I 
i X 
i zm 
0 100 20 
(c) 
s feeding 
ition of birds after 20 
ter 100 iteration 
a swarm of particle 
optimal solutions will 
mputation (iterative 
> themselves through 
m, called individual 
found by the particle 
| £Bes, 15 the optimal 
n. 
flowed. Suppose in a 
nber of particles is 7. 
ition of particle i. 
ion which is searched 
',£2..gp) means the 
whole particle swarm 
te(speed) of particle ; 
eed and position of 
m, and expresses the 
of particle i; 
item, and means the 
to present position of 
rticle 7 is considered; 
of information item, 
ıl optimal position of 
on of particle 7; c,,c, 
st the particle flying 
is used to adjust the 
)ptimal position. r;,7; 
Xj, 1$ the position in 
iterative. pj; is the 
'nsional for particle i. 
d dimensional for the 
particle swarm are 
re goes into iterative 
till the satisfactory 
can ensure the globe 
G4, are employed to 
Zeng, 2004). 
3. IMPROVED PARTICLE SWARM OPTIMIZATION 
WITH INERTIA WEIGHT FACTOR 
There is the advantage of fast convergence for PSO, but the 
disadvantage also is lower accuracy. For PSO algorithm, if 
acceleration factors and maximum speed are too high, particles 
may fly over optimal solution and the result is not converge. 
However, under the convergent situation, because all of 
particles fly to the direction of optimal solution, those particles 
will lose diversity, and the convergent speed of algorithm will 
be obviously slow down later. In order to solve the problem, Shi 
etc. put forward improved particle swarm optimization with 
inertia weight factor (Shi, 1998), whose equation is: 
v, t+) =w-Gl1+G2+G3 Q) 
x, 0+ D=x ()+v, +l) 15i<n 
Where w is inertia weight factor which relates to former speed. 
Its function is to control the influence of former speed on 
present speed. Larger w value can strengthen global search 
capability of PSO, while smaller w value can strengthen local 
search capability of PSO (Parsopoulos, 2001). This improved 
method can speed up converging and increase the effect of PSO 
algorithm. 
Shi suggests w be within [0~1.4]. However, the experiment 
result shows that when w is within [0.8~1.2], converging could 
be much faster, whereas when w>1.2, the algorithm will be 
more likely stuck in local extremum (Shi, 1998). The usual way 
to set w is below (Shi, 1999). 
X Wein) ; run run... (3) 
WS MX (Wera 
Where, Wmax» Wmin are respectively maximum inertia weight, 
minimum inertia weight, run is present number of iteration, 
FUNmax 1S maximum number of iteration, which could be 
interpreted as inertia weight factor w could be taken as the 
function of run. By the testing result (Shi, 1999), the insertion 
of inertia weight factor can bring about better effect. 
4. STRATEGY AND PROCEDURE OF CALCULATING 
APPROXIMATE VALUES OF EXTERIOR 
ORIENTATION ELEMENTS BASED ON PSO 
In order to increase the speed and accuracy of calculating the 
approximate values of exterior orientation elements using PSO, 
the method of limiting the number of searching is applied. 
Through many experiments, the maximum searching number is 
set as 500. 
In object space coordinate system O-XYZ, point S is projection 
center, and CP{i=1,2...n) is object control point, shown in 
Figure 2. 
57 
  
  
Figure 2. Diagram of Photography 
The flow chart of calculating the approximate values of exterior 
orientation elements of a image using PSO is shown as Figure 3. 
| Set Particle Size and Dimension | 
Set Objective Function 
Set Solution Space Area 
Set Maximum and Minimum Flying Speed 
Set cC1,C2,W 
  
     
  
  
  
  
   
    
  
   
    
Optimal 
Solution? 
Figure 3. Flow chart of calculating the approximate values of 
exterior orientation elements of a single image using PSO 
4.1 Define of Objective Function 
n(n23) object control points are employed in PSO. Image point 
coordinate Residual errors (v,;,v,i) of each control point can be 
calculated. Minimum Sum of residual errors absolute value of 
all image points of control points in this image is regarded as 
the objective function, shown as in equation(4). 
mn V=Y| G-12.523) (4 
izl 
where, |v{=|vel+|vyil|Va| is the residual error absolute value of x 
coordinate of image point i which corresponds to object control 
point CP; and |v,| is the residual error absolute value of y 
coordinate of image point i which corresponds to object control 
point CP;, and vj; vj; can be expressed as: