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Abstract
Active polarization imaging techniques have tremendous potential for a variety of underwater applications. However, multiple polarization images as input are necessary for almost all methods, thereby limiting the range of applicable scenarios. In this paper, via taking full advantage of the polarization feature of target reflective light, the cross-polarized backscatter image is reconstructed via introducing an exponential function for the first time, only based on mapping relations of co-polarized image. Compared with rotating the polarizer, the result performs a more uniform and continuous distribution of grayscale. Furthermore, the relationship of degree of polarization (DOP) between the whole scene and backscattered light is established. This leads to an accurate estimation of backscattered noise and high-contrast restored images. Besides, single-input greatly simplifies the experimental process and upgrades efficiency. Experimental results demonstrate the advancement of the proposed method for objects with high polarization under various turbidities.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Due to the striking advantages of high sensitivity, fast imaging speed, and high spatial resolution, underwater optical imaging technologies have been widely used in re-source exploration, fishery monitoring, underwater archaeology, and underwater warfare [1–3]. However, the image quality is often severely degraded by the scattering and absorption effects in scattering mediums, which results from the nonuniform distribution of the intensity or polarization properties [4–7]. With further technological developments, polarization imaging shows great application potential, several studies have shown remarkable improvement by mining the uniqueness and difference of the polarization information of the scattered light field. At the same time, the new polarization regulation technology with plasmonic nanostructures array and metasurfaces [8,9] provided more possibilities for imaging miniaturization and integrated applications. For better utilization of polarization features, Schechner et al. presented a passive underwater polarization imaging model in 2005 [10], this is the first study to introduce underwater image formation model for descattering. Then some recent works, including the polarization parameter optimization by the network [11], and polarization descattering without prior knowledge [12] in response to more improvements. The effectiveness of these optimizations is proven by massive experimental results. To adapt to deep underwater dark environments, the introduction of an active light source can reduce the effect of absorption and modulate the incident polarization signal. Treibitz [13] et al. proposed an active polarization descattering model in turbid water to further improve the imaging contrast and clarity. Furthermore, the correlation parameter PCE (Peak-to-correlation energy) was applied to determine the brightest and darkest polarization images [14,15], which is meaningful to obtain accurate polarization parameters, but one limitation is time-consuming. On the other hand, to meet different types of targets and improve imaging quality, Li [16] et al. put forward underwater image restoration approach via Stokes decomposition, this method requires orthogonal polarization illuminations. Wei [17] et al. deduced the DOP and angle of polarization (AOP) by exploiting Stokes vectors, besides, the nonuniform of polarization information was also considered [18]. Zhao [19] et al. obtained the DOP of target and backscattered light based on a genetic algorithm but ignored the difference in global pixel positions. In addition, Hu [11,20] et al. firstly introduced deep learning to recover polarimetric underwater images. After that, a physics-informed neural network [21] and light weight convolutional neural network [22] were further used to obtain clear de-scattered images. It is worth noting that some algorithms based on Mueller matrix [23,24] and polarimetric purity excellent metrics [25] all show excellent effect in identification. It can be found from the implementation process of previous methods that multiple polarization images needing to be as input to obtain the brightest and darkest orthogonal polarized images, Stokes vectors images, or training data, which means the process of acquiring images is complicated and time-consuming. Therefore, further simplifying the acquisition process of polarization imaging and ensuring imaging clarity are what we expect.
By mining the polarization feature of target and backscattered light, the brightest backscatter image is reconstructed through a fitting method based on moving least squares, and the darkest backscatter image is also obtained by introducing an exponential function, only based on a co-polarized image. These measures avoid the influence of non-uniformity from the light source and polarization state analyzer (PSA). Meanwhile, we establish the link of DOP between the whole scene and backscattered information, finally obtaining more accurate DOP spatial information of backscattered noise. Furthermore, via introducing image quality feedback parameter contrast, a wonderful recovery result is achieved. Compared with other approaches available in terms of imaging process, the proposed method only needing single-input improves efficiency of decattering. Finally, the feasibility and the superiority are also verified by actual imaging experiments. More importantly, our method provides a novel notion for polarization descattering imaging, particularly for reflective targets with polarization.
