Color Compensation of an Underwater Imaging System Using Electromagnetic Wave Propagation

Abstract

Images can be obtained by collecting rays from objects. The characteristics of electromagnetic wave propagation depend on the medium. In particular, in an underwater imaging system, the interface between air and water must be considered. Further, reflection and transmission coefficients can be found by using electromagnetic theory. Because of the fact that the values of these coefficients differ according to the media, the recorded light intensities will change. A color image sensor has three different color channels. Therefore, the reflection and transmission coefficients have to be calculated individually. Thereafter, by using these coefficients, we can compensate for the color information of underwater objects. In this paper, we present a method to compensate for the color information of underwater objects by using electromagnetic wave propagation theory. To prove our method, we conducted optical experiments and evaluated the quality of the compensated image by a metric known as mean square error.

I. INTRODUCTION

Imaging of underwater objects has various applications and benefits in the fields of marine sciences, inspection of vessels, security and defense, underwater exploration, unmanned underwater vehicles, etc. [1-5]. There are many optical effects to consider when approaching an in-water imaging situation. Water and the varying particles in it are responsible for numerous effects such as wavelength-dependent absorption, attenuation, scattering, reflection, and the index of refraction variations [5, 6]. Thus, underwater imaging is inherently different from aerial imaging. Absorption and scattering problems may be solved using statistical image processing techniques [7]. However, since other wave propagation parameters in water are caused by the difference in the medium features between in air and in water, the recorded underwater image has some distortions.

In the underwater color imaging case, a color image sensor has three different basic color sensors, namely red (R), green (G), and blue (B). Each color sensor detects light information at a different wavelength (R: 620–750 nm, G: 495–570 nm, and B: 450–475 nm). This means that each channel has different wave propagation parameters. Therefore, we need to consider these differences among basic colors for the acquisition of accurate underwater images. Further, since the refraction index of water is different from that of air, the image magnification should be adjusted.

In this paper, we describe wave propagation parameters for each color channel by using electromagnetic theory. Then, color compensation is presented. To prove our compensation method, we conduct an optical experiment and evaluate the quality of the results by using mean square error as the metric.

 

II. MAGNIFICATION OF UNDERWATER IMAGING

At the interface between air and water as shown in Fig. 1, the waves are refracted by Snell’s law as per the following equation [8, 9].

where n1 and n2 denote the refraction index of medium 1 (air) and medium 2 (water), respectively, and θ1 and θ2 represent the incident wave angle and the refraction wave angle, respectively.

Fig. 1.Underwater imaging with refraction.

According to this law, the underwater objects seem to float. However, since on-axis underwater imaging is used in this study, the range parameter zwater as shown in Fig. 1 should be changed as follows [10]:

where zwater denotes the actual distance between the water surface and the objects, and z'water represents the distance between the water surface and the object image as depicted distance is shorter than the actual distance between the in Fig. 1. Therefore, the object image image sensor and the object. To obtain an image with the correct magnification, we need to resize the underwater image by using Eq. (2). The following equation presents the adjusted magnification in water [10].

where f denotes the focal length of the imaging lens and zair represents the distance between the lens and the water surface.

 

III. UNDERWATER IMAGE RECORDING PROCESS

The underwater image recording process has two major steps: illumination and recording. In the illumination step, the illumination wave propagates from air to water. Further, in the recording step, the object wave comes from water to air.

Step 1. Illumination

Fig. 2 illustrates the illumination step. The light bulb emits the incident illumination plane wave. Hereafter, we consider the electric field only for the simplicity of calculation.

Fig. 2.Illumination step.

As shown in Fig. 2, we have two different media (air and water). Therefore, the wave impedance Zw1 and Zw2 can be calculated by using the following equations [9]:

where μ0 denotes the magnetic permeability in air, ε0 indicates the electric permittivity in air, εr represents the relative permittivity in the medium, and n2 refers to the refraction index of medium 2 (water).

The wave impedance Zw1 is always constant. On the other hand, Zw2 can be changed for each color channel (R, G, and B). The wave impedance for each color channel can be found by using the following equations [9]:

where ωR = 2 ωfR, ωG = 2ωfG, ωB = 2 ωfB, and σ denotes the conductivity of the medium. However, in this case, we can use the following equation instead of Eqs. (7)–(9) to find the wave impedance of each color channel because of the very low conductivity of water [9].

where n2R,G,B denotes the refraction index of each channel.

