Frontiers in Computing and Intelligent Systems 
ISSN: 2832-6024 | Vol. 4, No. 1, 2023 

 

17 

An	Underwater	Target	Ranging	System	based	on	
Binocular	Vision	
Yian Wang * 

Northeast Petroleum University, Daqing, China 

* Corresponding author Email: llswya@163.com 

 

Abstract: In order to accurately measure the distance and size information of underwater targets, an underwater target ranging 
and size measurement system based on binocular vision is proposed. Underwater binocular calibration method is used to obtain 
the underwater parameters of binocular camera, and the underwater images are calibrated to make them coplanar and aligned. 
The improved CLAHE algorithm is used to process underwater images and improve the image contrast. The parallax map is 
obtained by SGBM stereo matching algorithm, and the distance and size of the target are measured and calculated according to 
the parallax map. The results of underwater experiment show that the measurement accuracy of the system is high for the distance 
and size of the close-range underwater target, and the measurement error conforms to the requirements of underwater experiment. 

Keywords: Underwater Binocular Vision; Underwater Calibration; Underwater Image Processing; Vision Measurement. 
 

1. Introduction  
With the continuous development of society and economy, 

countries are constantly seeking new resources. The ocean 
accounts for more than 70% of the earth's total area and 
contains a large number of biological, mineral and other 
resources, which has become the object pursued by various 
countries [1]. No matter the development of Marine resources, 
or underwater operations such as deep-sea exploration [2], 
underwater pipeline detection [3], salvage and rescue [4], etc., 
are inseparable from underwater target location and size 
measurement. Compared with radar, infrared, laser and other 
sensors are expensive and require high deployment conditions. 
Underwater optical vision is characterized by high resolution, 
and the introduction of binocular vision technology can 
accurately measure close-range targets [5], and reduce the use 
cost. The uneven illumination in underwater environment, 
coupled with the influence of water on the absorption, 
scattering and refraction of light, will greatly reduce the 
image quality. Therefore, in view of the underwater 
environment and other problems, this paper processed the 
obtained underwater images by improved CLAHE image 
processing algorithm, and obtained the internal and external 
parameters of the underwater camera by underwater 
calibration method. Based on this, a binocular stereo vision 
system is designed and implemented, which is suitable for 
underwater target ranging and size measurement. 

2. Underwater Ranging System based 
on Binocular Vision 

The overall process of underwater target ranging and size 
measurement based on binocular vision is shown in Figure 1. 
Firstly, the improved CLAHE algorithm is applied to the 
underwater image processing. In this paper, the left and right 
checkerboard images collected underwater are calibrated by 
the improved Zhang's calibration method, and the underwater 
parameters of the binocular camera are obtained, including 
rotation matrix, translation vector, etc. Image processing was 
carried out for the input underwater images, and binocular 
correction was carried out by using the parameters after 

underwater calibration. The stereo matching algorithm of 
SGBM is used to match the corrected underwater images, and 
then the underwater parallax map is obtained. Finally, the 
distance and size of the target are measured according to the 
principle of binocular distance measurement and the space 
two-point distance formula. 

 
Underwater left 

checkerboard image
Underwater right 

checkerboard image

Image processing Image processing

Single 
targeting

Single 
targeting

Binocular 
calibration

Internal and 
external 
parameters

Underwater image 
of left camera

Underwater image 

of left camera

Binocular 
correction

SGBM stereo 
matching

Measure distance and 
dimensions

Use the mouse 
to select 
points

Image processing Image processing

 
Figure 1. Flow chart of underwater target ranging system based on 

binocular vision 

3. Underwater Binocular Imaging 
Model and Underwater Calibration 
Method 

For underwater shooting, the camera container shell needs 
to be sealed and waterproof, and transparent glass cover plate 
is usually used in front of the container. As a result, light is 
refracted twice as it travels from underwater objects to the 
camera lens, at the interface between water and glass, and at 
the interface between glass and air. Since the glass is thin and 
homogeneous, and the target distance is much larger than its 
thickness, the propagation process of light in the glass can be 
ignored [6]. The simplified underwater imaging model of the 

camera is shown in Figure 2.  , ,
WW W

P X Y Z in Figure 2 is the 

target point to be measured; 
1 
O   is the real position of the 

camera; 
2 
O  is the intersection point of the extension line of 

incident light in water on the optical axis of the camera, which 
is taken as the virtual camera position; O  is the refraction 
point of incident light on the interface between water and air; 