2. Active polarization descattering based on a single polarized image
2.1 Theory
Regarding physical modeling, underwater optical images are composed of the target, the forward scattered, and the backscattered information [13]. Ignoring the forward scatter part of the total signal which is responsible for image blurring, the total intensity $I(x,y)$ can be described as:
Where $D(x,y)$ is the target information, and $B(x,y)$ corresponds to the backscattered information. The cross-linear polarized image is gated with a given polarization illumination and detection in the orthogonal state. A co-linear polarized mage is also obtained with detection in the same state as the illumination. The brightest image ${I_{\max }}(x,y)$ and the darkest image ${I_{\min }}(x,y)$ are corresponding to the co-linear and the cross-linear polarization respectively, and expressed as:The intensity of target and the backscattered light can be expressed as:
The degree of linear polarization (DOLP) of the whole scene image can be described as:
The degree of linear polarization (DOLP) of target and backscattered information can be described as:
2.2 Brightest and darkest backscatter images
The spatial distribution of the brightest backscatter ${B_{\max }}$ and the darkest backscatter ${B_{\min }}$ are vital for obtaining the DOP of backscattering. Therefore, we try to find the law of backscattered light in orthogonal polarization analysis by experiments, and the setup is depicted in Fig. 1. The light source utilized is an LD Laser emitting at a wavelength of 532 nm. The emitted light is collimated through a beam expander before passing through a polarization state generator (PSG) to produce a linearly polarized light beam with a horizontal orientation. The acquisition of polarized images is facilitated by a rotatable polarization state analyzer (PSA) in conjunction with an 8-bit digital monochrome CCD camera.
The turbid water was contained within a high-permeability glass sink, and the walls are covered with black light-absorbing material to reduce the impact of specular reflection. The choice of skim milk as a turbid solute is motivated by its widespread use as a simulation of turbid aquatic environments in prior studies [18]. According to Mie scattering theory, the scattering coefficient in the case of independent scattering is affected by the particle sizes and scatterer concentration. So, the adjustment of scattering effect can be achieved by controling the volumes of milk solution. With regard to the targets, the differences between reflective objects and diffuse objects are mainly reflected in the direction and polarization of the reflected signal. Most of specular reflected light is the same polarization as the incident light for highly reflective targets [26]. While the signal reflected from diffuse target is transformed into other linear polarization, elliptical polarization, and partial polarization light, and the propagation direction is random [27]. Here, we selected metal signs and smooth transfer labels, which perform polarization-maintain and reflection characteristics. Besides, the turbid water with four turbidities (from 140 ml to 200 ml) was also used to simulate different scattering environments. As shown in Fig. 2(a)-(d) of two types object, it can be found that target information is fully preserved in co-polarized images, while cross-polarized image contains nothing. Meanwhile, as the scattering is exacerbated, the target information in co-polarized image is gradually covered by noise light.
Fig. 2. The co-polarized and cross-polarized images with two types of targets under different turbidities (a) co-polarized images of metal sign (b) cross-polarized images of metal sign (c) co-polarized images of transfer lable (d) cross-polarized images of transfer lable. The adding amount of skimmed milk is 140 ml, 160 ml, 180 ml, and 200 ml respectively
Considering the distribution law of backscattered and target light in the full scene, we introduced location sampling to explore the variation of the gray value. For the target scenario of metal signs, we drew red and blue horizontal solid lines in the background (BG) and target area (TA) of co-polarized images respectively, as shown in Fig. 2(a). Meanwhile, the red and blue horizontal dotted lines were marked in cross-polarized images to distinguish differences, as shown in Fig. 2(b). Then, to verify the randomness of gray value distribution, the direction of the red and blue lines were taken as vertical in the target scenario of transfer lable, as can be seen in Fig. 2(c) and (d). Then, the grayscale values lying on the lines of the images were captured and then processed through Matlab ‘loess’ local regression, doing so is more conducive to analyzing trends.
