For polarization-based restoration methods, most methods can reduce scattering and improve contrast to some extent under low turbidity conditions, but their restoration results usually exhibit spatial inhomogeneity, with limited enhancement of fine textures; under high turbidity conditions, blurring residue and loss of local details are more pronounced. Taking the metal coin region as an example, the Chen method has insufficient consistency in embossed texture restoration, with local contrast still being low and the overall visual effect relatively dark. The Shen et al. method performs relatively stably in global scattering suppression, but its ability to separate local details is limited; the Schechner and Dong methods can maintain brightness distribution well under low turbidity conditions, but the texture blurring gradually worsens as turbidity increases. The Li method performs well in areas with strong polarization contrast, but its ability to restore fine structures such as coins is limited, and it relies on orthogonal illumination configuration, increasing the complexity of system implementation.

[0058] For learning-based methods, HCLR and TACL typically produce relatively smooth visual results, but tend to over-suppress high-frequency details. SAM preserves structural information well under low turbidity conditions, but its performance degrades significantly under high turbidity conditions, which may be related to the mismatch between training data and test scenarios in terms of water type, turbidity level, lighting conditions, and imaging geometry. Overall, at 19 ml turbidity, most contrastive methods require a trade-off between over-smoothing and obvious artifacts.

[0059] In contrast, the method of this invention achieves a more balanced recovery effect under both turbidity conditions, which not only significantly improves the clarity of the target boundary, but also has better resolution of fine textures such as coin inscriptions and small characters, while maintaining a relatively uniform dehazing effect and not introducing obvious brightness unevenness or structural artifacts.

[0060] like Figure 8 As shown, the method of this invention exhibits significant advantages under different imaging conditions and material scenarios. For each scenario, the region of interest (ROI) of the restored image is displayed with a yellow box, arranged from left to right as follows: original image, image processed by the method of this invention, and details of the ROI. In strong scattering environments, the original light intensity image commonly suffers from severe background fog, low target contrast, and blurred boundaries, making it difficult to discern target details. After processing by the method of this invention, the contrast between the target area and the background is significantly improved, the target outline is clearer, and details such as surface texture, fine scratches, and printed text are effectively restored. Furthermore, in complex scenarios containing various materials such as metal, plastic, and paper, the method of this invention can effectively distinguish the differences in light scattering and polarization responses of different material surfaces, thereby enhancing the identifiability of material features. The restoration results show a balance in overall brightness and local detail, without obvious over-enhancement, structural distortion, or artifacts, indicating that the method of this invention has good cross-scenario adaptability and robustness in practical applications.

[0061] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the systems disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the descriptions are relatively simple; relevant parts can be referred to the method section.

[0062] The above specific embodiments illustrate the principles and implementation methods of the present invention using specific examples. The descriptions of the embodiments are merely for the purpose of helping to understand the method and core ideas of the present invention. Furthermore, those skilled in the art will recognize that, based on the ideas of the present invention, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of the present invention. Any modifications, equivalent substitutions, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention. Additionally, any improvements and modifications made without departing from the principles of the present invention should also be considered to fall within the protection scope of the present invention.

Claims

1. A method for restoring scattering environment polarization images based on manifold-constrained transmittance refinement, characterized in that, Includes the following steps: S1. A single exposure using a split-focus plane camera is used to obtain multi-angle polarization information. To address the asymmetric energy characteristics of the channels in the scattering medium, the energy difference of the positive channels is physically compensated by the global parameter ρ to obtain an energy-balanced improved Stokes vector. S2. Based on the total light intensity and polarization information obtained from the Stokes vector analysis in S1, the background region dominated by scattering is dynamically screened through dual constraints of brightness and gradient, and the background polarization characteristics and background radiation intensity are estimated according to the selected region. S3. Based on the background polarization characteristics estimated in S2, calculate the polarization contrast of each pixel and map it to the optical thickness surrogate parameter. Combine the parameterized attenuation law to generate the initial transmittance field. At the same time, introduce a weighting mechanism based on polarization degree confidence to suppress error propagation in low signal-to-noise ratio regions. S4. Associate the polarization features obtained in S1 with the initial transmittance field obtained in S3, map each pixel to the five-dimensional polarization feature space, and construct an affinity map that integrates feature similarity and spatial proximity; using this map as a manifold constraint, use the Charbonnier penalty term to perform regularization optimization on the initial transmittance field, and output a smooth and boundary-preserving refined transmittance field. S5. Based on the background radiation intensity estimated in S2 and the transmittance field optimized in S4, the preliminary restored scene radiance is obtained by inversion according to the atmospheric scattering physical model. Construct a multi-index evaluation function that integrates image contrast, information entropy, and naturalness, and employ particle swarm optimization algorithm on the global parameter set. Unsupervised optimization is performed; the optimized parameter set is used to return and execute S1 to S5, thereby achieving a closed-loop improvement in parameter adaptation and restoration performance.

2. The method for restoring scattering environment polarization images based on manifold-constrained transmittance refinement according to claim 1, characterized in that, The Stokes vector is constructed using an orthogonal channel asymmetric weighting mechanism, which adaptively compensates for channel energy unevenness caused by anisotropic scattering, target reflection, and residual polarization of illumination through global parameter ρ.