 

18 

A is the intersection point of camera optical axis and the 

interface between water and air; 
1 
  and 

2 
  are respectively 

the incidence Angle and the refraction Angle. 
Z

θ1

θ2

O2

O1

O A

P(XW , YW , ZW) 

Camera

Camera_V

Air

Water

 
Figure 2. Underwater imaging model 

1
n   and 

2 
n   are the refractive indices of water and air 

respectively. According to the triangle similarity and 

refraction law 
1 1 2 2 

sin sinn n  , it can be obtained: 

 1 1 1 1 2 

2 2 2 2 1

tan sin

tan sin

O

O n

O

O

n  

  
     

Because the optical axis of the real camera coincides with 
that of the virtual camera, the projection length of OA  on the 

two cameras is the same, that is, 
1 2 
X X  , where 

1 
X  and 

2 
X  are the imaging lengths of OA  in the real camera and the 

virtual camera respectively. Therefore: 

 1 1 

1  

X f

OA OO
  

 2 2 

2  

X f

OA OO
  

According to formula 2 and 3, we can get: 

 1 1 2

2  2  1  

f nOO

OOf n
   

Formula 4 shows that the focal length of the camera when 
used underwater will change with the refractive index of 
water and air. 

Suppose that the coordinate of point P   in the world 

coordinate system is ( , , )
w w w
X Y Z , point 

u
P  is the projection 

of point P  in the pixel coordinate system, and its coordinate 
in the pixel coordinate system is ( , )u v  , then the 
transformation formula of point P   from the world 
coordinate system to the pixel coordinate system is[7]: 



0

0

1
0

0 0 0
1 1

0 0 0 0
0 1

1 0 0 1 0
0 0 1 1

w

w

w

u
Xdxu f

R T Y
v v f

ZZ dy


 
   

                        
      

  
 

 

Where, dx  and dy  are the physical length of unit pixel 
along the X   and Y   axes[8], Z   represents the depth of 

point P  ,  
0 0
,u v   is the coordinate of the origin of image 

coordinate system in pixel coordinate system, f  is camera 
focal length, R   is rotation matrix, and T   is translation 
vector. 

When the camera is placed underwater, due to the influence 
of water on light scattering, the refraction of incident light in 
the water at the front cover glass of the camera, and the 
distortion of imaging caused by the camera itself, the 
underwater imaging of the camera will have relatively serious 
distortion. In this paper, Zhang's calibration method is 
improved, and the first three distortion coefficients of the 
camera radial distortion polynomial are obtained through the 
high-order polynomial function, so as to eliminate the 
distortion problem of the camera underwater imaging better 
and ensure the measurement accuracy of the system. 

(1) As the distance between the imaging point and the 
image center increases, the radial distortion increases 
correspondingly, so the quadratic and higher-order 
polynomial functions related to the distance are used to 
correct the radial distortion [9]. Radial distortion correction 
formula is as follows: 


2 4 6

1 2 3

2 4 6

1 2 3

(1 )

(1 )

r

r

x x k r k r k r

y y k r k r k r

   

   





 

In the formula, ( , )x y   is the coordinate of the distortion 

point in the image before correction; ( , )
r r
x y   is the 

coordinate of the distortion point in the image after correction; 
r  is the distance from the distortion point to the image center, 

and 
1
k , 

2
k  and 

3
k  are the radial distortion coefficients. 

(2) The optical axis of the lens is not perpendicular to the 
image plane, causing tangential distortion. Tangential 
distortion correction formula is as follows: 


2 2

1 2

2 2

1 2

2 ( 2 )

( 2 ) 2

t

t

x x p xy p r x

y y p r y p xy

   

   





 

In the formula, 
1
p   and 

2
p   are tangential distortion 

coefficients. 

