An underwater polarized image restoration method based on augmented Lagrange multiplier method

Abstract

This invention belongs to the field of underwater image restoration technology, and specifically to a method for underwater polarization image restoration based on the augmented Lagrange multiplier method. The method includes the following steps: Step 1: Obtain the polarization angle of the backscattered light; Step 2: Normalize the direction of the backscattered light to 0°; Step 3: Calculate the difference in polarization angle between the target reflected light and the backscattered light, and restore the target polarization angle; Step 4: Establish a polarization degree solution model; Step 5: Construct a global optimization objective function; Step 6: Solve the function; Step 7: Restore a clear image. This invention uses the augmented Lagrange method and the bounded Nelder-Mead algorithm for global optimization, making the polarization degree parameter solution more convergent and physically consistent in highly polarized target scenarios. In summary, the method of this invention is more suitable for highly polarized targets with obvious polarization characteristics and stable polarization directions.

Description

Technical Field

[0001] This invention relates to the field of underwater image restoration technology, specifically to an underwater polarization image restoration method based on the augmented Lagrange multiplier method. Background Technology

[0002] Underwater image restoration is a crucial research area in optical imaging and image processing. Currently, it has garnered widespread attention in applications such as ocean exploration, underwater robot navigation, and underwater archaeology. Because suspended particles in water absorb and scatter light, the light signal received by imaging devices typically consists of both reflected and backscattered light from the target. Backscattered light significantly reduces image sharpness, making the restoration of high-quality underwater images a challenging task.

[0003] In recent years, polarization imaging technology has gradually become a research hotspot due to its ability to acquire additional polarization information and its outstanding performance in suppressing scattering. While traditional methods can recover images under different turbid conditions to some extent, they do not fully utilize the difference in polarization angle between the reflected and backscattered light from the rotated target to improve the accuracy of polarization parameter solutions. Furthermore, they do not consider using image quality evaluation metrics (such as contrast or EME) to optimize polarization parameters, nor do they establish constraints to ensure global consistency of the solution. Therefore, when the local polarization characteristics of the target change significantly, the recovery results may be unstable.

[0004] To address these issues, we propose an underwater polarization image restoration method based on the augmented Lagrange multiplier method. Summary of the Invention

[0005] The purpose of this section is to outline some aspects of the embodiments of the present invention and to briefly describe some preferred embodiments. Simplifications or omissions may be made in this section, as well as in the abstract and title of this application, to avoid obscuring the purpose of these documents; however, such simplifications or omissions should not be construed as limiting the scope of the invention.

[0006] To address the aforementioned technical problems, according to one aspect of the present invention, the present invention provides the following technical solution:

[0007] An underwater polarization image restoration method based on the augmented Lagrange multiplier method includes the following steps: Step 1: Obtain the polarization angle of the backscattered light. ;

[0008] Step 2: Normalize the direction of the backscattered light to 0°;

[0009] Step 3: Calculate the difference in polarization angle between the reflected light and the backscattered light from the target. Restore the target polarization angle ;

[0010] Step 4: Establish the polarization degree solution model:

[0011]

[0012]

[0013] The degree of polarization of the reflected light from the target, This represents the degree of polarization of the backscattered light. For direct transmission of light intensity, The intensity of backscattered light;

[0014] Step 5: Construct the global optimization objective function;

[0015] Step Six: Solve:

[0016] Introduce constraints:

[0017]

[0018] Constructor:

[0019]

[0020] and These are the Lagrange multipliers and the penalty factor, respectively, for the parameters. Within the physical range The goal is to perform continuous optimization and minimize:

[0021] ;

[0022] Step 7: Restore a clear image.

[0023] As a preferred embodiment of the underwater polarization image restoration method based on the augmented Lagrange multiplier method described in this invention, wherein the polarization angle in step one is... The specific calculation method is as follows: in the AOP matrix obtained from the four polarization images, the background region without foreground target is selected. Calculate the mode of AOP as an estimate of the polarization angle of the backscattered light:

[0024] .

[0025] As a preferred embodiment of the underwater polarization image restoration method based on the augmented Lagrange multiplier method described in this invention, the specific method of step two is to rotate the coordinate system counterclockwise. This yields a new Stokes vector:

[0026]

[0027] Where the rotation matrix for:

[0028]

[0029] The polarization angle after rotation is:

[0030] At this moment, the backscattered light in the rotating coordinate system satisfies .

