Rethinking of Underwater Image Restoration Based on Circularly Polarized Light

Abstract

Polarimetric imaging technology plays a crucial role in de-scattering, particularly in the field of underwater image restoration. Circularly polarized light (or the underlying circular polarization memory effect) has been proven to better preserve the polarization characteristics of detected light. Utilizing circularly polarized light as illumination can further enhance the effectiveness of polarization de-scattering techniques. After rethinking the advantages of circularly polarized light, this paper proposes a new method for underwater polarimetric imaging restoration that leverages the pre-processing of polarized sub-images and the correlation of polarization characteristics (i.e., the angle of polarization and degree of polarization). Additionally, to address the challenge of selecting scattering light parameters due to uneven light fields in target scenes, an intensity adjustment factor search algorithm is designed. This algorithm eliminates the need for the manual selection of scattering light parameters, effectively solving the problem of uneven illumination in restoration results. A series of experiments demonstrate that, compared to traditional algorithms, the proposed method offers superior detail restoration and higher robustness.

1. Introduction

Under turbid water, due to the absorption by the water itself and the scattering and absorption by suspended particles, the energy (the intensity power) of the light transmission process decreases sharply [1,2,3,4]. Specifically, the light signals collected by cameras include both the attenuated reflected light from the target object (desired) and the background scattered light (undesired); as a result, the image quality is significantly reduced, greatly limiting the application of underwater optical imaging in many fields [5,6,7,8]. To address this issue, various methods have been proposed, mainly divided into two approaches: enhancing the reflected light from the target object and suppressing or eliminating the backscattering light [9,10,11,12].

Particularly, the discovery that backscattering light exhibits partial polarization characteristics has made polarized light and polarimetric algorithms one of the mainstream methods for underwater image restoration [13,14,15,16,17]. These methods can be traced back to 2001, when Tyo et al. proposed an underwater polarization difference model (PDM), which improved the imaging contrast by calculating the difference between two orthogonal polarized sub-images [10]. Later, based on the traditional atmospheric scattering model, Schechner et al. developed a polarimetric restoration technique for underwater imaging with active light illumination [11]. This technique involves acquiring two sub-images of orthogonal polarization states to calculate the degree of polarization (DoP) of the backscattering light, thereby achieving the transmittance corresponding to the scattering medium, and eliminating the backscattering light and reconstructing the target light. Liang et al. further developed Schechner’s model, proposing a new model based on the analysis of the polarization angle of backscattering, which has greater robustness compared to the traditional PDM [18]. The core of this method involves acquiring images corresponding to three polarization states and solving the Stokes vector. Zhu et al., not strictly following the mathematical expressions of the atmospheric scattering model, proposed a differential imaging theory based on common-mode suppression theory, which suppressed backscattering light and enhanced target contrast [19]. All these methods have effectively restored underwater images, but they have one thing in common: their physical models and algorithmic foundations are based on linearly polarized light, and the active illumination sources used are either natural light or linearly polarized light [20,21,22,23,24].

Early studies have shown that circularly polarized light maintains its polarization better than linearly polarized light, meaning that after passing through the same optical thickness of scattering media, circularly polarized light tends to retain a higher degree of polarization; this characteristic is also known as the “memory effect”. Based on this, researchers began to explore the introduction of circularly polarized light into underwater image restoration [25,26,27]. From the perspective of analyzing the polarization state of the illumination source and the reflected light from the target scene, methods based on linear polarization only consider the first three components of the Stokes vector, while methods based on circular polarization must consider the fourth component. This component is related to the phase difference (i.e., retardance) caused by different vibration directions in the scattering medium [28,29]. In fact, compared to linearly polarization-based underwater image restoration techniques, the development of techniques related to circular polarization has been relatively slow [30,31]; although there are many recent mainstream underwater polarization de-scattering imaging techniques, few are based on circularly polarized light. This is understandable, as the physical imaging systems for circularly polarized light tend to be more complex. For example, in 2018, Hu et al. first proposed an underwater de-scattering method based on circularly polarized illumination and a two-steps processing way [32]. Zhang et al. explored the effect of the circularly polarized light in dehazing and proposed a polarimetric method that jointly considers the linear and circular polarization effects of backscattering [30]. Even so, re-evaluating underwater image restoration techniques based on circularly polarized light is considered meaningful, not only as an effective supplement to linearly polarized light algorithms, but also as a potential solution for scenarios where linearly polarized light algorithms fail.

