990 
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.