In order to obtain the coordinates ( , , )
w w w
X Y Z  of point P  

in the world coordinate system, the value of Z  needs to be 
calculated. In an ideal situation, binocular ranging is to obtain 
the left and right pictures of the target respectively from two 
identical and parallel cameras, so as to calculate the target 
distance value [10]. The principle diagram of binocular 
ranging is shown in Figure 3: In the figure, P   is the 
coordinate point of the three-dimensional space to be 

measured; 
l
O  and 

r
O  are the optical center of the left and 

right cameras; T  is the optical center distance of the left and 

right cameras, namely the baseline length; 
l
P  and 

r
P  are the 

coordinates of point P  in the image coordinate system of the 
left and right cameras; the horizontal coordinates of pixel 

points of point P   in the left and right images are 
l
X   and 

r
X   respectively; Z   is the vertical distance between point 

P  and the camera. 



 

19 

P

T

Z

Xl Xr

Pl Pr

Ol Or

f f

 
Figure 3. Binocular visual ranging principle 

As can be seen from Figure 3, 
l r l r

PPP POO ∽ . According 

to the triangle similarity relationship [11]: 


( )T X X Z fl r

T Z

  
  

The expression of distance Z   between the target to be 
measured and the camera can be summarized as follows: 


fT fT

Z
X X dl r

 


 

In the formula, d  is the parallax between the left and right 

cameras, 
l r

d X X  ; T  are known. Thus, the depth Z  of 

point P  can be found simply by obtaining parallax d . 

4. Improved Limited Contrast 
Adaptive Histogram Equalization 
Image Processing Method 

The main feature of the limited contrast adaptive histogram 
equalization algorithm (CLAHE) is that it limits the contrast 
[12], overcomes the problem of excessive amplification noise 
and blocky effect, and mainly enhances the local contrast, 
thus enhancing the image details [13]. Common CLAHE 
algorithm enhances R, G and B components respectively in 
RGB color space, and then combines them into RGB images 
[14]. In this paper, the improved CLAHE algorithm is used 
for color space conversion on the obtained underwater left 
and right eye images, converting the input RGB space into 
LAB space. Due to the separation of brightness components 
in LAB space, it is easier to process the image and improve 
the operational efficiency. Finally, RGB synthesis is carried 
out. The improved CLAHE algorithm is used to process the 
underwater image, as shown in Figure 4. It is obvious that the 
processed image has enhanced the details, improved the 
contrast, and significantly improved the visual effect. 

 

 
(a)                                 (b)  

Figure 4. Improved CLAHE algorithm seabed scene processing 
effect((a) Original view of submarine scenery ;(b) Improved 

CLAHE algorithm handles graphs) 

5. Underwater Experiment  

5.1. Underwater Experiment Software and 
Hardware Environment  

The hardware used in the experiment includes: 
experimental water tank, laptop and MSK-SM binocular 
camera, as shown in Figure 5. The experimental tank size is 
1m×1m×1m, and the actual water discharge depth is 0.8m. 
The configuration of the notebook is as follows: CPU is AMD 
5800H; The memory is 32GB; The GPU is NVIDIA GeForce 
RTX 3070. Underwater binocular camera configuration: 
MSK-SM binocular camera, image resolution 640×480, 
baseline length 25mm. The software environment is windows 
10, MATLAB 2021b, OpenCV. 

5.2. Underwater Calibration Image Acquisition  
In this paper, improved Zhang's calibration method is used 

to calibrate binocular camera underwater. GP400 standard 
checkerboard calibration board with specification of 12*9 
was adopted, and the size of each square was 30mm*30mm. 
The calibration board was shown in Figure 5. The underwater 
binocular camera and checkerboard calibration board were 
placed underwater, and the checkerboard images of the 
underwater left and right cameras with different positions 
were shot. Among them, 16 pairs of clear underwater 
calibration maps with a total of 32 were selected for 
underwater calibration. 

 

 
Figure 5. Experimental environment and checkerboard calibration 

board 

5.3. Improved Limited Contrast Adaptive 
Histogram Equalization Image Processing 
Method  

 

 
Figure 6. Improved CLAHE algorithm for image processing 

contrast graph 
 

The improved CLAHE algorithm is used to process the 
acquired calibration images and underwater object images, 



 

20 

and the processing results are shown in Figure 6. The 
processing results show that the color and contrast of the 
underwater image after processing are enhanced obviously, 
which can effectively represent the object features. 

