An underwater imaging method based on suppressing forward scattered light

Abstract

An underwater imaging method based on suppressing forward scattered light. It belongs to the technical field of underwater polarization imaging, and specifically relates to the technical field of underwater polarization image restoration. The method comprises the following steps: S1, defining a global coordinate system and a local coordinate system of a water body; S2, constructing a forward scattering Mueller transmission matrix of water body particles; S3, converting the forward scattering Mueller matrix into an equivalent Jones matrix to obtain a forward scattering wavefront phase; S4, performing an inverse Fourier transform according to the obtained forward scattering wavefront phase, and constructing a forward scattering point spread function model of a water body; S5, suppressing underwater forward scattering according to the forward scattering point spread function model of a water body, and restoring the degraded image using an image restoration algorithm. The method of the present invention can be applied to the technical field of underwater target polarization imaging detection.

Description

Technical Field

[0001] The present invention belongs to the technical field of underwater polarization imaging, and in particular to the technical field of underwater polarization image restoration. Background Art

[0002] At present, with the increasing depletion of marine resources and the intensification of environmental pollution, the urgent need for underwater resource development has put forward requirements for high-performance underwater detection technology. Underwater imaging technology has the advantage of being able to intuitively and effectively reflect the underwater environment, which has established its key position in the fields of seabed topography imaging, underwater resource exploration, biological population monitoring, underwater target detection, archaeological excavation, etc.

[0003] However, the strong scattering of underwater light leads to the degradation of underwater imaging image quality, such as low contrast, dark overall image brightness, image blur, low resolution, etc., which brings difficulties to the detection process. The scattering effect of water on light waves is the main reason for the degradation of image contrast and resolution and image blur. Scattering mainly includes two processes: forward scattering and backscattering. After forward scattering, the light will deviate from the original transmission path, resulting in reduced image resolution and image blur; backscattered light will cause image contrast to decrease due to the information of suspended particles. At present, there are relatively mature backscattering suppression methods and technologies to reduce the impact of backscattering on underwater imaging quality; however, there are relatively few studies on forward scattering, and existing studies generally only focus on quantitative analysis of forward scattering imaging degradation models, while the underwater environment is relatively complex. Therefore, it is necessary to study the PSF model of the water environment in detail to improve the model precision and accuracy, so as to achieve clear imaging of underwater targets.

[0004] In 1908, G. Mie and P. Debye proposed that: when the particle radius is much smaller than the wavelength, the particle scattering effect and angular distribution are the same as the Rayleigh scattering law; when the particle radius is close to or greater than the wavelength, the scattering intensity does not obey the fourth power inverse law of the wavelength, and has little correlation with the wavelength, which is the same as the Mie scattering law. In 2012, the China Academy of Engineering Physics established a theoretical model of forward scattering for underwater laser imaging using the radiation transmission theory, and simulated and analyzed the variation of the forward scattering light power and influence coefficient of underwater imaging with water depth and attenuation coefficient. However, the research is only in the theoretical exploration stage, and has not been combined with experiments to further verify the accuracy and reliability of the theoretical model. In 2018, Xidian University studied an underwater polarization dehazing imaging method based on the optical correlation method, and used the edge method to estimate the scattering degradation function to restore the image in the scattering medium, but this research is only for polarization images, and the conclusion lacks universality. In 2022, the Xi'an Institute of Optics and Precision Mechanics of the Chinese Academy of Sciences studied the quality degradation problem of the underwater imaging process, constructed a mathematical model between underwater forward scattering and underwater imaging resolution, and conducted corresponding experiments to verify it, but did not consider how to suppress the influence of underwater forward scattering on underwater imaging effects.

[0005] When the underwater imaging system is imaging, the scattered light of near-field particles occupies a large proportion of the incident light of the optical system, which will have a certain impact on the imaging effect of the measured target, and forward scattering is prone to occur in the near-field environment, resulting in reduced underwater image resolution and image blur. At present, the water point spread function used by most researchers is relatively simple in form, and the imaging process represented is not accurate. Among them, the underwater point spread function model proposed by Jaffe and Wells is the most classic. Although it can effectively describe the characteristics of underwater light transmission to a certain extent, the model is based on a series of simplified assumptions. These simplified assumptions may not cover the complex underwater environment, resulting in limited applicability of the model; and because the underwater environment is extremely complex, the Jaffe and Wells model lacks a lot of experimental verification and data support in practical applications, so we urgently need an accurate water forward scattering PSF model to improve the resolution of underwater polarization imaging images and provide support for underwater search and rescue work in rivers and offshore areas. Summary of the invention