As given in Fig. 3(a) and (b), for the lowly scattering environment, the gray appears a more drastic trend in the target area of co-polarized images than in the background area due to direct reflected light from the target. On the contrary, the brightness after cross-polarized analysis is weak and the curves are flat to the approximate level. The reason for this is that less scattering cannot fully convert backscattered light to cross-polarization direction. With more scattering, it can be seen from the 140ml-column images of Fig. 3 that the variation of the red and blue solid curve tends to be flattened, and the gradient of curves change is gradually consistent. The phenomenon mainly stems from the fact that a large amount of backscattered noise is not fully filtered out. Besides, we also find that the intensity of the cross-polarized image is higher compared with lowly scattering. Other than this, there is an interesting phenomenon, the grayscale values of cross-polarized target area and cross-polarized background are approximately coincident, as shown in the red and blue dotted curves of Fig. 3, especially in highly scattering.
Fig. 3. The approximate varying trend of gray value with co-polarized and cross-polarized images under different scattering effects. (a) metal sign as the target (b) transfer lable as the target. The adding amount of skimmed milk is 140 ml, 160 ml, 180 ml, and 200 ml respectively.
Based on experimental results, the intensity of target light can be further expressed as:
So, the total intensity of the full scene is:
Since the total backscattered light is continuously distributed in space, the data of local background area is usually used for surface fitting based on the least squares method in previous studies, ignoring the discrete data contained in the target area [28]. Besides, the selection of the combined area maybe causes discontinuous surface and low smoothness, resulting in estimation errors. We adopt the moving least squares method (MLS) [29], where the weight function is defined through the introduction of compact support. The ${B_{\max }}(x,y)$ is reconstructed, and the approximation function expression is expresses as Eq. (11) and (12).
As in Eq. (11), the $p(x,y) = {[{p_1}({x_i},{y_i}),{p_2}({x_i},{y_i}),{p_3}({x_i},{y_i})]^T}$ a basis function, which is a k-order complete polynomial. The m is the number of terms of the basis function. Where $a(x,y) = {[{a_1}({x_i},{y_i}),{a_2}({x_i},{y_i}),{a_3}({x_i},{y_i})]^T}$ is the coefficient to be solved is a function of (x, y), it can be obtained from weighted least squares fitting of local approximation as Eq. (13). The J is a defined fonctionelle that requires a minimum value and the w is weight function with compact support property.
The data collection $\Sigma $ includes the continuous data of the background region and the discrete data which are the dark pixels of the target area. Here, the delineation of target and background regions is achieved by adopting histogram stretching to the co-polarized image, which expands the difference between foreground and background gray levels [30].
As we know, the LD source shows Gaussian characteristics during transmission in scattering medium. Meanwhile, it can be seen from Fig. 3 that the non-uniform of cross-polarized backscatter is similar to that of co-polarized image and the trend of grayscale values changing with position is consistent. Thereforce, we considered the cross-polarized backscatter image can be constructed based on mapping relations about the co-polarized image as the input image. Based on the above analysis and precedent of an exponential function used to reconstruct polarization information [31], introducing a relationship between ${B_{\min }}(x,y)$ and ${B_{\max }}(x,y)$ through an exponential function is a feasible approach. It can be expressed as Eq. (14).
The ${\hat{B}_{\max }}/255$ is transformed to (0, 1) and can be used to simulate the non-uniform distribution, and the b is the coefficient to be optimized. Thereby, the mapping relation based on ${B_{\max }}(x,y)$ is established. It is worth noting that the ${B_{\min }}(x,y)$ should satisfy the following Eq. (15):
The boundary condition for the coefficient b is (0, 1) and the maximum value of ${B_{\min }}(x,y)$ should be less than the minimum value of ${B_{\max }}(x,y)$.
