nay then be
; non-linear
the control
e invariance
In this case,
cluded the 6
meters, and
\Ithough the
n obtaining
5, the use of
parameters
on a triplet of
y established
the F-matrix
e collinearity
s of two near
aerial frame
see Figure 3.
ge coordinate
compute the
"he results for
ort Hood Data
n
rees.
1-3 in order to
ns, the imag
Edward M. Mikhail
coordinates must be scaled in order to prevent the solution from becoming unstable. A degenerate case occurs for
Models 2 and 3 for this particular case of aerial photography where the air base direction between the two near vertical
photographs is parallel to the image x coordinate direction, and an independent subset of the trilinearity equations is
selected.
2.2 Modeling For Non-Frame Imagery
One of the significant accomplishments of the MURI project has been the integration of remote sensing analysis with
the task of extraction of urban features. This has been made possible by the availability of high spatial and spectral
resolution image data such as generated by sensor systems known as HYDICE and HyMap.
2.2.1 HYDICE Modeling (Push-broom)
One HYDICE image contains 320 columns, and typically consists of four major frames each containing 320 lines,
resulting in a 320 column by 1280 line image for each of the 210 bands of the hyperspectral sensor. At constant time
intervals associated with each individual line of the pushbroom scan, 320 by 210 pixel arrays called minor frames are
exposed; see Figure 6(a). Since the geometric distortions that exist
among the 210 bands are negligible, rectification is performed on just
one of the bands which depicts features on the ground clearly. The
same transformation may then be applied to any of the other bands, or
later to the thematic image after each pixel has been classified.
line = -640
1 minor frame (a pushbroom line)
Instantaneous
Perspective
} Center
Mathematical modeling includes sensor and platform models. The
objective of sensor modeling is to relate pixels on an image to
coordinates in an orthogonal 3-dimensional sensor coordinate system
y (SCS). At any given instant of time, we can imagine the HYDICE
sensor positioned along its flight trajectory at the instantaneous
Eee. imei \ perspective center, coinciding with the origin of the SCS; see Figure
i 6(b). At this time instant 1 minor frame consisting of a line of 320
pixels is exposed.
1 major
frame
= 320 lines
ANE
WM
ONU
QN
SN Image Vector
NN
\
to ground point N
(b)
Platform modeling involves determining the exterior orientation of the
instantaneous perspective center, i.e. origin of the SCS, with respect to
the ground coordinate system. Three items are considered: the data
that is recorded in real time in the header of the HYDICE imagery;
piecewise polynomial as platform model; and the concept of a Gauss-
Markov process and its application to platform modeling.
Figure 6. (a) HYDICE Image, (b)
HYDICE Geometry
There are six time-dependent elements of exterior orientation consisting of three coordinates for position and three
angles for orientation. At one second intervals, the easting, northing, and height are recorded from the Global
Positioning System (GPS), which is operating in differential mode on board the aircraft. When functioning properly,
the standard deviations on the horizontal and vertical components of position are 0.4 and 0.9 meters, respectively. The
GPS data are used as a priori values, although they are not fixed, in both of the platform models considered.
Roll, pitch, and yaw angular values and rates are supplied by the inertial navigation system (INS) of the aircraft for
every minor frame of the HYDICE image; i.e., for each line. These data express the orientation of the aircraft with
respect to an inertial ground system in terms of three non-sequential angles. A flight stabilization platform (FSP) is
used aboard the aircraft to keep the orientation of the sensor roughly constant by compensating for changes in the
orientation of the aircraft. Three non-sequential angles for the FSP are recorded for each minor frame. Errors in the
INS data prevented it from being fully exploited in our experiments.
The piecewise polynomial approach involves the recovery of polynomial coefficients for each of the six elements of
exterior orientation. A different set of coefficients may be recovered for each segment of an image that has been
divided into sections. Constraints on the parameters, such as continuity, may be imposed at the section boundaries.
Although sufficient for the modeling of satellite pushbroom scanners, which are in a stable orbit, this method appears to
be too rigid for the modeling of an aircraft flight path, and therefore a more flexible approach was sought.
In the Gauss-Markov approach, six parameters per line are carried to model the instantaneous exterior orientation for
each pushbroom line. Parameters for each image line are tied, or constrained, stochastically to those of the previous
image line. This model allows for greater flexibility for linear feature constraints to contribute to parameter recovery
International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000. 595
