The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B4. Beijing 2008
Ephemeris Time (ET) when the center of the TDI block is
exposed.
be processed together under a uniform rigorous sensor model in
the bundle adjustment instead of being processed strip by strip.
The HiRISE instrument kernel provides the calibrated interior
orientation parameters needed to calculate the pixel view
direction with respect to the HiRISE frame
(MRO HIRISE OPTICAL AXIS). In the raw image, the row
position of each pixel is related to the Ephemeris Time, which
then determines the position and orientation of the HiRISE
frame. The CCD ID and the column position are translated into
the physical position of a pixel in the HiRISE frame. If a pixel
in CCD i is located at column m, the following equations can be
used to retrieve the ideal focal plane coordinates.
u = TDI/2 - 64 - (BIN/2 - 0.5)
v = (m - 0.5) • BIN - 1024
x = transxjo + transxjj • v + transx i>2 ■ u
y = transyj o + transtyj ] • v + transy i 2 • u
(1)
r = (x 2 + yV /2
dr/r =-0.0048509 + (¿-2.41312 ■ 10 ' 7 )
+ (r 4 -l.62369- 10 - 13 )
xp = x - (dr/r) • x
YP = y ~ (dr/r) • y
where u, v = pixel position with respective to CCD center
TDI = number of TDI elements in the along-track
direction (8, 32, 64 or 128)
BIN = binning mode (1,2, 3, 4, 8, or 16)
m = pixel position in column direction
x, y = pixel position with respect to HiRISE optical
axis
transx i k , transy i k = calibration parameters (k = 0,1,2)
xp, yp = ideal focal plane coordinates after
elimination of radial distortion
2.2 Image Pointing Data
Exterior Orientation (EO) parameters, which are the positions of
the camera perspective center and pointing angles at a specific
time, are provided in SPICE kernels. The EO parameters of
each image line can be retrieved by interpolating the
spacecraft’s trajectory and pointing vectors. Previous research
has shown that the change in EO parameters over short
trajectories can be well modeled using polynomials (Yoon and
Shan 2005; Li et al., 2007, 2008). In this research, second-order
polynomials are used to model this change
X‘ ( . — a 0 + a x t + a 2 t~
Y . = b 0 + b x t + b 2 t
Z c j. = c 0 +c { t + c 2 t 2
of, = d 0 + d x t + d 2 t 2
qfj. =e 0 + e x t + e 2 t 2
K °i = fo + f\ t + fi r
(2)
To apply the above strategy, one reference CCD strip must be
assigned; this strip can be arbitrarily chosen. Then the offsets
between other CCD strips and the reference strip are calculated
by comparing their EO data line by line. The line (row) index of
the EO polynomials of the reference strip starts from zero. For
the other non-reference strips, it starts from the offsets. The
initial value of the EO polynomial coefficients can be estimated
by least-squares fitting of the line-by-line telemetry EO data.
Small motions of the spacecraft around its nominal pointing,
called jitter, will distort the images. This problem was originally
identified in the Mars Orbiter Camera (MOC) images, but was
found to be more severe for HiRISE because of HiRISE’s
higher resolution (Kirk et al., 2007). High-frequency jitter can
be filtered out by subtracting the best-fitting polynomial from
the original telemetry HiRISE pointing angle data. For the
80,000 line image of Gusev Crater that was used in this study,
Figure 2 shows the extracted jitter on co, <p, k with the horizontal
axis being the image row index and the vertical axis being the
jitter magnitude in arc-seconds. An analysis of the extracted
residuals in the spectral domain does not show any significant
frequency. Therefore, it would be very difficult to incorporate
this “jitter” into a mathematical model.
Figure 2. Residuals after subtracting best fitting polynomial
from original telemetry EO data
Topographic effect of orbital jitter needs to be evaluated for
topographic capability analysis of HiRISE camera. For
evaluation, a single CCD pixel was projected onto the Martian
surface using telemetry EO data under the assumption that Mars
is a sphere with its radius derived from the nearest MOLA point.
The projected footprint was compared with another projected
footprint using EO parameters adopted using third-order
polynomials under the same spherical assumption. A maximum
difference of 2 meters, corresponding to 7 pixels on image, was
detected from the comparison in a 20-kilometer track at the
landing site of Mars Exploration Rover (Spirit). Further
investigation on jitter will be performed so that its effects can be
removed or reduced when mapping large areas.
where A 1 ), Y c il zf) = position of the perspective center of the
sensor of the i th line (time t)
a>i, tpi, K t = pointing angles of the i th line
a 0 , —,/2 = polynomial coefficients
t = time-dependent image line index number
Modeled this way, EO parameters can be adjusted by refining
the 36 polynomial coefficients of the stereo pair. Since all 14
CCDs are fixed to the HiRISE frame, they share the same
perspective center and focal plane. Therefore, changes in the
EO parameters of all 14 CCDs yield one set of polynomial
coefficients. This critical characteristic significantly reduces the
complexity of the bundle adjustment of HiRISE stereo images.
Images simultaneously generated by multiple CCD arrays can
3. PHOTOGRAMMETRIC PROCESSING OF HIRISE
STEREO IMAGES
3.1 Image Matching and Tie Point Generation
We have developed a coarse-to-fme hierarchical stereo
matching process (Figure 3). Raw HiRISE images contain
systematic noise such as offset in the image data numbers (DN),
dark current, and column-to-column gain variations (Becker,
2007). In HiRISE EDR (Experiment Data Record) data sets, the
image acquired by each CCD strip (14 in total) is stored as two
sub-image strips, each of which is 1024 pixels wide. Brightness
values of the two sub-image strips may be inconsistent. We
adjusted brightness values and then combined them together
into one seamless image with a 2048-pixel wide swath.
Afterwards, we removed any systematic strip noise. Then, an
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