[0031] As a preferred embodiment of the underwater polarization image restoration method based on the augmented Lagrange multiplier method described in this invention, the polarization angle in step three is... The solution method is as follows: in the rotating coordinate system, the polarization angle... The difference between the polarization direction of the target reflected light and the background is represented by the value of the difference. Transforming this difference back to the original reference coordinate system yields the polarization angle of the target reflected light.

[0032] .

[0033] As a preferred embodiment of the underwater polarization image restoration method based on the augmented Lagrange multiplier method described in this invention, the specific method of step five is to introduce EME contrast constraints. To enhance details, smoothness constraints To suppress noise, polarization consistency constraints The overall loss function is obtained by combining these results:

[0034] .

[0035] As a preferred embodiment of the underwater polarization image restoration method based on the augmented Lagrange multiplier method described in this invention, the specific method for restoring a clear image in step seven is as follows: after obtaining the globally optimal polarization parameters, according to the imaging model:

[0036]

[0037] in The image can be estimated from the brightest part of the background area, and finally a high-contrast, clear underwater image can be obtained.

[0038] Compared with existing technologies, the advantages of this invention are: it has higher accuracy and stability in solving polarization parameters and restoring images of highly polarized targets; and after obtaining the polarization angle of the backscattered light, it utilizes the polarization angle difference obtained by coordinate rotation. and through " By using the "+rotation angle" method to deduce the true polarization angle of the target's reflected light, the reliability of polarization angle estimation for highly polarized targets is significantly improved. Furthermore, this invention uses the polarization degree of the target's reflected and backscattered light as optimization variables, introducing EME contrast constraints, smoothness constraints, and polarization consistency constraints. It employs the augmented Lagrangian method and the bounded Nelder-Mead algorithm for global optimization, making the polarization degree parameter solution more convergent and physically consistent in highly polarized target scenes. In summary, the method of this invention is more suitable for highly polarized targets with obvious polarization characteristics and stable polarization directions, enabling the acquisition of more stable polarization parameters and higher-quality restored images. Attached Figure Description

[0039] To more clearly illustrate the technical solutions of the embodiments of the present invention, the present invention will be described in detail below with reference to the accompanying drawings and detailed embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort. Wherein:

[0040] Figure 1 This is a flowchart of an underwater polarization image restoration method based on the augmented Lagrange multiplier method according to the present invention;

[0041] Figure 2 This image shows the verification results of image restoration capability in high polarization feature scenarios in an embodiment of the underwater polarization image restoration method based on the augmented Lagrange multiplier method of the present invention. Detailed Implementation

[0042] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0043] Secondly, the present invention is described in detail with reference to the schematic diagrams. When detailing the embodiments of the present invention, for ease of explanation, the cross-sectional views illustrating the device structure may be partially enlarged, not according to the usual scale. Furthermore, the schematic diagrams are merely examples and should not limit the scope of protection of the present invention. In addition, actual fabrication should include three-dimensional spatial dimensions of length, width, and depth.

[0044] To make the objectives, technical solutions, and advantages of the present invention clearer, the embodiments of the present invention will be described in further detail below with reference to the accompanying drawings.

[0045] This invention, after obtaining the polarization angle of the backscattered light, obtains the difference in polarization angle between the target reflected light and the backscattered light by rotating the coordinate system, and thereby calculates the true polarization angle of the target reflected light in the original coordinate system. Simultaneously, an image quality evaluation index (such as EME) is introduced as an optimization constraint function to construct a global optimization model to solve for the optimal polarization degree parameters of the backscattered light and the target reflected light under the condition that the two polarization angles are known. Through the above method, this invention can stably and efficiently separate the target reflected light and the backscattered light, thereby obtaining underwater images with higher contrast and higher clarity.

[0046] This invention is an underwater image restoration method based on polarization parameter optimization, which aims to obtain more accurate polarization parameter estimates in complex underwater environments, thereby improving image clarity and contrast. The method relies on acquiring original polarized images in four polarization directions and combining steps such as polarization angle calculation, polarization space rotation, and global optimization to complete image restoration.

[0047] In the method of this invention, the Stokes vector is first calculated based on four polarization angle images (0°, 45°, 90°, and 135°) obtained from the captured images, and the AOP (polarization angle) matrix of the scene is obtained from this. Then, the mode of the AOP is counted in the background region of the image and used as an estimate of the polarization angle of the backscattered light. Based on this polarization angle, the polarization space coordinate system is rotated so that the backscattered light approximates a polarization angle of 0° in the new coordinate system, thereby obtaining the polarization angle difference between the target reflected light and the backscattered light. This difference is then added to the rotation angle to obtain the polarization angle of the target reflected light in the original coordinate system.

