1. INTRODUCTION
As a non-contact measurement method, close-range
photogrammetry has been used in many fields, such as
industrial field, biomedical field, etc. Admittedly, the generally
accepted way in close-range photogrammetry is to firstly set up
some control points around the object or on the surface of object
when the images of object are taken according to multi-
intersection photography mode. Then the exterior orientation
elements can be calculated using the space coordinates and
image coordinates of these control points. And in the rest
bundle adjustment, the exterior orientation elements are
employed as the initial values and recalculated, and space
coordinates of unknown points are also calculated at the same
time.
There are several typical methods, namely Space Resection,
Pyramid Principle and Direct Linear Transformation etc., to
compute exterior orientation elements in close-range
photogrammetry (Feng, 2003). Wang put forward a method to
slove approximate values of exterior orientation elements based
on 4 points on a same plane(Wang, 2006), and 2D direct linear
transformation is used to calculate approximate values of
exterior orientation elements (Zhang, 2002), and Guan Yunlan
etc. raise a space resection method based on unit quaternion
(Guan, 2008). These methods will be invalid if a small portable
plane control frame with few control points. Haralick
summarizes all prior work on the minimal solution for the
absolute orientation problem and recommends a solution
which is numerically stable (Haralick, 1994).
Through researching bird flocking, Reynolds found that a bird
only trace its limited number neighbour birds and want to find
food. But the final result is that the whole bird flock is likely
controlled under a same center. Namely, when a bird flock is
looking for food, the simplest way for the bird flock is to seek
the birds who are nearest to the food. Particle Swarm
Optimization (PSO) was put forward by an American social
psychologist Kennedy, J. and an electrical engineer Eberhart,
R.C., is a stochastic global optimization method based on
swarm intelligence, which was inspired by social behavior of
bird flocking or fish schooling (Kennedy, 1995).
Based on the strong global search feature of PSO, a improved
PSO method is put forward in this paper to calculate
approximate values of exterior orientation elements of close-
range images in this paper.
2. PARTICLE SWARM OPTIMIZATION ALGORITHM
For example, suppose there is a food (the black triangle) in a
plane, shown as in Figure 1(a). It is located at the center in the
area, which are X,Y€[0,200]. At the beginning, twenty
birds(shown as the black points) randomly fly without object in
the area. When the bird flock find the food in the area, almost
all birds will fly to the food point through certain time flying,
shown as in Figure 1(b)(c).
PSO for solving a optimization problem, a bird is called as
particle or agent, a solution of the problem corresponds to a
bird's position in search space. The fitness of all of the particles
is determined by a objective function, and the flying direction
and distance of each particle are defined by its' flying speed.
Then the particles will trace the current optimal particle and
search for the optimization in the solution space
36
Y Y Y
ne et 2 ee 20 ;
° o To ds. a
10h c2] 100] 2 gle fof ode
tp je | Hs
SR | a a e re = 1
0 — 100 200 0 — 100 200 0 100 20
(a) (b) (c)
Figurel. Stimulation of birds feeding
(a) initial distribution of birds (b) distribution of birds after 20
iteration (c) distribution of birds after 100 iteration
At the beginning of PSO procedure, a swarm of particle
(random solution) are initialized, and the optimal solutions will
be found through evolutionary computation (iterative
computation). Each particle will update themselves through
tracing two extremum. One extremum, called individual
extremum pg; is the optimal position found by the particle
itself, the other, called globe extremum gg,,, is the optimal
position found by the whole particle swarm.
The mathematical description of PSO is flowed. Suppose in a
D-dimensional search space, the total number of particles is n.
Vector x;7(xi,xXj..x;p) means the position of particle i.
Danes" (DiPi2--.Dip) means the optimal position which is searched
by particle ; till present step. SBes(g,g»..gp) means the
optimal position which is searched by the whole particle swarm
till present step. The position changing rate(speed) of particle ;
is shown as v;-(vi,vp..v;ip. So the speed and position of
particle i are described as equation (1).
v,(t+1)=G, TG, FG, (1)
KHAO. Sin
Where, G;-v;4(t), is the former speed item, and expresses the
influence of former speed to present speed of particle i;
G2 =c,r1(pidt)-xia(t)), is the self-cognition item, and means the
influence of the historical optimal position to present position of
particle i while only the experience of particle i is considered;
G3 =c2r2(pgdlt)-x;a({)), is the social sharing of information item,
and indicates the influence of the historical optimal position of
the whole particle swarm to present position of particle i; cı,c,
are acceleration factors.c; is used to adjust the particle flying
step size toward itself optimal position. cz is used to adjust the
particle flying step length toward global optimal position. r,,r;
are two random numbers belong to [0,1]. x;; is the position in
No.d dimensional for particle i at No./ iterative. p;; is the
individual extremum position in No.d dimensional for particle i.
Pga is the globe extremum position in No.d dimensional for the
whole particle swarm.
The initial position and initial speed of particle swarm are
generated randomly, and then the procedure goes into iterative
computation according to equation(l) till the satisfactory
solution is found. In equation(1) item G; can ensure the globe
convergence performance, and G; and G; are employed to
ensure the local convergence performance (Zeng, 2004).
Ther
disa«
acce
may
How
parti
will
beo
etc.
inert
Whe
Its 1
pres
capa
sear
met]
algo
Shi
resu
be 1
mor
to Se
Whe
min
run,
intei
func
of ir
In o
app!
the
Thr
set €
In o
cent
Figt