[0006] In order to solve the above technical problems, the present invention provides an underwater imaging method based on suppressing forward scattered light, the method comprising the following steps:

[0007] S1. Define the global coordinate system and the local coordinate system of the water body;

[0008] S2. Construct the forward scattering Mueller transmission matrix of water particles. The forward scattering Mueller transmission matrix of water particles is recorded as , is a 4×4 matrix whose elements are express;

[0009] S3, converting the forward scattered Mueller transmission matrix into an equivalent Jones matrix to obtain the forward scattered wavefront phase;

[0010] The forward scattered Mueller transmission matrix is ​​converted into an equivalent Jones matrix to obtain the forward scattered wavefront phase, specifically:

[0011] Remove the depolarization matrix from the forward scattering Mueller transmission matrix and then use: ; Get the forward scattered wavefront phase ,in,

[0012] ;

[0013] ; represents the solution phase operation;

[0014] S4, performing Fourier transform according to the obtained forward scattering wavefront phase, and constructing a water body forward scattering point spread function model;

[0015] The forward scattering point spread function model of the water body is constructed by performing Fourier transform according to the obtained forward scattering wavefront phase, by: ;

[0016] To achieve, is the forward scattering point spread function of water, is an empirical constant, is the inverse Fourier transform, is the attenuation coefficient, is the distance light travels in water, The operation represented by is solving the natural exponential;

[0017] S5. Underwater forward scattering is suppressed according to the water body forward scattering point spread function model, and the degraded image is restored using the image restoration algorithm.

[0018] The beneficial effects of the method of the present invention are:

[0019] (1) By constructing the forward scattering Mueller transmission matrix of water particles, the light propagation and interaction process in water can be simulated more accurately, thereby improving the accuracy of light transmission simulation;

[0020] (2) The new forward scattering point spread function model of water bodies constructed in the present invention can develop a more effective underwater image restoration method, achieve clear imaging of forward scattered light underwater, improve image resolution, and enhance the stability and robustness of the underwater imaging system.

[0021] The method of the present invention can be applied in the field of underwater target polarization imaging detection technology. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] Figure 1 is a flow chart of the method of the present invention;

[0023] Figure 2 It is a schematic diagram of the transformation between the global coordinate system of the water body and the local coordinate system of the water body;

[0024] Figure 3 The figures are image restoration results using the method of the present invention, wherein Figure (a) is the original image taken with underwater polarization imaging, Figure (b) is the underwater polarization imaging effect image obtained by other methods; and Figure (c) is the underwater polarization imaging effect image obtained by the method of the present invention. DETAILED DESCRIPTION

[0025] The technical solution of the present invention will be described clearly and completely below in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the protection scope of the present invention.

[0026] like Figure 1 The flowchart of the method of the present invention is shown, and the method of the present invention is specifically:

[0027] S1. Define the global coordinate system and the local coordinate system of the water body;

[0028] S2, construct the forward scattering Mueller transmission matrix of water particles;

[0029] S3, convert the forward scattering Mueller transmission matrix into an equivalent Jones matrix to obtain the forward scattering wavefront phase;

[0030] S4. Perform inverse Fourier transform based on the obtained forward scattered wavefront phase to construct a water body forward scattering point spread function (PSF, Point Spread Function) model;

[0031] S5. Underwater forward scattering is suppressed according to the water body forward scattering point spread function model, and the degraded image is restored using the image restoration algorithm.

[0032] Each operation step is further described in detail.

[0033] For step S1, the definition of the global coordinate system and the local coordinate system of the water body is as follows: select a fixed geographical point underwater as the reference point (origin), use the X-axis, Y-axis and Z-axis to represent the horizontal direction (geographic east and west), vertical direction (geographic south and north) and depth direction (vertically up or down), use the right-handed coordinate system to describe the absolute position and direction of the entire water area, and thus establish an underwater global coordinate system. The local coordinate system provides detailed information and changes of underwater objects. In an underwater environment, the position and other information in the local coordinate system need to be converted to the global coordinate system through a coordinate transformation matrix for description and analysis, such as Figure 2 As shown in the figure, a schematic diagram of the transformation between the global coordinate system of the water body and the local coordinate system of the water body is shown. Both the global coordinate system of the water body and the local coordinate system of the water body adopt the Cartesian coordinate system.

[0034] Assume that the incident light is in the global coordinate system {x, y, z} of the water body The propagation vector is ,in, a , b , c They respectively represent the spatial coordinate vectors corresponding to the three axes of the global Cartesian coordinate system of the water body, and a transformation matrix T is introduced to realize the rotation transformation between the local coordinate system of the water body and the global coordinate system of the water body.