In this paper, we propose a novel method based on circularly polarized light illumination (specifically using the Stokes vector) for underwater de-scattering imaging. This method involves histogram stretching pre-processing of polarized sub-images and leveraging the correlation between polarization characteristics, that is, the DoP and the angle of polarization (AoP) to obtain sub-images in other polarization directions. By integrating Liang et al.’s model, we achieve significantly enhanced de-scattering effects. Additionally, we introduce a method for determining scattering light parameters based on the intensity adjustment factor search, effectively ensuring the uniformity of the restored results. The following sections will introduce the basic model of underwater polarization imaging, describe the proposed method, present the experimental and comparative results, and provide conclusions and future outlooks.

2. Models and Methods

The process of imaging through a turbid medium like underwater environments involves a complex interaction of light transmission and scattering. The imaging model can be fundamentally divided into two main components: the direct transmission and backscattering. The mathematical formulation is as follows [11]:

$$I(x,y)=D(x,y)+B(x,y)=T(x,y)L(x,y)+A_{\infty }\left(1-T(x,y)\right)$$

(1)

where $I(x,y)$ represents the image captured by the camera, which is a composite of the following components: (1) Direct Transmission $D(x,y)$, which accounts for the light that travels directly from the underwater object to the camera without being scattered by the medium. It combines the inherent radiance $L(x,y)$ of the object with the medium transmittance $T(x,y)$, which decreases with increasing water depth and particulate concentration. (2) Backscattering $B(x,y)$, representing light that is scattered back towards the camera; this component arises from light interactions with suspended particles in the water. The coefficient $A_{\infty }$ represents the intensity of light that is backscattered, which is assumed to be a constant across the viewing field but varies with the clarity and composition of the water. The transmittance can be expressed as

$$T(x,y)=exp\left[-\beta z\right(x,y\left)\right]$$

(2)

where the attenuation coefficient $\beta$ is particularly crucial in underwater environments. The transmittance $T(x,y)$ primarily depends on the optical path length through the water, which varies spatially based on the distance $z(x,y)$ from the object to the camera and the water’s optical properties.

The subsequent step involves the restoration process to acquire a clear image, specifically by solving for $L(x,y)$:

$$L(x,y)={\displaystyle \frac{I(x,y)-B(x,y)}{1-B(x,y)/A_{\infty }}}$$

(3)

A conventional polarimetric restoration technique developed by Schechner enables a more accurate representation of the underwater scene by compensating for the light absorption and scattering effects, providing clearer and more detailed underwater images [11]. However, it relies on linearly polarized light and often encounters difficulties under heavily turbid conditions due to intense scattering. Research demonstrates that circularly polarized light better preserves its polarization in scattering environments—a phenomenon known as the polarization memory effect, as documented in references [25,26].

In addition, we also conducted Monte Carlo simulation experiments to further elucidate these phenomena. In these experiments, particles with a diameter of 1 μm were utilized, and illumination was provided by a 520 nm light source (within the “blue-green window” region of the ocean). The refractive index of the particles is 1.59, and the refractive index of the water is 1.33, which results in scattering effects that are crucial to consider in our light scattering calculations. The particle concentration was initially established at 5 × 10⁻⁵/μm³ and subsequently increased to 1 × 10⁻³/μm³ throughout the course of the experiment. The simulation results are shown in Figure 1. For the linearly polarized light source, the corresponding Stokes vector is [1, 1, 0, 0]^T, indicating horizontally polarized light. For the circularly polarized light source, the corresponding Stokes vector is [1, 0, 0, 1]^T, indicating right-handed circularly polarized light. Additionally, we also presented the simulation results by using a light source with a 630 nm wavelength, as shown in Figure 1 (red lines). From this figure, we see that although there is a minor difference between the light sources with two wavelengths, both of them suggest potential advantages in employing circularly polarized light for image recovery.