2.3 Estimation and removal of backscattered light
By reconfiguring the brightest backscatter and the darkest backscatter image, according to Eq. (6) and (9), the DOLP of the whole scene can also be expressed:
It can be obtained from Eq. (8) that
The function relationship of degree of linear polarization (DOLP) between the whole scene and backscattered information is established, as shown in Eq. (17). According to the definition of degree of polarization, the values of DOLP are always less than 1. Meanwhile, the ${I_{\max }}(x,y)$ is always greater than ${\hat{B}_{\max }}(x,y)$. From this, it can be deduced as:
It can be noted that the distribution ${p_B}(x,y)$ and $\textrm{DOLP}(x,y)$ is consistent at background area, while the ${p_B}(x,y)$ is less than DOLP that of the full scene at target area.
Based on Eq. (2), Eq. (3), Eq. (7), and (8) and ${p_B}(x, y)$, this leads to the expression for the target estimation $D$ without backscattered noise as Eq. (19).
According to Eq. (19), the target information $D$ can be restructured only from one measurement ${I_{\max }}$, for highly reflective target, the degree of linear polarization (DOLP) of target ${p_D} \simeq 1$.
It can be seen from Eq. (19) that ${\hat{B}_{\min }}$ affects the descattering of final target information. Therefore, considering the effect to express the details, the widely used underwater image evaluation parameter contrast is selected [10,32] as a feedback parameter, the calculation process is as follows Eq. (20).
The optimal coefficient b is restricted through Eq. (14) and (18), and then the target image D with minimal noise light is finally obtained by iterative calculation. In this work, only the co-polarized image with the incident polarization direction is necessary for recovery instead of obtaining a set of orthogonal polarized images or Stokes vectors images. The flowchart of underwater polarization descattering is shown in Fig. 4.
Fig. 4. Flowchart of underwater polarization reconstruction based on the input of a single polarized image
3. Results and discussion
3.1 Estimation of the DOLP of backscattered light
As shown in Fig. 5, we conducted polarization imaging experiments with smooth coin in strongly scattering water, the aim is to make a comparison between two methods used to obtain cross-polarized image. One is obtained via rotating the polarizers and the other is fitting based on co-polarized image as in Eq. (14). It can be seen from Fig. 5(a) that the grayscale values exhibit a high degree of dispersion in cross-polarized images because of rotating the polarizer, and the maximum difference of grayscale value under different pixels is greater than 4. The reason is that the polarization direction of backscattered light is mostly concentrated at a small angle near the incident polarization direction. On the other hand, the inconsistency of the camera's response to weak signals and the non-uniformity of light sources also leads to discrete data in background. On the contrary, the gray distribution of cross-polarized image via fitting in our method is more continuous as Fig. 5(b), which overcomes the impact of non-uniformity.
Fig. 5. Comparison of key parameters during target image restoration (a) 3D mesh of cross-polarized image by rotating the polarizers (b) 3D mesh of cross-polarized image by fitting in our method (c) 3D mesh of DOLP in full scene (d) 3D mesh of ${p_B}(x,y)$(e) the target image via classic descattering model [13] (f) the recovered image through our method. The additional amount of skimmed milk is 220 ml.
For active polarization descattering model, the background areas of the co-polarized and cross-polarized images are selected to obtain the DOLP of the backscattered light [13], which is usually assumed to be a constant. However, it can be noted from Fig. 5(c) that the difference of DOLP values in the diagonal background area comes to 0.1. As a consequence, determining the optimal DOLP of backscattered light becomes difficult. In addition, the discontinuity from cross-polarized images as in Fig. 5(c) will also lead to the appearance of an annular shielding area in the recovered target image as shown in Fig. 5(e). In contrast, as shown in Fig. 5(d), the DOLP distribution of backscattered light is more continuous in the full area and the result in Fig. 5(f) also proves that our method can effectively recover the target information.
