Page 229 - Digital Analysis of Remotely Sensed Imagery

Image Geometric Rectification 193

at the instant of exposure determined from the INS/GPS. s is the
a
scalar factor of the image, implicitly derived during the photogram-
metric reconstruction of a 3D model from a pair of stereoscopic
images, so does not need special computation to determine. R is
INS
the rotation matrix involving the three orientation angles of w, j,
and k derived from the INS/GPS integration. r is a matrix of coor-
a
dinates for point a in the focal plane, measured from the principal
point of the photograph. It is expressed as

⎛ n − n ⎞ T
r = ⎜ e − e a pp − f ⎟ (5.29)
a ⎝ a pp k ⎠

where (e , n ) = image coordinates of point a corresponding to the
a a
ground point A
(e , n ) = offsets of the principal point from the CCD center
pp pp
k = factor accounting for the nonsquare shape of the
CCD pixels
f = calibrated focal length of the camera lens

R INS (boresight) is the transformation matrix which rotates the
c
INS body-frame into the camera frame, or the INS/camera orienta-
tion offset (Mostafa and Schwarz, 2000). Similar to R and R , R INS
INS O c
is a function of time. Its value is based on time measurements from a
spacecraft constellation. There are two ways of computing it: either
measured with an extra sensor carried aboard or via tight coupling of
the INS with a camera during photography. In the second method, a
tight bundling of the INS and the camera during photography is
advantageous because it keeps the orientation offset constant. How-
ever, the camera model needs validation in a test flight over a perma-
nent ground field or a part of the area to be photographed. Test flights
are also needed to calibrate the bundled system and INS boresight
R INS , a pivotal parameter in transforming the INS-measured altitude
c
and angles into photogrammetric angles with respect to a local
mapping frame of reference. Since the INS and the camera can rotate
independently of each other, the offset needs to be computed for each
flight if the INS is detached from the camera between flights. If the
two are permanently coupled, then the constant offset needs only
occasional calibration.
The accuracy of direct georeferencing is affected by a number of
factors, such as the GPS/INS system used, the reliability of the coef-
ficients (e.g., how accurately the system is calibrated overall), and
camera interior orientation parameters (Skaloud, 2002). Integration
of GPS and INS allows the determination of attitude (roll, pitch, head-
ing) and position (E, N, H) of the camera at the time of exposure.