In the field of circular polarization-based methods, a typical example is that which Hu et. al. proposed: a method by using both the circular and linear polarization information derived from the measured Stokes vector of the scene [32]. This method divides the reflected light from the target scene (which includes backscattering light) into three parts: circular polarization, linear polarization, and non-polarization. And then it applies a model similar to Schechner’s to both the circular and linear polarization components. However, this stepwise approach to suppressing circularly and linearly polarized scattering light disrupts the original polarization characteristics of the scene. To avoid this issue, we propose a new one-step processing algorithm, based on Liang et al.’s Stokes de-scattering model that utilizes DoP and AoP [18].

In this model, one first needs four polarized images related to different polarization states; for example, three linearly polarized images $I_{0°}$, $I_{90°}$, $I_{45°}$, and the right circularly polarized $I_c$. All these are achieved by adjusting the polarization state analysis (PSA) module before the camera [17,32,33]. Then, one can calculate the Stokes maps $\mathbf{S}$ $={[s_0,s_1,s_2,s_3]}^T$. Based on $\mathbf{S}$, the degree of linear polarization, i.e., DoLP ($p_l$), DoP (p), and AoP ($\theta$), can be calculated by the following expressions.

$$\begin{array}{cc}\hfill p_l(x,y)& ={\displaystyle \frac{\sqrt{s_1^2(x,y)+s_2^2(x,y)}}{s_0(x,y)}},\hfill \\ \hfill p(x,y)& ={\displaystyle \frac{\sqrt{s_1^2(x,y)+s_2^2(x,y)+s_3^2(x,y)}}{s_0(x,y)}},\hfill \\ \hfill \theta (x,y)& ={\displaystyle \frac{1}{2}}arctan{\displaystyle \frac{s_2(x,y)}{s_1(x,y)}}.\hfill \end{array}$$

(4)

According to Liang’s model, the intensity image of backscattering, i.e., $B(x,y)$, can be expressed by:

$$\begin{array}{cc}\hfill B(x,y)& ={\displaystyle \frac{I_{0°}(x,y)-s_0(x,y)(1-p(x,y))/2}{p_B{cos}^2{\theta }_B}}\hfill \\ \hfill & ={\displaystyle \frac{I_{90°}(x,y)-s_0(x,y)(1-p(x,y))/2}{p_B{sin}^2{\theta }_B}},\hfill \end{array}$$

(5)

where $I_{0°}$ and $I_{90°}$ denote the $0°$ and $90°$ linearly polarized images. $p_B$ and ${\theta }_B$ denote the DoP and AoP of the backscattering underwater. Once the backscattering light $B(x,y)$ is estimated, the clear image $L(x,y)$ related to the target scene can be obtained according to Equation (3). It should be noted that in the original model by Liang et al. [18], the parameters p and $p_B$ actually represent the DoLP. In the model under circularly polarized light illumination, they could be adjusted to represent the total degree of polarization, i.e., DoP.

To further enhance the performance of the original model, and also inspired by the work in Ref. [1], we proposed a method combining the imaging preprocessing and polarimetric imaging model. This method first uses histogram stretching for one of the polarized sub-images, for example, $I_{90°}$; this preprocessing method can be substituted with others, such as the frequency domain filtering [34,35]. The processed polarized image can be expressed as:

$$I_{90}^{new}(x,y)={\displaystyle \frac{I_{90°}(x,y)-I_{90}^{min}}{I_{90}^{max}-I_{90}^{min}}}$$

(6)

where $I_{90}^{min}$ and $I_{90}^{max}$ denote the minimum and maximum pixel values in the $I_{90°}(x,y)$ image.

The next step is to obtain new polarized images for other directions. In fact, these polarization sub-images are interconnected through the polarization degree and polarization angle, which are their intrinsic associations. Therefore, when one changes, we can update the other polarization sub-images by using the polarization characteristics, such as the DoP and AoP, associated with the original scene.

$$\begin{array}{cc}\hfill & I_0^{new}(x,y)={\displaystyle \frac{I_{90}^{new}(x,y)\left(1+p_{l}cos2\theta \right)}{1-p_{l}cos2\theta }}\hfill \\ \hfill & I_{45}^{new}(x,y)={\displaystyle \frac{I_{90}^{new}(x,y)\left(1+p_{l}sin2\theta \right)}{1-p_{l}cos2\theta }}\hfill \end{array}$$

(7)

It should be noted that, in Equation (7), we did not show the updated right circularly polarized light $I_c$, as it is not directly used for obtaining the final result; we just need the map of DoP.