Now, we know the wave impedance of each color channel. Therefore, we can calculate the reflection and the transmission coefficient for each channel by using the following equations [9]:

To calculate the attenuation coefficient of a medium, we need to figure out (σ/εω)2. In the case of visible light propagation through water, ωε is sufficiently large and σ is very small. Therefore, (σ/εω)2 is set to <<1 so that the medium can be good dielectric [9]. In a good dielectric, the attenuation coefficient α can be defined as follows [9]:

For each color channel, we can find the attenuation coefficient by using the following equation:

To find the electric field of the illumination light, we assume that the incident electric field is Ei = E0e-jβ1zair. Therefore, the reflected electric field and the transmitted electric field of the illumination light can be Er = Γ1E0e+jβ1zair and Et = T1E0e-αzwatere-jβ2zwater.

Step 2. Recording of underwater image

Fig. 3 describes the recording of an underwater image. The transmitted illumination light can be the incident object light in this step. We do not need to consider the reflected object light because it cannot reach the image sensor. Therefore, here, we only consider the transmission coefficient through the air to be as follows [9]:

Fig. 3.Recording of an underwater image.

In the air medium, the attenuation coefficient can be ignored because the conductivity of air is almost zero. Thus, the electric fields of the incident and the transmitted object lights can be defined as follows [9]:

where represents the object light intensity.

Therefore, the total recorded electric field can be calculated as follows:

 

IV. COMPENSATION OF EACH COLOR CHANNEL USING ELECTROMAGNETIC THEORY

Thus far, we have calculated the wave propagation parameters in both the illumination and the recording steps. However, our goal is to estimate the original image (in-air image) from the underwater image. Further, the image sensor can detect only the average power of the propagated wave. Therefore, we need to calculate the average power of each step, underwater image, and the original image as follows [9]:

where Srav, Stoav, Stotav, and Soriav denote the average power of the reflected illumination light, the transmitted object light, the total underwater image light, and the original image light, respectively.

Using Eqs. (25)–(28), we can estimate the original image from the underwater image as follows:

 

V. EXPERIMENTAL RESULTS

To prove our compensation method for an underwater image, we conducted an optical experiment. Fig. 4 shows the experimental setup.

Fig. 4.Diagram of the experimental setup.

In the optical experiment, a camera with the focal length of f = 50 mm is used. It has 2496 (H) × 1664 (V) pixels. The distance between the imaging lens and the water surface, zair = 234 mm, the distance between the water surface and the object, zwater = 56 mm, and the distance between the imaging lens and the object image, z'water = zwater/n2 = 42 mm, respectively. Fig. 5 shows the in-air image and the underwater image used in this experiment.

Fig. 5.Images used in the optical experiment: (a) in-air and (b) underwater.

To compare the underwater image with the in-air image, we adjust the magnification of the underwater image by using Eqs. (3) and (4). The experimental images with the adjusted magnification are shown in Fig. 6. Then, we evaluate the quality of the processed image by using mean square error (MSE) as the metric:

Fig. 6.Images with the adjusted magnification: (a) in-air and (b) underwater.

MSE in the case of the non-processed image is always constant, MSEnon-processed = 461.86. However, MSE in the case of the processed image changes with a change in the conductivity of water. Fig. 7 shows the plot of MSE in the cases of the processed image and the non-processed image versus the conductivity of water.

Fig. 7.Plot of MSE in the cases of the non-processed image and the processed image versus the conductivity of water. The optimum conductivity of water is 0.013.

As shown in Fig. 7, the best MSE result is obtained at the optimum water conductivity of 0.013. Using this optimum conductivity and Eqs. (29)–(31), we can obtain the color-compensated underwater images as depicted in Fig. 8(b) and (d).

Fig. 8.Experimental results: (a) and (c) show the in-air images with the original scale and the enlarged scale, and (c) and (d) show the color-compensated underwater images with the original scale and the enlarged scale.

In Fig. 8(c) and (d), the colors yellow and blue have a similar intensity value. Thus, the MSE in the case of the processed image is better than that in the case of the non-processed image.

 

VI. CONCLUSIONS

In this paper, we present the color compensation method for an underwater imaging system. Using electromagnetic theory, we can find the wave propagation parameters such as the reflection, transmission, and attenuation coefficient of a wave for each basic color channel. Since the image sensor detects only the average power of a wave, we need to calculate the average power of the wave for each color channel. As shown in the experimental results, the color-compensated image is better than the non-processed image. Further, through the optimization process for the conductivity of water, we can find optimum conductivity because we do not know the exact conductivity of water. The range of water conductivity is 5 × 10−4 to 5 × 10−2 S/m. Using optimum conductivity, we can estimate the original image well. Therefore, we can expect underwater object recognition to be implemented well by using this color compensation method.