[0035] Specifically: ;

[0036] in, is the coordinate in the underwater global coordinate system, are the coordinates in the underwater local coordinate system, and ,in, is the angle between the incident light and the z-axis of the global coordinate system of the water body, i.e. the scattering angle, is the angle between the incident light and the x-axis of the global coordinate system of the water body, i.e., the azimuth. , .

[0037] For step S2, the forward scattering Mueller transmission matrix of water particles is constructed as follows:

[0038] S1. Set the number of water particles to m, and the outgoing light of the previous water particle is the incident light of the next water particle;

[0039] S2. Starting from the first water particle, the global coordinate representation of the Mie scattering coherent transmission matrix of each water particle is solved in turn;

[0040] S3. Multiply the global coordinate representations of the Mie scattering coherent transfer matrices of m water particles in sequence, and the result is recorded as , is a 9×9 matrix whose elements are express;

[0041] S4, the forward scattering Mueller transmission matrix of water particles is recorded as , is a 4×4 matrix whose elements are express, pass Solve the elements in , and the conversion relationship is as follows:

[0042] ;

[0043] ; ; ; ; ; ; ; ; ; ; ; ; ; ;

[0044] ;

[0045] in, i represents the imaginary part, i The square of is -1.

[0046] The global coordinate representation of the Mie scattering coherent transmission matrix of each water particle is as follows:

[0047] ;

[0048] in, is the propagation vector of the light emitted by the mth water particle, is the propagation vector of the incident light of the mth water particle, is the local coordinate representation of the Mie scattering coherent transfer matrix of the mth water particle, and the operator " " represents the operation of tensor product, operator " The operation represented by ” is conjugation.

[0049] = ;

[0050] in, ; ; ; ; ; ; ; ; ; ; ; ; ; ; ;

[0051] ;

[0052] in, ;

[0053] ;

[0054] ;

[0055] ;

[0056] in, is the intensity of the polarization component of the scattered light perpendicular to the scattering plane after the incident light passes through the mth water particle, is the intensity of the polarization component of the scattered light parallel to the scattering plane after the incident light passes through the mth water particle; , , , , , , , , , , and Both are 0.

[0057] Let's take the first water particle as an example to further explain How to obtain:

[0058] The global coordinates of the Mie scattering coherent transfer matrix of the first water particle are expressed as ,but , where k in 1 represents the propagation vector of the initial incident light,

[0059] , is the angle between the incident light of the first water particle and the z-axis of the water body global coordinate system, i.e. the scattering angle, is the angle between the incident light of the first water particle and the x-axis of the water body's global coordinate system, i.e., the azimuth;

[0060] = , is the angle between the outgoing light of the first water particle and the z-axis of the water body global coordinate system, i.e. the scattering angle, is the angle between the outgoing light of the first water particle and the x-axis of the water body global coordinate system, i.e., the azimuth;

[0061] Will , , , Bring in separately

[0062] ; That is, we can get the simplified :

[0063]

[0064]

[0065] For step S3, the forward scattered Mueller transmission matrix is ​​converted into an equivalent Jones matrix to obtain the forward scattered wavefront phase, specifically:

[0066] After removing the depolarization matrix from the forward scattered Mueller transmission matrix, the non-depolarized Mueller matrix is ​​converted to an equivalent Jones matrix using the following relationship:

[0067] ; ; ; ;

[0068] in, represents the amplitude and phase changes of the horizontal polarization component of the incident light, It indicates the amplitude and phase change of the horizontal polarization component of the incident light being converted into the vertical polarization component. It indicates that the vertical polarization component of the incident light is converted into the amplitude and phase change of the horizontal polarization component. represents the amplitude and phase changes of the vertical polarization component of the incident light, represents the phase operation to be solved, and then by: ; Get the forward scattered wavefront phase .

[0069] For step S4, the forward scattering wavefront phase is obtained and Fourier transform is performed to construct a water body forward scattering point spread function model, by:

[0070] ;

[0071] To achieve, is the forward scattering point spread function of water, is an empirical constant, is the Fourier transform, is the attenuation coefficient, is the distance light travels in water, The operation represented by is to solve the natural exponential.

