Thus, the refracted ray can be calculated if the directional 
cosines of the incident ray, the point of intersection of the 
incident ray with the surface, and the directional cosines of the 
normal to the surface at that point are known. In our case, the 
functions of refractive surfaces are reduced to a simple plane 
equations. 
4. SYSTEM CALIBRATION SCHEME 
An efficient calibration scheme for the underwater imaging 
system is proposed (see Figure 4). The system calibration 
procedure can be divided into four stages: 
(1) Several pairs of images of a calibration control frame are 
taken in air without the waterproof front cover. Thus the 
conventional collinear equations with the lens distortion 
corrections and the CCD pixel scale factor are used to perform 
the calibration. As a result, the values of pixel scale factor, 
focal length, lens error distribution parameters and relative 
orientation parameters are obtained. Also, the errors caused by 
the electronic sources such as CCD linejittle and image 
recording (A/D conversion) can be identified in preprocessing. 
(2) Mount the front covers and repeat the above operations. In 
this case, the medium refraction should be considered. Firstly, 
we apply the medium refraction corrections and employ DLT 
(Direct Linear Transformation) to solve the approximate values 
of orientation parameters. And then the 3D ray tracing model is 
used to achieve the accurate results of the parameters. 
  
  
  
  
  
  
  
  
  
Figure 4. Schematic representation of calibration procedures 
and object measurement 
(3) Place the control frame into the water tank and repeat the 
above test. The water tank has a cylinder shape with a height 
and a diameter of about 2.5m. 
(4) After the above calibration procedure, the real sea survey 
can be performed. In a recent test, the imaging system was 
mounted on a ROV. The stereo image sequences of underwater 
objects and the control frame on the shallow water seafloor 
were captured. 
322 
5. EXPERIMENTS 
5.1 In-air Test With The Front Covers 
In the recent test, the baseline of the imaging system was fixed 
to 400mm and the typical camera-object distance was about 
2m. A 1.4x1.4x 0.7m aluminum control frame with 24 control 
targets was used. Table 1 shows the results of the reduced 
central perspective model using DLT. In this case, the media 
indices are treated as 1.0(air) and 1.34(cover). By Comparing 
the deference of measured camera exterior orientation 
parameters and computed ones, the computed results are 
satisfactory. It also demonstrates the derived model is correct. 
The RMS of adjusted control points (12 control points) are 
m,=3.5mm, m,=3.8mm, m=14.9mm, and the final vector RMS 
is 15.7mm. The accuracy of check points (10 points) are 
m,=3.6mm, m,= 4.0mm, m,=15.0mm and my,;=16.1 mm. 
Table 1. In-air test with the front covers 
  
  
Parameter Left camera Right camera 
f (pixel) 588.61 598.70 
Xp (pixel) 275.27 280.62 
Xp (pixel) 227.28 213.68 
Sy 1.075 1.078 
X0(m) 100.4935 100.8951 
Yo(m) 100.6375 100.6376 
Z0(m) -97.8093 -97.8027 
Q (rads) -0.0560 -0.0328 
ó (rads) -0.0089 0.0084 
K (rads) -0.0034 -0.0096 
Kj(102) 0.00001 -0.00001 
Ka(10-5) 0.00001 0.00010 
P1104 -0.01 0.04 
P2(10-4) -0.08 0.02 
  
  
  
  
  
5.2 Real Sea Site Test 
A group of stereo pairs of images of the control frame merged 
in the sea water were obtained. Due to the uncontrolled 
exterior orientations of the imaging system, the reduced central 
perspective model using DLT was applied to compute the 
parameters. The calibration results are shown in Table 2. The 
computed interior parameters (xp,y,,f) are different from the 
ones in Table 1. The differences may be caused by the 
correlation existing between the refraction corrections and the 
lens distortion corrections. These calibrated parameters are 
employed as approximate values for the 3D ray tracing model. 
The final results of ray tracing model are that the RMS of 
control points is my=8.4mm, my=9.3mm and m,=2.lmm, 
respectively. Totally, 13 control points are used for this 
adjustment. For detail processing of this model, interested 
readers can find the description in (Li, 1995). 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B5. Vienna 1996 
  
  
  
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