5.4. Calibration and Correction of Underwater 
Binocular Camera  

Using MATLAB, 13 pairs of checkerboard images were 
read in turn, checkerboard corner points were extracted from 
the input images, and the left and right underwater cameras 
were calibrated respectively. 

After corner points were extracted, the parameters of the 
corresponding monocular camera were obtained through 
calculation. The corner error distribution diagram of a single 
camera was obtained, as shown in Figure 7(a), and the relative 
position diagram between a single camera and the 
checkerboard calibration board was shown in Figure 7(b). It 
can be seen from Figure 7(a) that most of the scattered points 
are clustered in the interval [-0.1, 0.1], with high precision. 

 

 
(a)                (b)                  (c)  

Figure 7. Underwater calibration effect diagram((a) Corner error 
distribution diagram ;(b) Position diagram of a single camera 

relative to the calibration plate ;(c) The relative position of 
binocular camera and calibration plate) 

 
According to the above analysis, the underwater refraction 

makes the underwater image distortion more serious. 
Therefore, the first three distortion coefficients of the radial 
distortion correction polynomial and the first two distortion 
coefficients of the tangential distortion correction polynomial 
are obtained by using the high-order polynomial for 
calibration calculation in this paper. The underwater 
calibration parameters of the binocular camera are shown in 
Table 1. Finally, the relative position diagram of binocular 
camera and calibration plate was obtained, as shown in Figure 
7(c). 

 
Table 1. Calibration parameters of underwater binocular camera 
Parameter Left camera Right camera
Internal 

parameter 
matrix 

441.9644 316.4981

441.58

0

0

0 0

39 234.520

1

 
 
 
  

 
440.2659 323.7030

439.92

0

0

0

12 225.5039

10

 
 
 
  

Distortion 
coefficient 

 0.7512 0.4994 0.0001 0.0014 0.5704
 

 0.7524 0.5419 0.0017 0.0015 0.6471 

Rotation 
matrix 

0.9999 0.0002 0.0037

0.0002 0.9999 0.0013

0.0037 0.0013 0.9999

 
 
 
  






 

Translation 
vector 

 24.9695 1.1318 1.4443   

 

The underwater image was corrected by using the internal 
and external parameters obtained from underwater calibration, 
so that the left and right eye underwater images were coplanar 
and aligned. The comparison of underwater images before 
and after correction is shown in Figure 8. 

 

 
(a) Underwater image before correction 

 
(b) Corrected underwater image 

Figure 8. Underwater image before and after correction 

5.5. Underwater Distance Measurement 
Experiment  

The images of underwater objects are obtained by 
binocular underwater camera, and the improved CLAHE 
algorithm is used to process the images. The SGBM algorithm 
is used for stereo matching and the depth map of the target at 
different distances is obtained. The binocular ranging 
principle is used to measure the distance of the target in the 
way of selecting points with the mouse. The actual 
underwater target ranging effect is shown in Figure 9. 

 

 
Figure 9. Underwater target ranging actual effect 

 
Images of underwater targets were collected by the 

binocular camera at a distance of 0.30m, 0.40m, 0.50m, 
0.60m, 0.70m and 0.8m. The depth of different positions is 
shown in Figure 10: 

 

(a) 0.30m           (b) 0.40m           (c) 0.50m 

 
(d) 0.60m              (e) 0.70m          (f) 0.80m 

Figure 10. Parallax map of target at different distances 
 
The average value of multiple measurements is taken. The 

results obtained from the underwater target ranging 



 

21 

experiment of the system are shown in Table 2 below 
 

Table 2. Experimental results of underwater target ranging 
True distance 

(m) 
Experimental ranging 

value (m) 
Absolute error 

(m) 
Relative error 

(%) 

0.300 0.3036 0.0036 1.20
0.400 0.4079 0.0079 1.98
0.500 0.5120 0.0120 2.40
0.600 0.5781 0.0219 3.65
0.700 0.6662 0.0338 4.83
0.800 0.7536 0.0464 5.80

 
According to the experimental results in Table 2, when the 

measured distance is within 0.5m, the error between the 
measured value of the target and the real distance between the 
target and the camera is small, the error is less than 2.4%, and 
the ranging effect is ideal. When the measured distance is 
greater than 0.5m, the error between the measured distance 
value of the target and the real distance value of the camera 
increases gradually, but the error is less than 6%, which meets 
the requirements of underwater experiment. 