[0048] In the polarization parameter solution stage, this invention constructs an optimization model that includes image EME constraints and smoothness constraints, and combines the augmented Lagrange multiplier method for global solution. By jointly optimizing the polarization degree of the target reflected light and the polarization degree of the backscattered light, this invention can obtain the globally optimal polarization degree values ​​for both. Finally, the optimized polarization parameters are used to deduce the true brightness component of the target reflected light, thereby obtaining a clear underwater image after scattering suppression.

[0049] Specifically, this invention provides an underwater polarization image restoration method based on the augmented Lagrange multiplier method, with known conditions (i.e., input variables):

[0050] (1) Set of four polarization images:

[0051] The four polarization images correspond to According to the Mueller–Stokes imaging model, the polarization direction of these four images satisfies:

[0052]

[0053] (2) Stokes vector Calculation method:

[0054] According to the polarization measurement formula, we have:

[0055]

[0056] (3) Polarization angle matrix (AOP) obtained from Stokes vectors

[0057]

[0058] in It is the polarization angle of each pixel.

[0059] Please see Figure 1 This includes the following steps:

[0060] Step 1: Obtain the polarization angle of the backscattered light .

[0061] In the AOP matrix calculated from the four polarization images, a background region without foreground objects is selected. Calculate the mode of AOP as an estimate of the polarization angle of the backscattered light:

[0062]

[0063] This step utilizes the stable polarization characteristics and low noise of the background region to make the estimation of the polarization angle of the backscattered light more robust.

[0064] Step 2: Rotate the polarization space coordinate system to normalize the direction of the backscattered light to 0°.

[0065] Rotate the coordinate system counterclockwise This yields a new Stokes vector:

[0066]

[0067] Where the rotation matrix for:

[0068]

[0069] The polarization angle after rotation is:

[0070]

[0071] At this point, the backscattered light in the rotating coordinate system satisfies:

[0072]

[0073] This eliminates the interference of the background polarization direction on the estimation of the target polarization angle.

[0074] Step 3: Calculate the difference in polarization angle between the reflected light and the backscattered light from the target. and restore the target polarization angle .

[0075] In a rotating coordinate system, the polarization angle This represents the difference in polarization direction between the target reflected light and the background. Transforming this difference back to the original reference coordinate system yields the polarization angle of the target reflected light.

[0076]

[0077] This formula ensures that the polarization direction of the reflected light from the target is accurately estimated, even if the target's polarization characteristics are complex or spatially non-uniform.

[0078] Step 4: Establish a polarization degree solution model (DOP solution).

[0079] According to the polarization imaging model:

[0080]

[0081]

[0082] in: These represent the degree of polarization of the reflected light and the degree of polarization of the backscattered light, respectively. These represent the intensity of directly transmitted light and the intensity of backscattered light, respectively. The core of this invention is to solve for the globally optimal polarization parameter using the hierarchical optimization method proposed in step 6. Then, we can deduce D and B from the reverse.

[0083] Step 5: Construct the global optimization objective function.

[0084] To ensure stable polarization parameter solutions, this invention introduces three energy terms: EME contrast constraint. To enhance details, smoothness constraints To suppress noise, polarization consistency constraints .

[0085] The overall loss function is obtained by combining the results:

[0086]

[0087] Step 6: Solve the problem using the augmented Lagrangian method and the bounded Nelder-Mead hierarchical optimization method.

[0088] (1) Outer layer optimization: augmented Lagrange method.

[0089] Introduce constraints:

[0090]

[0091] Construct an augmented Lagrangian function:

[0092]

[0093] in and These are the Lagrange multiplier and the penalty factor, respectively.

[0094] (2) Inner layer optimization: Bounded Nelder-Mead simplex method.

[0095] In the given and Under the condition of parameters Within the physical range Perform continuous optimization.

[0096] The goal is to minimize:

[0097]

[0098] Update via outer ALM By solving the polarization degree parameters in the inner NM layer, this invention can obtain the globally optimal polarization parameters.

[0099] Step 7: Restore a clear image.

[0100] After obtaining the globally optimal polarization parameters, based on the imaging model:

[0101]

[0102] in It can be estimated from the brightest part of the background area. The final result is a restored high-contrast, clear underwater image.