3.2 Qualitative comparison for recovered images
Underwater descattering techniques that have been developed to restore the image quality can be classified into two categories, non-physical and physical model-based methods [7]. The classic active polarization imaging methods [13] (Treibitz) and revised polarization imaging model based on Stokes parameters [17] (Wei) belong to the second class. Contrast limited adaptive histogram equalization (CLAHE) [33] belongs to the first class. These methods are classic and representative. Where CLAHE and our method only require the input of a single image, Treibitz’s and Wei’s methods both require more than two polarized images as inputs. To verify the feasibility of the proposed method, the target selected in the experiments is a stainless steel metal sign with a smooth finish, imaging experiments were carried out in lowly and highly scattering water by adding different volumes of skim milk.
As shown in Fig. 6, at lowly scattering environment, the target information of intensity imaging is partially lost. Wei’s and our method show better contrast, which is reflected in the black-and-white contrast between the letters and the background. However, there exist some difference, which is incarnated in that the proposed method has a purer black background. It is mainly derived from precise estimation of backscattered light. Although, the other two methods show an improved effect, the image is still covered with a layer of mist. At highly scattering environment, the intensity image is completely submerged by noise light, and the target image enhanced by CLAHE method is ambiguous. Through Treibitz’s method, the restored results demonstrate better imaging contrast, but there are extremely low brightness values in local areas. The reason for this phenomenon is the DOLP estimation of the local pixel exceeds the actual value. Besides, via Wei’s method, the brightness of the whole scene image is more uniform than other approaches, but the background noise is not well removed. In contrast, our method filters out stray light in background areas and restores the target information well.
Fig. 6. Restoration results of different underwater imaging methods and comparison of local features (a) lowly scattering corresponding to adding 160 ml skim milk (b) highly scattering corresponding to adding 220 ml skim milk. The target is a stainless steel metal sign with a smooth finish
The effect of recovering local details is typically characterized the advancement of imaging methods. Taking the letter “XJTU” in target as an example, from the enlarged image of local details, it can be concluded that noise is growing with the superposition of scattering. For other polarization imaging methods, including Treibitz’s and Wei’s methods, the imaging performance is satisfactory at lowly scattering, but more scattering would destabilize the imaging stability. It is reflected in the boundary of the target letter is no longer clear. Despite this, the black letters “XJTU” on the sign can be distinguished and fits well to its shape with our method. Meanwhile, it is worth noting that the attenuation of target information is exacerbated due to scattering, finally reflected in a small amount of noise in the restored image.
3.3 Suppression effect of noise light for different methods
The major reason for the decline of imaging contrast is the spatial aliasing of noise light and target light. Therefore, the suppression effect of noise under fully retaining target information is a reasonable measure of underwater imaging methods. We continued to select the rectangular laboratory sign as the target and conducted experiments in two scattering environments same as in section 3.2. Making a comparison with the final results via different methods, it can be seen that good imaging clarity is still maintained well by our method, and the characteristics of the elements stand out and are easy to identify as shown in Fig. 7.
Fig. 7. Restoration results of different underwater imaging methods (a) lowly scattering corresponding to adding 160 ml skim milk (b) highly scattering corresponding to adding 220 ml skim milk. The target is a rectangular laboratory sign.
In order to characterize the resolution ability of the target elements more intuitively, the four letters “XJTU” in the upper part of the target in Fig. 7 were chosen as the feature area, and we made a horizontal midline to discover the gray value distribution. The results are shown in Fig. 8(a) and (b), from which it can be observed that the ratio of the peak to the trough of the quasi-rectangular wave represents the degree of noise filtering. Under lowly scattering, as shown in Fig. 8(a), due to black letters, the different peak of the rectangular wave is consistent through Wei’s and our method. However, the maximum peak-to-valley ratio with our method is more than 6 times, and Wei’s method achieves more than 2 times, much higher than other methods. Under highly scattering, for intensity imaging or CLAHE methods, it can be observed from Fig. 8(b) that the curves can be hardly observed the peak-to-valley changes of the rectangular wave, which means that the target information has been approximately submerged. On the contrary, the remaining three methods all achieve the discrimination between black letters and white background, but the peak-to-valley ratio of our method is the highest. Besides, the brightness uniformity of the target image with Wei’s method is best, and the effect of our method is second only to it.