[0072] Further explanation of the point spread function solution process:

[0073] The forward scattered wavefront phase corresponds to the phase part of the complex amplitude. The forward scattered point spread function of water is the Fourier transform of the wavefront phase and can be expressed as:

[0074] ;

[0075] The forward scattered component is similar to the direct transmission, but it represents the part of the incident light reflected by the target that is scattered at a small angle before entering the detector. The forward scattered light component reaching the detector is related to the direct target information light, which produces convolution and causes image blur:

[0076] ;

[0077] here, represents the forward scattered light signal, Represents direct target information light, The distance light travels in water d For example, the operator " " represents the operation of convolution, because the farther the object is, the wider the support range of the blur kernel is. The blur kernel represents the weight relationship between each pixel in the image and the surrounding pixels. It is used to describe the degree of image blur and the way the blur effect is produced. Therefore, the point spread function The calculation method is:

[0078] .

[0079] For step S5, the underwater forward scattering is suppressed according to the water body forward scattering point spread function model, and the degraded image is restored using the image restoration algorithm, by:

[0080] ;

[0081] To achieve, is the restored image after the k+1th iteration, is the restored image after the kth iteration, is the forward scattering point spread function of the water body obtained in step S4, For degraded images.

[0082] The process of restoring a degraded image using an image restoration algorithm is further described as follows:

[0083] The Lucky-Richardson restoration algorithm is used to restore the degraded image to eliminate the influence of forward scattering on the image and improve the clarity and resolution of the image;

[0084] The Lucy-Richardson algorithm uses the expectation maximization algorithm and maximizes the likelihood of the restored image after a certain number of iterations. This algorithm requires a good estimate of the image degradation process to achieve the optimal estimate. The algorithm is based on Bayesian theory to derive image iterative restoration. The formula of continuous Bayesian theory can be written as follows:

[0085] ;

[0086] The formula of discrete Bayesian theory can be written as follows:

[0087] ;

[0088] in, represents conditional probability, which means Under the conditions of the event, The probability of an event occurring; It means in Under the conditions of the event, The probability of an event occurring; express The probability of an event occurring.

[0089] The image degradation process is modeled as a water body forward scattering point spread function model and an observed blurred image. Suppose the original input image is , the forward scattering point spread function of water is , here This is the forward scattering point spread function of the water body obtained in step S4, and the additive noise is , the observed blurred image, that is, the degraded image is g ( x , y ), the restored image reconstructed after restoration filtering is , if the system is a linear, position-invariant process, then the degradation image given in the spatial domain can be given by:

[0090] ;

[0091] From the knowledge of digital signal processing, we know that spatial convolution can be expressed by product in the frequency domain, so the above formula is equivalent to the following frequency domain expression:

[0092] ;

[0093] in, for Represented in the frequency domain, for Represented in the frequency domain, for Representation in the frequency domain.

[0094] After normalizing the pixel values ​​in the image, if the pixel values ​​are regarded as probability values, the entire image can be regarded as a probability map. The probability of is the largest, among which, That is , That is , by maximizing the posterior probability , the most likely restored image can be found , that is, given a degraded image In the case of , the clearest image that best fits the statistical model can be expressed as follows after Bayesian solution:

[0095] ;

[0096] In the above formula and is a constant, Equivalent to , That is , so just use The maximum value is sufficient. For the above formula The Poisson model can be used for calculation. The Poisson statistical model formula is:

[0097] s)= ;

[0098] In the formula, represents the average number of times an event occurs within a given time frame, and , ;

[0099] According to the Poisson equation statistical model, if each pixel of the degraded image is independent of each other, then the conditional probability distribution It can be expressed as the following formula:

[0100] ;

[0101] According to the maximum likelihood estimation principle, taking the logarithm of the above formula yields:

[0102] ;

[0103] Taking the derivative of the above formula and making the result equal to 0, we can get:

[0104] ;

[0105] The solution is:

[0106] =1;

[0107] After iteratively solving the above equation using Newton's descent method, we can get:

[0108] ;

[0109] in, is the restored image after the k+1th iteration.

[0110] At the beginning of the algorithm, the residual after each iteration (i.e., the difference between the original image and the current estimated image) is set to be monitored. The threshold of the difference value can be adjusted and evaluated in the range of 5% to 10%. When the change in the residual is less than the set threshold, the algorithm can be terminated.

[0111] The Lucky-Richardson algorithm convolves the known forward scattering point spread function model of water with the observed blurred image, and then compares it with the current image estimate to calculate an update. This update is used to update the estimated value of the image to make it closer to the original clear image. Finally, the effectiveness of the newly established forward scattering point spread function model of water is verified through experiments, and the restored image is compared and analyzed with the original image to evaluate the restoration effect. According to the experimental results such as the blur degree and noise level of the image, the parameters or structure of the forward scattering point spread function model of water are adjusted, and the forward scattering point spread function model of water is optimized to obtain a better restoration effect.