[0103] Example

[0104] An underwater polarization imaging platform was set up in the laboratory, and the experimental setup is as follows:

[0105] An LED (Thorlabs M625L4-C1) with a center wavelength of 625nm was selected as the illumination source. The light emitted by the LED was polarized by a polarizing filter (PSG). A polarizer in front of the light source was used to rotate in any direction to produce incident polarized light. In this case, the difference in the polarization characteristics of the light source was only a difference in the polarization direction. Then, four images of the same scene were taken with a polarizing camera to obtain the Stokes vector. Since the Stokes vector of the input image is independent of the polarization state of the incident light, the angle of the polarizer in front of the light source has no effect on the results. The imaging device was a polarizing camera (Daheng imagingMER2-503-36U3 M POL). The polarizing camera simultaneously acquired intensity and polarization images in four polarization directions: 0°, 45°, 90°, and 135°. To simulate the underwater environment, a transparent glass tank (100cm × 40cm × 35cm) filled with water was used. To minimize the impact of reflected light from the inner surface of the tank on the experimental results, the inner wall was coated with light-absorbing black paper, and different proportions of skim milk were added to simulate different levels of turbidity in the underwater environment.

[0106] To verify the image restoration capability of the proposed method in highly polarized scene scenarios, we conducted experiments, and the results are as follows: Figure 2 As shown;

[0107] Using SSIM and PSNR as evaluation metrics, the results are as follows:

[0108] Table 1. SSIM and PSNR results of restored images under different turbidity conditions.

[0109] NTU SSIM PSNR 46.6 0.3394 16.4152 56.6 0.4188 16.8447 66.6 0.4827 15.2719 76.6 0.4031 16.4836 86.6 0.3270 15.8181 96.6 0.2825 13.3216

[0110] Experiments show that this method is practical and effective.

[0111] Although the present invention has been described above with reference to embodiments, various modifications can be made and components can be replaced with equivalents without departing from the scope of the invention. In particular, as long as there is no structural conflict, the features in the disclosed embodiments can be combined with each other in any manner. The lack of an exhaustive description of these combinations in this specification is merely for the sake of brevity and resource conservation. Therefore, the present invention is not limited to the specific embodiments disclosed herein, but includes all technical solutions falling within the scope of the claims.

Claims

1. An underwater polarization image restoration method based on an augmented Lagrange multiplier method, characterized by, Includes the following steps: Step one: Acquire the polarization angle of backscattered light ; Step two: Normalize the backscattered light direction to 0°: Rotate the coordinate system counterclockwise by to get the new Stokes vector: where the rotation matrix is: The polarization angle after rotation is: At this moment, the backscattered light in the rotating coordinate system satisfies ; Step 3: Calculate the difference in polarization angle between the reflected light and the backscattered light from the target. Restore the target polarization angle ; Step 4: Establish the polarization degree solution model: The degree of polarization of the reflected light from the target, This represents the degree of polarization of the backscattered light. For direct transmission of light intensity, The intensity of backscattered light; Step 5: Construct the global optimization objective function; Step Six: Solve: Introduce constraints: Constructor: and These are the Lagrange multipliers and the penalty factor, respectively, for the parameters. Within the physical range The goal is to perform continuous optimization and minimize: ； Step 7: Restore a clear image.

2. The underwater polarization image restoration method based on the augmented Lagrange multiplier method according to claim 1, characterized in that, The polarization angle in step one The specific calculation method is as follows: in the AOP matrix obtained from the four polarization images, the background region without foreground target is selected. Calculate the mode of AOP as an estimate of the polarization angle of the backscattered light: 。 3. The underwater polarization image restoration method based on the augmented Lagrange multiplier method according to claim 1, characterized in that, The polarization angle in step three The solution method is as follows: in the rotating coordinate system, the polarization angle... The difference between the polarization direction of the target reflected light and the background is represented by the value of the difference. Transforming this difference back to the original reference coordinate system yields the polarization angle of the target reflected light. 。 4. The underwater polarization image restoration method based on the augmented Lagrange multiplier method according to claim 1, characterized in that, The specific method for step five is to introduce EME contrast constraint. To enhance details, smoothness constraints To suppress noise, polarization consistency constraints The overall loss function is obtained by combining these results: 。 5. The underwater polarization image restoration method based on the augmented Lagrange multiplier method according to claim 1, characterized in that, The specific method for restoring a clear image in step seven is as follows: after obtaining the globally optimal polarization parameters, based on the imaging model: in The image can be estimated from the brightest part of the background area, and finally a high-contrast, clear underwater image can be obtained.

Images