Fig. 8. The pixel gray value with the spatial position in horizontal midline (a) lowly scattering corresponding to adding 160 ml skim milk (b) highly scattering corresponding to adding 220 ml skim milk. The target is an ectangular laboratory sign. At the top of the figure, we give the pseudo-color image of the sample target images corresponding to the pixel position of the curve
It should be noted that there is no comprehensive evaluation criterion for image quality, with subjective judgment required in most cases. No-reference evaluation metrics are used to characterize the imaging quality, and then we calculated the value of the measure of, contrast [34], the underwater image sharpness measure (UISM), and the underwater image quality measure (UIQM) according to Eq. (21)–(24) [2].
As shown in Table 1, Treibitz’s and our method both achieve better imaging contrast, and our method is the highest, which represents an advantage in backscattered noise suppression. Wei’s method and the proposed method perform better human eye vision. It is reflected in the maximum image sharpness (UISM) and image quality (UIQM) with our method. This comparison further proves that the proposed method can handle scattering noise problems in underwater imaging and improve vision. More importantly, a single polarized image as input significantly promotes the efficiency of imaging.
Table 1. Using contrast, UISM, UIQM to evaluate the results of different methods, the higher the score, the better the enhancement effect
3.4 Influence of turbidity on recovered image
Considering the influence of turbidity on the imaging, the volume of skim milk changing from 140 ml to 220 ml at 20 ml intervals is simulate different scattering effect. To ensure the credibility of the experiments, the observed target is replaced by signs with small holes and small letters. These features of target are conducive to measure the clarity of the image. Here, intensity imaging is used as a reference, and contrast is regarded as an imaging evaluation parameter. The curves of the imaging contrast with intensity imaging, Treibitz’s active descattering, and our imaging method under different turbidities are shown in Fig. 9. Meanwhile, to more intuitively reflect the imaging clarity of the results as the scattering intensifies, the recovered images are added below the corresponding curve.
Fig. 9. The contrast of target images with intensity imaging, Treibitz‘s and our method under different turbidity
The results show that backscattered noise is gradually increasing due to multiple scattering as the skim milk rises. This leads to a reduction in imaging contrast for all three imaging methods. However, it is worth noting that the magnitude of the decline is different. Intensity imaging contrast always far lower than other imaging methods, especially at 180 ml, target information is completely overwhelmed. The enhancement with Treibitz’s imaging method is also limited at different levels of scattering. A major reason is that multiple scattering causes errors in estimating the polarization of backscattered light. In contrast, the proposed method is the most effective, especially, the small hole of metal sign is visible in the recovered images. Besides, under highly scattering environment, such as 220 ml, the overall brightness of the final restoration results of our method and Treibitz’s methods both darken. The cause for this is the loss of target information that the detector can receive, mainly derived from transport attenuation. On the whole, the developed method presents robustness to the water turbidity increase.
4. Conclusion
In this study, a novel underwater polarization desacttering method based on a single polarization image is developed. Based on the polarization feature of target reflected light, we adopt histogram stretching to input image and obtain co-polarized backscatter image via MLS method. Meanwhile, the spatial distribution of cross-polarized backscatter image is reconstructed through introducing a specific exponential function based on mapping relations. These measures overcome the challenges posed by non-uniform due to illumination and PSA. Furthermore, the link of degree of polarization between the whole scene and backscattered information is established, which leads to the removal of backscattered noise and higher contrast target images. Compared with previous methods, single-input simplifies the polarization imaging process and is suitable for practical imaging scenarios. The experiment results under various turbidities conditions, with variety of target types, demonstrate the effectiveness and superiority of the proposed method.
The reflective polarization feature of targets is considered as polarization maintaining or depolarizing in the current study. Fully combining the specific polarization characteristics of the target is the direction of our future study.
Funding
National Natural Science Foundation of China (61890961, 62127813, 62201568); Natural Science Basic Research Program of Shaanxi Province (2018JM6008, 2022JQ-693).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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