rmula,
NS in
the
iS
red
ne
Aras
-~
Mu om om ow om om ww me mm wm me we ws
14
U.
om the
; of the
| extend
ates the
e vector
e vector
Yo are
determined through calibration procedures before the survey.
Table 3. outlines how different quantities are obtained and their
expected accuracy. For more details on the georeferencing
process see Schwarz et. al. (1993b) and El-Sheimy and Schwarz
(1994).
The georeferencing equation (1) contains four unknowns (3
coordinates and one scale factor) in three equations. Having a N
images of the same scene will add Nx3 extra equations and N
unknowns (scale factors) for the same point (i). A least squares
solution of the space intersection between the N rays is computed
with (3xN - 3 - N) degree of freedom.
Variable Obtained from Expected
accuracy
m
m. o Interpolated from the GPS/INS
INS positions at the time of exposure(t) 10-15 cm
gi Unknown (1) scale factor
Ry (t Interpolated from INS gyros output | 1.5 arcmin
at the time of exposure(t)
R° Calibration 1-5 arcmin
r Measured image coordinates 0.5 pixel
b
a Calibration 2-5 mm
Table 3. Elements of the Georeferencing Formula
- 3. SYSTEM CALIBRATION
Highly accurate calibration of all sensors of the integrated system
is an essential requirement to ensure accurate 3-D positions.
System calibration includes the determination of camera
parameters which define the internal geometry of the camera.
They are termed the inner orientation parameters. The relative
location and orientation between the camera cluster and the
navigation sensors (GPS and INS) are defined by the relative
orientation parameters. The relative orientation parameters will
be used in the transformation of the 2-D image coordinates into
the 3-D world coordinates in the georeference process.
The calibration requires a number of Ground-Control-Points
(GCP). A test-field of circular reflective targets of 5 inch
diameter were used. An automatic detection method was
implemented for measurement of the target centers (Cosandier
and Chapman, 1992). In order to determine the relative position
and orientation between the cameras and the GPS/INS, the
coordinates of the target points were determined in the m-frame
using a total station on the end points of a baseline which had
been measured previously using GPS receivers. In the remainder
of this chapter, the mathematical model for each set of
parameters will be discussed.
97
3.1 Inner Orientation
Inner orientation is a standard problem which has to be
performed before using any uncalibrated metric or digital
camera. It determines the interior geometry of the cameras. A
self-calibration bundle adjustment is used for this purpose. It
solves for the basic position (Xo, Yo, Zo) and the orientation (o,
®, x) parameters for each camera. These parameters will be used
to relate the cameras to the navigation sensors. In addition, the
nine elements which define the inner geometry of the camera are
solved for, namely principal point coordinates (xp, yp), lens focal
length (f), y-axis scale factor (ky- used when pixels are not
square) , three radial lens distortion coefficients (k1, k2, and k3),
and two tangential distortion coefficients (pl and p2) .
The mathematical model of the bundle adjustment with self-
calibration is based on the collinearity conditions. They are
formulated as follows:
U
Fr (xp) I + Ax
V
Fy-(y-yp *-fuy . ky * Ay Q)
Using the auxiliary parameters,
UT. foe
us 1° (3)
Ww Z-Zo
where,
X y Image coordinates,
RT Orthogonal matrix defining the rotation between the
m-frame and the camera coordinate system (c-frame)
X,Y,Z Object coordinates in the m-frame (WGS 84),
Ax, Ay Correction terms of additional parameters, mainly
the lens distortion parameters.
ky y axis scale factor.
3.2 Relative Orientation
The imaging component of the VISAT system consists of 8
video cameras with a resolution 640 x 480 pixels. The cameras
are housed in a pressurized-case and mounted inside a two
fixed-base towers on top of the VISAT-Van (Figure 4), thus
eliminating any chance for the cameras to move during the
survey.
The relative orientation parameters can be divided into two
groups. The first group contains the parameters which define the
relative position and orientation between different stereo-pairs.
The second group consists of the parameters that define the
relative position and orientation between the cameras and the
navigation sensors. The latter are essential for the georeferncing
process. To estimate the two group of parameters, some
constraints , are added to the bundle adjustment program (El-
Sheimy and Schwarz 1994). The constraint equations make use
of the fact that both the cameras and the INS are fixed during the
mission. This is achieved by acquiring a number of images at
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B2. Vienna 1996