3. The method for restoring scattering environment polarization images based on manifold-constrained transmittance refinement according to claim 1, characterized in that, The background representative area is represented by the total intensity map. The medium-intensity region intersects with the low-gradient region to reduce interference from target reflection and specular reflection, while retaining sufficient sample to counteract background radiation. A stability estimate is performed. The intermediate intensity region is the total intensity map. The set of pixels with medium grayscale values ​​between the 30th and 70th percentiles of the overall image pixel intensity; the low gradient region is the total intensity map. gradient magnitude The set of pixels below the 40th percentile of the gradient magnitude of the entire image; the background representative area is the intersection of the above two types of pixel sets. When the number of pixels in the intersection is insufficient, only the low gradient area is used as the background representative area. If it is still insufficient, the entire image pixels are used as the background representative area.

4. The method for restoring scattering environment polarization images based on manifold-constrained transmittance refinement according to claim 1, characterized in that, The transmittance field is constructed to satisfy a parameterized attenuation relationship: in, It is based on polarization transmittance. It is an optical thickness proxy parameter constructed based on polarization contrast. This indicates the optical thickness scaling parameter. Represents the nonlinear sensitivity index, controlling the effect of transmittance on... The response intensity.

5. The method for restoring scattering environment polarization images based on manifold-constrained transmittance refinement according to claim 1, characterized in that, The data adaptive manifold constructs a reliable affinity relationship between polarization features and spatial coupling by treating each pixel as a node in a sparse graph and associating it with a five-dimensional polarization feature vector. in, Represents the two-dimensional coordinates of node i. This represents the five-dimensional polarization eigenvector associated with node i. Controlling sensitivity to feature discontinuities enhances edge preservation capabilities at physical boundaries. Controlling spatial locality prevents the non-physical diffusion of smooth constraints in space.

6. The method for restoring scattering environment polarization images based on manifold-constrained transmittance refinement according to claim 1, characterized in that, The manifold regularization satisfies the following relationship: in, This represents the refined transmittance. Indicates the initial transmittance. This represents the transmittance at node i. Indicates the regularization strength. This indicates a Charbonnier penalty.

7. The method for restoring scattering environment polarization images based on manifold-constrained transmittance refinement according to claim 1, characterized in that, The restored scene radiance satisfies the following relationship: in, express Processing weight parameters The corrected total light intensity For the estimated background radiation, This represents the transmittance after manifold constraint refinement.

8. The method for restoring scattering environment polarization images based on manifold-constrained transmittance refinement according to claim 1, characterized in that, The unsupervised particle swarm optimization method constructs an optimization evaluation function by selecting multiple image quality evaluation indicators and weighting them together, thus optimizing global parameters. .

9. A system for restoring polarized images of a scattering medium based on manifold-constrained transmittance refinement for implementing the method according to any one of claims 1 to 8, characterized in that, Stable estimation of the transmittance field is achieved through a collaborative architecture of polarization physics model and data adaptive manifold regularization, comprising the following modules that operate in a sequential and collaborative manner: The information acquisition and compensation module is configured to use a single exposure of a split-focus plane camera to acquire multi-angle polarization information. In view of the asymmetric characteristics of channel energy in the scattering medium, the energy difference of the positive channel is physically compensated by the global parameter ρ to obtain an improved Stokes vector with energy balance. The background characteristic estimation module is connected to the information acquisition and compensation module. It is configured to execute the total light intensity and polarization information based on the Stokes vector analysis, dynamically filter the background region dominated by scattering through dual constraints of brightness and gradient, and estimate the background polarization characteristics and background radiation intensity based on the selected region. The initial transmittance field construction module is connected to the background characteristic estimation module. It is configured to execute the calculation of polarization contrast of each pixel based on the estimated background polarization characteristics and map it to the optical thickness surrogate parameter. The initial transmittance field is generated by combining the parameterized attenuation law. At the same time, a weighting mechanism based on polarization degree confidence is introduced to suppress error propagation in low signal-to-noise ratio regions. The transmittance manifold optimization module is connected to the transmittance field initial construction module. It is configured to associate the polarization features with the initial transmittance field, map each pixel to a five-dimensional polarization feature space, and construct an affinity map that integrates feature similarity and spatial proximity. Using this map as a manifold constraint, the initial transmittance field is regularized and optimized using a Charbonnier penalty term to output a smooth and boundary-preserving refined transmittance field. The restoration and closed-loop optimization module is connected to the transmittance manifold optimization module and is configured to execute the preliminary restoration of scene radiance based on the estimated background radiation intensity and the optimized transmittance field, according to the atmospheric scattering physics model. Construct a multi-index evaluation function that integrates image contrast, information entropy, and naturalness, and employ particle swarm optimization algorithm on the global parameter set. Unsupervised optimization is performed; the optimized parameter set is returned for execution, achieving a closed-loop improvement in parameter adaptation and recovery performance.

10. The scattering environment polarization image restoration system based on manifold-constrained transmittance refinement according to claim 9, characterized in that, The scene radiation restoration and unsupervised parameter closed-loop optimization module integrates a particle swarm optimization algorithm unit, which is used to automatically optimize the global parameter set based on a multi-index evaluation function. The system then feeds back to control the aforementioned modules to re-run with optimized parameters, forming a closed-loop optimization system.

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