According to Equations (3) and (5), to obtain the final restoration result $L(x,y)$, we still need to estimate three additional parameters (i.e., $p_B$, ${\theta }_B$, and $A_{\infty }$). Traditional methods typically start by selecting a background region to estimate the backscattering parameters (i.e., $p_B$ and ${\theta }_B$). It ensures the reliability of the backscattering estimation but may fail when there is no obvious background region, such as in highly turbid scenes [1]. The conventional solution multiplies the DoP/DoLP of the backscattering by a modulation factor, which may deteriorate the uneven light intensity distribution in underwater scenes with active illumination [36]. To address this, we first eliminate the influence of selecting background areas on parameter estimation by taking the average value of the top $1/1000$ of p and $\theta$ values across the entire scene as the estimate. In reality, most objects in nature exhibit weak polarization, whereas backscattering light tends to have relatively evident polarization characteristics; this forms the fundamental assumption underlying traditional polarization despeckling models and algorithms [1,11].

The estimation of parameter $A_{\infty }$ directly influences the uniformity of the restoration results, especially in underwater scenes with active illumination. This arises from the fact that active illumination produces light spot energy that decays in a Gaussian distribution along the optical axis. Furthermore, when the scene’s range exceeds the size of the illumination spot, there is a higher concentration of light energy near the spot and reduced energy in more distant regions. To represent the program’s logic in a consolidated mathematical formulation, we can express it as an optimization problem that seeks to find the optimal parameter $ϵ$ that minimizes the maximum value of $L_s$ (which is the result after applying CLAHE, i.e., Contrast Limited Adaptive Histogram Equalization, normalization to the final recovered result L) while ensuring it remains within the acceptable bounds. The optimization objective can be expressed as:

$$\begin{array}{cc}\hfill {minimize}_{ϵ}& max{L}_s\left(ϵ\right)\hfill \\ \hfill \mathrm{subject}\mathrm{to}& L_s\left(ϵ\right)=CLAHE\left({\displaystyle \frac{I(x,y)-B(x,y)}{1-\frac{B(x,y)}{A_{\infty }}}}\right)\hfill \\ \hfill & A_{\infty }=ϵ·Ma{x}_B\hfill \\ \hfill & max{L}_s(ϵ,x,y)\le 1,ϵ\ge 1\hfill \end{array}$$

(8)

where $Ma{x}_B$ denotes the top $1/1000$ of $B(x,y)$ values across the entire scene. The process iterates over a range of potential $ϵ$ to find the minimum value that keeps $L_s$ within the upper bound of 1, thus ensuring the restored image’s uniformity and intensity are within realistic limits. It is noteworthy that the objective function in the above formula is single-parameter and only involves simple operations, resulting in a very low computational cost. Finally, by putting the optimal value of $ϵ$ into $L_s(x,y)$, one can obtain the final recovery result.

3. Experiments and Results

To validate the image recovery method detailed in Section 2, we conducted real-world underwater imaging experiments. The experimental setup, depicted in Figure 2, is meticulously designed to replicate turbid underwater conditions and facilitate polarization measurements. The setup utilizes a light source, which is passed through a beam expander (BE) to shape the light beam appropriately. An optical filter in conjunction with a light-emitting diode (LED) generates the active illumination, centered at a wavelength of about 630 nm. This illumination light is further modulated by a Polarization State Generator (PSG), which comprises a linear polarizer and a quarter-wave plate (QWP) [37]. The PSG modulates the light to produce circularly polarized light, ensuring controlled and consistent illumination for the experiments. A transparent polymethyl methacrylate (PMMA) tank is filled with water and made turbid by adding milk (with a protein content of 3.6 g/100 mL and fat content of 4.4 g/100 mL), simulating realistic underwater conditions. The target object is submerged in this turbid water, providing a challenging environment for imaging and testing the algorithm. Finally, the images are captured using a monochrome CCD camera (AVT Stingray F-033B, Stadtroda, Germany). To analyze the polarization state of the reflected light, a Polarization State Analyzer (PSA) is placed in front of the camera. The PSA, also comprising a linear polarizer and a QWP, ensures that the polarization information is well-captured [32].

