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reconstructed in space. 
The prerequisite for precise positioning is the 
system calibration which determines the 
parameters that define the camera geometry, 
the relative location and attitude of the camera 
pair, as well as the relationships between the 
stereo vision and positioning system. 
Image pairs are taken sequentially while the 
mobile mapping system drives at normal speeds. 
Through time, every image pair is tagged with 
the position and rotation of the van in a global 
coordinate system. Any information extracted 
from the image pairs is immediately available in 
the unique global coordinate system by the 
following two-step transformation: 
* Calculation of a local coordinate from left 
and right image coordinates 
* Transformation of a local coordinate to a 
global coordinate 
Fast, accurate acquisition of digital data is the 
major purpose of the mobile mapping system. In 
the following, we present the calibration of the 
GPSVan and the analysis of the positioning 
accuracy of the system. 
2. System Calibration 
The calibration of the GPSVan consists of 
camera calibration, relative orientation and 
rotation offset determination. The camera 
calibration is performed by analytical methods 
which include: capturing the images with 
different position and view angles of known 
control points from the test field, measuring all 
image coordinates, and performing computations 
to obtain camera parameters. The relative 
orientation and rotation offset are determined 
using constraints. 
2.1 Camera Calibration: 
The calibration itself is done by the well-known 
bundle adjustment method. The camera 
parameters which are treated as unknowns are 
calculated using known control points based on 
the collinearity equation. The camera parameters 
are defined by the focal length (c), the principal 
point (xp, yp) and the lens distortion. We use six 
distortion parameters, specifically, two for 
radial distortion, two for decentering distortion 
and two for affine transformation. The lens 
distortion is defined by: 
481 
dx x(r? — Da, + x(r* — Da, + 
(r^ — 2x as + 2xya, + xa5 + yag m" 
dy = yr? - Da, + yc -— Da, + 
2xya, + (r^ = 2y%)a, — yas 
where 
a,,a, Radial distortion 
a,,a, Decentering distortion 
as, a, Affine parameters 
r Distance to the principal point 
When we process the calibration data, all images 
are defined in a common coordinate system by 
their positions (X, Y, Z ) and three rotation 
angles. Different rotation systems, e.g. 
(P,œ,K), (W,P,K) etc. (Kraus, 1992), are 
available, and we chose the (W,@,K) system 
which is the most popular one in 
photogrammetry. Collinearity equations are 
defined by : 
Nx 
Xex,ytdt—6C-—— 
Nz 
(2) 
—-y,tdy- ey 
y p Nz 
with : 
Nx = r1 (X 7 X9) * rj3(Y = Yo) + ra, (Z - Zp) 
Ny=r,, (X-Xo tr) (Y-Yo)+r3, (Z-Zg) 
NZ = r13(X = Xo) + r23(Y- Yo) +r33(Z - Zo) 
C focal length, 
Xp» Yp Coordinate of principal point 
X,y Image coordinate 
X, Y,2 Coordinate of an object 
point(targets) 
X,,Y,,Z, Perspective center of the 
camera 
F'j,,....,74, Elements of rotation matrix 
dx,dy Correction terms (additional 
parameters) defined by (2). 
All camera parameters are treated as unknowns 
in equation(2). With a least squares solution, the 
camera parameters, the position and rotation of 
every image can be computed using known 
control points.