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The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B4. Beijing 2008
Region
ID
Terrain
Type
Number
of
Points
Residuals (pixel)
Mean
Standard
Deviation
Maximum
1
Flat
50
0.06
0.24
1
2
Crater
50
0.04
0.20
1
3
Summit
50
0.10
0.3
1
4
Dune
50
0.09
0.30
1.41
5
Flat/Ridge
50
0.11
0.33
1.41
Table 2. Matching residuals at level 7 for five test regions
For each region, 50 check points were randomly selected to
verify the quality of matching results with manually generated
tie points. Region 2 (crater) produced the smallest mean
residuals, though only slightly lower than Region 1 (flat). Both
areas contain a lot of small rocks that provide distinctive point
features beneficial to matching. Region 3 includes rather
smooth texture especially in the north side, while Region 4
mainly consists of a striped pattern caused by dunes. The Home
Plate area (Region 5) gave the largest mean residual, which can
be explained by its relative lack of detailed texture. The
performance of the automatic matching varied based on the type
of terrain. However, the five test regions showed consistently
low residuals, averaging less than 0.11 pixel, with a maximum
residual of less than 1.41 pixels.
3.3 Bundle Adjustment of HiRISE Stereo Images
Bundle adjustment aims at removing the inconsistencies
between HiRISE stereo images by adjusting their EO
parameters through the tie points. In our study, the initial EO
parameters were retrieved from the SPICE kernel and stored
line by line. The tie points were selected automatically from the
matched interest points on stereo images to make sure they were
evenly distributed. These tie points were then included in the
bundle adjustment as measurements after the interior orientation
procedure. A total of 500 tie points were selected from matched
interest points for the HiRISE stereo pair in the Columbia Hill
area.
In forming of the observation equations for bundle adjustment,
image tie points were related to the corresponding ground
coordinates and EO parameters via the collinearity equations
v , f a u (X i -X c ) + a n (Y-Y c ) + a n {Z-Z c )
' aM-X^ + a^-n + a^-Z 0 ) ( 3 >
| a 2i (X j -X c ) + a 22 (Y j - Y c ) + a 23 (Z j -Z c )
' a ìì (X,-X e )+a ì2 (Y i -r) + a 3ì (Z l -Z e )
where x, = along-track coordinate of the detector on the focal
plane of the i‘ h point which can be calculated using
Equation 1
y, = corresponding cross-track image coordinate of the
i' h point
X„ Y h Zi = ground coordinates of the i th point
X, T, 7T = position of the perspective center of the
sensor
an,...,a 33 = elements of the rotation matrix formed
by the sensor pointing angles
/= focal length of the sensor
To improve the stability of the adjustment computation,
telemetry data were treated as pseudo observations and were
combined with linearized collinearity equations in the bundle
adjustment system. The initial values of the EO polynomial
coefficients were from the least-squares fitting of the telemetry
EO data before bundle adjustment. The initial ground positions
of tie points were obtained through a space intersection using
telemetry EO data.
After bundle adjustment, the refined EO parameters were
compared with those obtained from telemetry data. Figure 5
presents their differences in graphic format. The horizontal axis
of Figure 5 is the image row index and the vertical axis is the
difference. The BA procedure modified the camera perspective
center and orientation by a maximum of close to 2 meters and
the pointing angles by less than 15 arc seconds.
(a) Differences in camera center positions
Change of Omega(red), Fai(green),
Kappa(blue)
(b) Differences in sensor orientations
Figure 5. Differences between telemetry-based and refined EO
parameters
Unlike the situation on Earth, no absolute ground truth is
available on the Martian surface. Therefore, the performance of
the bundle adjustment was evaluated in terms of back-projection
residuals in the image space. Besides the tie points, a
comparable number of evenly distributed check points that are
matched interest points and not used in the bundle adjustment
were also selected for evaluation. The differences between the
measured image points and the corresponding back-projected
image points represent the inconsistencies between HiRISE
stereo images. Table 2 shows the corresponding statistics of the
back-projection residuals on the images covering a part of
Columbia Hills before and after bundle adjustment.