[0112] Figure 3 The figures are image restoration results using the method of the present invention, wherein Figure (a) is the original image taken with underwater polarization imaging, Figure (b) is the underwater polarization imaging effect image obtained by other methods; and Figure (c) is the underwater polarization imaging effect image obtained by the method of the present invention.

Claims

1. An underwater imaging method based on suppressing forward scattered light, characterized in that: The method comprises the following steps: S1. Define the global coordinate system and the local coordinate system of the water body; S2. Construct the forward scattering Mueller transmission matrix of water particles. The forward scattering Mueller transmission matrix of water particles is recorded as , is a 4×4 matrix whose elements are express; S3, converting the forward scattered Mueller transmission matrix into an equivalent Jones matrix to obtain the forward scattered wavefront phase; The forward scattered Mueller transmission matrix is ​​converted into an equivalent Jones matrix to obtain the forward scattered wavefront phase, specifically: Remove the depolarization matrix from the forward scattering Mueller transmission matrix and then use: Get the forward scattered wavefront phase ,in, ； , i represents the imaginary part, i The square of is -1; represents the solution phase operation; S4, performing Fourier transform according to the obtained forward scattering wavefront phase, and constructing a water body forward scattering point spread function model; The forward scattering point spread function model of the water body is constructed by performing Fourier transform according to the obtained forward scattering wavefront phase, by: To achieve, is the forward scattering point spread function of water, is an empirical constant, is the inverse Fourier transform, is the attenuation coefficient, is the distance light travels in water, The operation represented by is solving the natural exponential; S5. Underwater forward scattering is suppressed according to the water body forward scattering point spread function model, and the degraded image is restored using the image restoration algorithm.

2. The underwater imaging method based on suppressing forward scattered light according to claim 1, characterized in that: The definition of the water body global coordinate system and the water body local coordinate system is specifically: Select a fixed geographical point underwater as the reference point, use the X-axis, Y-axis and Z-axis to represent the horizontal direction, vertical direction and depth direction respectively, use the right-handed coordinate system to describe the absolute position and direction of the entire water area, thereby establishing the global coordinate system of the water body and defining the coordinate transformation matrix , to realize the conversion between the global coordinate system of the water body and the local coordinate system of the water body: ； in, is the coordinate in the global coordinate system of the water body, are the coordinates in the local coordinate system of the water body, and ,in, is the angle between the incident light and the z-axis of the global coordinate system of the water body, i.e. the scattering angle, It is the angle between the incident light and the x-axis of the water body's global coordinate system, that is, the azimuth.

3. The underwater imaging method based on suppressing forward scattered light according to claim 2, characterized in that: The construction of the forward scattering Mueller transmission matrix of water particles is specifically as follows: S31, setting the number of water particles to m, and the outgoing light of the previous water particle is the incident light of the next water particle; S32, starting from the first water particle, solving the global coordinate representation of the Mie scattering coherent transfer matrix of each water particle in turn; S32. Multiply the global coordinate representations of the Mie scattering coherent transmission matrices of the m water particles in sequence, and the result is recorded as , is a 9×9 matrix whose elements are express; S34, the forward scattering Mueller transmission matrix of water particles is recorded as , is a 4×4 matrix whose elements are express, pass Solve the elements in , and the conversion relationship is as follows: ； ； ； ； ； ； ； ； ； ； ； ； ； ； ； 。 4. The underwater imaging method based on suppressing forward scattered light according to claim 3, characterized in that: The global coordinate representation of the Mie scattering coherent transmission matrix of each water particle is as follows: ； in, is the propagation vector of the light emitted by the mth water particle, is the propagation vector of the incident light of the mth water particle, is the local coordinate representation of the Mie scattering coherent transfer matrix of the mth water particle, and the operator" "The operation represented by the tensor product operator" The operation represented by ” is conjugation.

5. The underwater imaging method based on suppressing forward scattered light according to claim 4, characterized in that: = ； in, ; ; ； ； ； ； ； ； ； ； ； ； ； ； ； ； in, ; ； ； ； in, is the intensity of the polarization component of the scattered light perpendicular to the scattering plane after the incident light passes through the mth water particle, is the intensity of the polarization component of the scattered light parallel to the scattering plane after the incident light passes through the mth water particle; , , , , , , , , , , and Both are 0.

6. The underwater imaging method based on suppressing forward scattered light according to claim 5, characterized in that: The method suppresses underwater forward scattering according to the forward scattering point spread function model of water body, and restores the degraded image using the image restoration algorithm, by: To achieve, is the restored image after the k+1th iteration, For the k The restored image after iterations is is the forward scattering point spread function of the water body obtained in step S4, is the degenerate image, the operator" ” represents the operation of convolution.

Images