aX, X.) rb(Y-Y.)t-o(Z,-Z;) 
a, (X, 7 Xs) AY, -YS)re(Z, -Z.) 
a, (X, - X) -b,(Y, - Y.) * c, (Z, 7 Z5) 
(X, — X.) t bh(Y, -Y eZ, -Z;,) 
VmxX-x tAxn-f 
  
  
VT NETS + Ay f 
Where (x;, y;) is image coordinates of point i, and Ax; Ay; are 
distortion correction of image point i. 
4.2 Setting of Number and Dimension of Particle 
When Particle Size is bigger than 60, the successful converging 
is more likely to happen; the increase in the population scale 
scan increase the stability of algorithm, whereas the calculating 
time will be more (Wei, 2008). Based on the amount of 
experiments, the author suggests setting range of the particle 
size between 40 and 50. 
The position of each particle represents a solution. Therefore, 
the dimension of solution vector decides the dimension of 
particle. Because there are six parameters, which could be taken 
as 6-dimensional vector, the dimension of particle in one image 
mode must be 6. 
4.3 Setting solution space range and maximum and 
minimum flying speed 
4.3.1 Setting of Solution Space Range: In the procedure of 
solving the approximate values of exterior orientation elements, 
the searching area of exterior orientation elements should be set, 
as the cube shown in Figure2. 
In the gross estimation of the position of exterior orientation 
elements, the solution space range is decided by the number of 
control points, or rather the gross range of line elements, angle 
elements. The more the control points, the wider the set range of 
solution space, and conversely, the fewer, the narrower. The 
experiments shows: if 3 object control points are used, the range 
of line elements of exterior orientation elements is set by line 
element standard value+Im, and the angle element range of 
exterior orientation elements is set by angle element standard 
value+0.5radian; if 6 object control points are used, the range of 
line elements of exterior orientation elements is set by line 
element standard value +5m, and the angle element range of 
exterior orientation elements is set by angle element standard 
value +1 radian. Here, the exterior orientation elements 
calculated by bundle adjustment are regarded as the standard 
value. Under this condition, the approximate values of exterior 
orientation elements calculated by PSO can be used in bundle 
adjustment. 
4.3.2 Setting of the Maximum and Minimum Flying 
Speed: The flying speed of particles decides the speed and 
quality of searching. If the speed is too high, the optimal 
solution couldn't be available; if the speed is too low, the 
searching area of particles would be too narrow and the 
possibility of finding optimal solution is also very low. That 
would lead to local optimization. The maximum and minimum 
flying speed is expressed as below: 
fe = K(X max = X4iin) (5) 
V min = EC ax = X imn) 
38 
where Vämax> Vdmin are the particle maximum and minimum 
flying speed in d-dimensional vector, and x,,,,, Xdmin are the 
maximum and minimum limited range for particle in d- 
dimension vector, and Æ is a scale factor. In general, the value of 
k is between 0.1~0.5. In this paper, the value of k which fits for 
solving of the approximate values of exterior orientation 
elements using PSO equal to 0.1 approximately. 
4.4 Setting of Acceleration Factors c;, c; 
In this paper, cj, c; are set as 2, which c, is a important 
parameter in self-cognition item G,, and c; also is a important 
parameter in the social sharing of information item G;. 
4.5 Setting of Inertia Weight Factor 
In this paper, the algorithm is improved based on the strategy of 
linear decreasing weight, and inertia weight factor w is 
determined by equation(6) and (7). 
m =1-run/runçax (6) 
0.6 (w,20.6) 
w=1w (0.4« w, « 0.6) en 
04 w <04 
Some constants used in PSO is set as in Table 1. 
  
  
  
  
  
  
  
  
  
  
Parameter Value | Parameter | Value 
Particle size 45 C1 2.0 
Particle dimension 6 €? 2.0 
k 0.12 
Residual (2-5)xnumber of control 
threshold(pixel) | points 
0.6 (w, 20.6) 
W, (0.4«w,«0.6) 
0.4 (w, €0.4) 
w 
run 
Ww, =1— 
run, 
(runmax=500) 
  
  
  
Table |. Setting of PSO Parameter 
where, wyax70.6 and WMin=0.4 are based on many experiments. 
4.6 Setting of Termination Condition 
Satisfactory solution will be found out through a lot of iterative 
calculation in PSO. In this paper, the maximum number of 
iteration and the threshold of sum of residual errors absolute 
value of all image points of control points in a image are set, 
and the sum of residual errors absolute value of image points is 
calculated using the approximate values of exterior orientation 
elements searched by PSO. If the difference between the sum 
and the threshold is less than a certain number or the number of 
iterations is more than the maximum number of iteration, the 
calculation procedure will be end. 
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