5.6. Underwater Dimensional Measurement 
Experiment  

The target images are collected and processed successively 
at 0.2m, 0.30m, 0.40m, 0.50m, 0.60m and 0.70m from the 
distance camera. SGBM algorithm is used for stereo matching 
and the depth map of the target at different distances is 
obtained. The dimensions between the selected two points on 
the target are obtained by using the binocular ranging 
principle and the distance formula. The known actual 
diameter of the target is 0.21m, and the measurement effect 
of the actual underwater target size is shown in Figure 11. 

 

 

Figure 11. Actual rendering of underwater target size measurement 
 

Images of underwater targets are collected at 0.20m, 0.30m, 
0.40m, 0.50m, 0.60m and 0.7m away from the underwater 
camera. The depth of different positions is shown in Figure 
12. 

 

 
(a) 0.20m         (b) 0.30m           (c) 0.40m 

 
(d) 0.5m             (e) 0.6m             (f) 0.8m 

Figure 12. Parallax map of target at different distances 
 
At different positions, two points around the edge of the 

target diameter are selected to calculate its size value. The 
average value of multiple measurements is the measurement 
value of the underwater binocular size of the system. The 
experimental results of the measurement of the underwater 
target size are shown in Table 3 below. 

 
Table 3. Experimental results of size measurement of underwater 

target 
Measuring 

distance (m)
Binocular size 

measurement(m) 
Absolute 
error (m) 

Relative 
error (%)

0.20 0.2129 0.0029 1.38
0.30 0.2136 0.0036 1.71
0.40 0.2132 0.0032 1.52
0.50 0.2041 0.0059 2.81
0.60 0.2027 0.0073 3.48
0.70 0.1997 0.0103 4.90

 
According to the experimental results in Table 3, when the 

measurement distance is less than 0.5m, the system has a 
small error between the measured value and the actual size of 
the underwater target, which is less than 2.81%, indicating a 
high accuracy. When the measurement distance is greater than 
0.5m, the error between the measured value and the actual 
size of the underwater target obtained by the system gradually 
increases, but the error is less than 6%, which meets the 
requirements of underwater experiment 

6. Conclusion  
In view of the technical requirements of underwater 

binocular vision target ranging and size measurement, a 
binocular vision based underwater target ranging and size 
measurement system is designed. The system uses underwater 
binocular proximity for underwater target image acquisition. 
Through improved CLAHE algorithm, the obtained 
underwater image is processed and the image contrast is 
improved. The first three distortion coefficients of the radial 
distortion correction polynomial and the first two distortion 
coefficients of the tangential distortion correction polynomial 
are obtained by using the improved Zhang's calibration 
method to calculate the camera underwater calibration. The 
left and right eye underwater images are corrected in stereo 
by using the internal and external parameters of the camera 
underwater calibration, so that the underwater images meet 
the requirements of coplanar and line alignment. SGBM 
stereo matching algorithm is used to obtain the parallax map 
of the corrected underwater image, and then the underwater 
target ranging and size measurement are completed. The 
results of underwater experiments show that the underwater 
images processed by the improved CLAHE algorithm can 
enhance the details, improve the contrast, and greatly improve 
the visual effect. In the distance of 0.5m, the average accuracy 
of the system measurement is 97.19%, which has a high 
accuracy. When the measurement distance is greater than 
0.5m, due to the scattering and refraction of light in the 
underwater environment, and the increase of distance, there 
will be more interference of invalid pixels in the imaging 
plane, which increases the difficulty of binocular stereo 
matching, decreases the matching accuracy, and leads to the 
corresponding increase of measurement error. However, the 
measurement error of the system is still within 6%, which 
meets the requirements of underwater experiment. 



 

22 

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