It is worth noting that during the actual imaging process, we fixed the angles of certain polarization components in the PSG to ensure that the Stokes vector of the illumination polarized light is ${\mathbf{S}}_{\mathrm{in}}={[1,0,0,1]}^T$, which is right-handed circularly polarized light (it can also be replaced with circularly polarized light in other directions). By adjusting the polarization components in the PSA four times, we obtained the corresponding polarization sub-images for four characteristic solutions. Based on this, we can solve the Stokes map of the reflected light from the target scene [33]. More details can be found in Refs [18,32].

For the first set of experiments, our target object is a Rubik’s Cube (with some text and patterns on it), and its clear image is shown in Figure 3a. When the target is placed in turbid water, the imaging result is also shown in Figure 3a. It can be observed that, compared to the clear image, the imaging quality of the target in turbid water is significantly degraded, and its detail becomes blurred and indistinguishable. Additionally, the implementation of active illumination introduces a degree of non-uniformity in the spatial distribution of light field intensity across the scene. Specifically, the intensity in the upper and lower corners on the right side of the image is markedly lower compared to the left side, attributable to the light source being positioned off-center toward the left. As previously mentioned, to obtain the four Stokes parameters $s_0$, $s_1$, $s_2$, and $s_3$, the directions of the linear polarizer and QWP in the PSA need to be modulated four times, and then the images are captured. Figure 3b shows the four images taken under specific directions of the linear polarizer and QWP. Based on these images, the four Stokes parameters can be calculated, as shown in Figure 3c. The first three polarized images ($I_{0°}$, $I_{45°}$, and $I_{90°}$) were captured when the polarizer (without placing QWP) was rotated to $0°$, $45°$, and $90°$, respectively. The last image related to the circular ($I_c$) was captured when the $45°$ polarizer was followed by a horizontal direction QWP. Then, we could calculate the Stokes maps based on the four polarized images; the detailed calculations are shown in Figure 3c.

We present the recovery results by different methods (Liang’s method [18], our proposed method, He’s method [38], Multi-scale Retinex [39], and CLAHE [40]) in Figure 4. From these images, we find that the proposed methods (i.e., ours) restore the detailed information well in the target and obtain better image contrast compared with others. Although Liang’s and He’s methods can also restore the scene well, there is still some blurring in the recovered results. To further validate the effectiveness of the proposed method, we magnified local details (highlighted by the yellow box in Figure 4) for comparison, as shown in Figure 5. The first row of Figure 5 displays the raw intensity image under turbid water conditions and the results recovered using different methods. The second row presents the corresponding three-dimensional (3D) gray-scale plots, providing a visual representation of the intensity variation and depth of detail restored by each method.

From the first row in Figure 5, it is evident that the raw image in turbid water suffers from severe degradation, with target details becoming unrecognizable. The image recovered using Liang’s method shows some improvement, but the details remain insufficient, such as the Chinese words. He’s method, Multi-Retinex, and CLAHE also demonstrate varying degrees of improvement, but none match the performance of our proposed method. Our proposed method, in the third position, significantly enhances the clarity and detail of the target object, outperforming the other methods. The 3D gray-scale plots in the second row offer a quantitative perspective on the restoration performance. Compared to other methods, the gray-scale plot corresponding to our method exhibits higher peaks and more distinct valleys, indicating better preservation of intensity variations and finer details. In contrast, the 3D surfaces of the other methods are relatively flatter and less detailed, corroborating the visual assessment from the first row. Notably, our proposed algorithm includes steps to optimize the estimation of scattering parameters, resulting in a more uniform light field distribution in the recovered image. In summary, these comparative results clearly demonstrate that our proposed method excels in restoring image details under turbid water conditions, highlighting its robustness and effectiveness in challenging imaging environments.

In terms of quantitative evaluation, we selected seven image quality assessment metrics to perform a quantitative analysis of the comparison results in Figure 4: Enhancement Measure Evaluation (EME) (defined in Ref. [1]), Standard Deviation ($\sigma$), Information Entropy, Contrast (C) [36], Average Gradient (AG), Underwater Image Quality Measures (UIQM), and Edge Intensity (EI) [41]. Higher values of these metrics indicate clearer images with higher contrast.

Table 1. Image quality evaluation results for the images in Figure 4.

