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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
x^
s
Ba mpeg
That is,
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