| 2004 
  
d to 
V) of 
ingle 
long 
). So 
se of 
ntrol 
thod 
y the 
) tilt 
nded 
otate 
y, as 
eras' 
tical 
mera 
"the 
ige is 
cipal 
ar to 
axes 
from 
ytical 
al 
P, consists of the rectification of image tilt and the correction 
of projecting center shifts. The principal of tilt rectification is 
a BEA 0 sif, x 
vo | 0 cost, sind, y 
- fy sin), —sin, cod, cod), | | -/ 
that is, 
f xcosQ, — f sinQ,. 
Xo =~ ; : 
e ofa —xsin0, — f sin0, + f cos0, cos0, 
; ycos0, — f sin0, 
3 Se 
—xsin6, — ysinO, ^ f cos, cos, 
  
  
Add the correction value AS, AS, , then 
  
  
: xcosQ, — f'sinQ,, 
Muf i i zAS. 
—xsin0, — fsin0, + f cos0, cos0, : 
ycos0, — fsin0, 
Y fg : = t zASS 
—xsin0, — vsin0, + f cos0, cos0, : 
Lj. MULTI-CAMERA SYSTEM CALIBRATION 
The design in part 2 actually is an ideal situation that no error 
occurs during the process of system manufacture and assembly. 
However, the system error is inevitable. The real wide-angled 
photography system made of combined small-sized CCD 
cameras needs system calibration of high precision. The 
parameters to be calibrated ought to include: 
1) Each camera's inner elements (X, Va fo) and optical 
distortion parameters. 
2) Relative exterior elements ( 0 ,0,.0 06. dS. ds. )in 
combination system. 
3.1 Indoor and outdoor calibration field 
In order to carry out the required calibration, we utilize 
both indoor (Fig. 9) and outdoor (Fig. 10) calibration 
field, which are built specially for the purpose of 
close-range camera calibration. Within the two 
calibration fields, controlling points array with rather 
big space depth are arranged. The coordinates of them 
are precisely determined by geodetic instrument and are 
checked for deformation correction caused by varied 
environment conditions periodically. So the coordinates 
values of controlling points in our calibration field can 
be used as true value in system calibration. 
p adeo 
  
  
  
  
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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part Bl. Istanbul 2004 
Fig. 9: Indoor calibration field Fig. 10: Outdoor calibration field 
3.2 Principle and algorithm of camera calibration 
To peel off the correlative influence between inner and 
exterior elements (including distortion parameters), we 
specially designed the solution called space resection with 
multiple images. The method uses several images that cover a 
certain number of controlling points of calibration field, takes 
the coordinates of controlling points in image as observation 
value, solves exterior elements, optical distortion errors, other 
parameters affecting light beam shape as well as exterior 
elements of multi-images as a whole, on the basis of collinear 
equation, with the controlling points’ coordinates in object 
space taken as true value. 
Denote exterior elements as. X 4, , inner elements of image 
as X,,, some added parameters as X 
in ^ 
observation values 
ad ? 
as V . According to collinear equation in photogrammetry, 
the error equation can be written as: 
K-d4X. CR c4 
Where, the  denotations carry the following matrix 
expressions: 
vo 
V = T Xu [Af Ax, Ay, I 
v 
ds gu 034 04 "05 06 
Gu Dy On Oy Oy be 
CA 
0.0 A GC, € A 
X =[AN, AN AZ, Ap Aw Ax] 
X xu a, A Lf ff AJ 
€ 
a a 
ba E L-|x-€G) »-o 
Q5; Og (ho 
Suppose three images LII,III are captured, and each one 
possesses the communal points 1,2, ...n and has four added 
parameters a,,d, , P4, f), , then the error equation is 
Pe AX + BX +CX ~L 
d 
6nx| 6nx18 18d 6nx3 m 6nx4 2d 6nxl 
3xl