	EME	$\mathit{\sigma }$	Entropy	C	AG	UIQM	EI
Raw	0.6872	3.3253	6.0829	0.0795	1.0864	2.8150	18.4175
Liang	1.8804	4.0688	6.7739	0.1657	2.4627	3.1304	34.3702
He	3.7739	14.8733	7.1624	0.3274	2.7528	3.0206	50.5679
Multi-Retinex	4.9161	9.2763	7.2734	0.3213	2.1493	3.2260	36.9054
CLAHE	1.9858	6.3183	7.1941	0.2216	2.3533	3.0513	37.8267
Ours	5.9522	4.6433	7.4390	0.2857	6.3862	3.8635	66.7597

presents the image quality assessment results, with the best values for each metric highlighted in bold. As shown in Table 1, the proposed method achieves the best values for most of the metrics, demonstrating its effectiveness in reducing the impact of non-uniform illumination, significantly enhancing image contrast and edge information richness. Additionally, it shows superior performance in improving image detail and clarity, thereby significantly enhancing overall image quality.

To further validate the effectiveness of the method under highly turbid water conditions, we added different volumes of milk to the water to create mediums with moderate and high densities of milk-induced turbidity. The intensity images captured in these turbid mediums are shown in the first row in Figure 6, where the severe degradation of image details is evident. The images recovered using Liang’s method are shown in the second row, and the images recovered using our method are shown in the third row. It can be observed that our method is able to clearly restore the scene details even in highly turbid conditions, outperforming the traditional method based on Stokes vectors (i.e., Liang’s) and such methods using only one image (i.e., He’s), highlighting its robustness and effectiveness in challenging imaging environments. In addition, we also presented the quantitative analysis of the comparison results under different turbidity conditions, and the results are shown in

Table 2. Image quality evaluation results for the images in Figure 6.

	Low Turbidity			Medium Turbidity			High Turbidity
	EME	AG	EI	EME	AG	EI	EME	AG	EI
Raw	0.4182	0.7761	14.7483	0.3737	0.7132	14.2427	0.3375	0.6703	14.0117
Liang	0.8587	1.3465	17.8492	0.6173	1.0668	15.4347	0.4931	0.9108	14.4237
He	1.6290	1.8592	34.4568	1.3932	1.6175	32.2107	1.1802	1.4110	30.8003
Multi-Retinex	0.9162	0.8871	13.4345	0.7339	0.7614	11.6922	0.9725	0.9416	15.4029
CLAHE	0.7546	1.3396	18.9075	0.6325	1.1702	16.5479	0.5834	1.1034	15.7609
Ours	3.6181	5.3229	45.1387	2.9013	4.7638	34.9485	2.3745	4.3875	29.9913

(from the view of three metrics due to the space limitation). The proposed method has the best values among these four methods; especially in a high scattering condition, the proposed method improves the values of EME and AG by about 2.0 and 3.1 times.

Furthermore, to demonstrate the general applicability of the proposed method, we conducted imaging and restoration experiments on target objects made of different materials, including metal coins, wooden and paper blocks, plastic products, etc. The comparison results are shown in Figure 7. It can be seen that the imaging clarity of such targets in turbid water significantly decreases, making details difficult to recognize. Although the methods of Liang and He show noticeable improvements compared to traditional methods based on Retinex and CLAHE, they still exhibit a layer of haze; and due to the uneven illumination of the light source, He’s method performed poorly in the uniformity of the results. In contrast, our method achieves the best performance, particularly for the metal coin, where it clearly restores the intricate details of the “coiling dragon” on the coin.

Finally, to enhance the reproducibility of our study, we conducted a set of quantitative experiments for comparison and demonstration. Based on this objective, we have included additional details of the experimental settings. For example, the size of the tank used (i.e., the volume of water) was 65 × 25 × 25 cm³. The tank was filled with water mixed with semi-skimmed milk to introduce turbidity. Notably, milk can effectively mimic the scattering properties of seawater [42], with a scattering coefficient (${\mu }_s$) of 1.40 c/cm, where c is the milk concentration [43]. By altering the milk concentration, different optical thicknesses ${\tau }_0$ can be simulated, which is proportional to ${\mu }_{s}d$, where d is the distance between the camera and the object [44]. Therefore, in the experiments, we adjusted the milk-to-water ratio to control the turbidity levels. We added 15 mL, 16 mL, 19 mL, 20 mL, and 21 mL of milk to the tank, respectively. The raw data collected by the camera in turbid water are shown in the first row of Figure 8. It can be seen that as the volume of milk increases, the image clarity progressively deteriorates. We compared the restoration results of the proposed method with those of Liang’s method, as shown in the second and third rows of Figure 8.

For instance, although Liang’s method can clearly restore the details on the left side of the image, it fails to effectively recover the text in the bottom right corner (highlighted in the red box). To more clearly demonstrate this result, we selected three concentration scenarios of 15 mL, 19 mL, and 21 mL, and plotted the corresponding 3D pixel values of the details, as shown at the bottom of Figure 8. It is evident that our method significantly enhances the contrast of local details, especially in highly turbid water conditions. In contrast, the raw images and the restoration results from Liang’s method show that the details are compressed into a very narrow pixel range. It is evident that in this series of comparative experiments, our method consistently demonstrated better restoration performance than Liang’s method, especially in terms of image uniformity, validating the superiority and robustness of the proposed method.

4. Discussion and Conclusions

4.1. Discussion

In actual application scenarios, the variability of the light field (including inherent and active illumination lighting) and the random fluctuations of the scattering medium can impact the final imaging and restoration results. For static target scenes, these issues can certainly be effectively circumvented by multiple captures; however, for dynamically changing scenes, a feasible approach is to appropriately increase the camera’s exposure time, while balancing the need for real-time responsiveness. Besides, polarization cameras can replace traditional intensity cameras. However, when utilizing a division of a focal plane polarization camera based on a linear polarizer array, it becomes necessary to position a rotatable retarder (e.g., waveplate) in front of the camera. This arrangement allows the calculation of the scene’s full Stokes parameters with just two captures [37]. Notably, commercialized full Stokes polarization cameras are now available that can determine the full Stokes parameters from a single image capture [45]. Therefore, a beneficial improvement for future applications would be to replace traditional systems with polarization cameras to eliminate the drawbacks of mechanical rotation. On the other hand, in our experiments, we used the mixture of water and milk to simulate turbid water. Although milk can effectively simulate the scattering properties of seawater [42], certain characteristics of milk may introduce a retardance effect [46]. In terms of circular polarization analysis, this may lead to discrepancies from the actual application scenarios. Further investigation into this aspect may be meaningful.

Additionally, it is worth noting that local artifacts appear in the restoration results of the proposed method (e.g., on the dark blocks in Figure 4). This is primarily because the regularized (i.e., CLAHE-processed) intensity images were used as the target images when determining the intensity factor, i.e., $ϵ$. As a histogram equalization-based algorithm, CLAHE can inherently introduce certain artifacts. Therefore, future improvements could focus on selecting an optimized CLAHE algorithm [4] or combining multiple regularization methods to avoid such situations [47]. Naturally, these artifacts can also affect the selection of image metrics, in other words, leading to cases where the visual quality of the image is poor but the evaluation metrics are high. To avoid this issue, a feasible solution is to use a multi-metric weighted evaluation objective function instead of using only the maximum intensity as the objective function in Equation (8) [47]. However, the downside of this approach is that it increases the computational cost of the optimization search. Balancing the overall image contrast, artifacts, quantitative evaluation metrics, and algorithm complexity is an interesting research direction.

4.2. Conclusions

In conclusion, this paper rethinks the application of the circular polarization memory effect in underwater de-scattering imaging. By performing histogram stretching-based pre-processing on polarization sub-images and utilizing the correlation between polarization characteristics (i.e., DoP and AoP), we obtain sub-images in other polarization directions. Subsequently, we implement the final polarimetric de-scattering technique based on Liang’s model, achieving significantly improved performance compared to the original algorithm. Additionally, this paper proposes a method for determining scattering light parameters based on the intensity adjustment factor search, which does not require prior knowledge of the backscattering region and effectively ensures the uniformity of intensity distribution in the restoration results. Experimental results show that the proposed method significantly enhances the quality of images restored in turbid water, even under conditions of high turbidity density (from both subjective visual evaluation and objective metric quantification). Moreover, the image quality restored by this method surpasses that of previous methods, including Liang’s traditional polarimetric method, adaptive histogram equalization, and the dark channel prior algorithm. This novel approach provides a new perspective on utilizing the polarization memory effect to tackle more complex scattering scenarios. It can be easily applied to practical underwater object detection and has the potential to achieve clear visual results in other scattering media.