International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XXXIX-B4, 2012 
XXII ISPRS Congress, 25 August - 01 September 2012, Melbourne, Australia 
3 
x10* Cross-Track Offset vs. SCS Temperature 
+ data 
ese lite d Curve 
. 4 
+. * 
  
  
Cross-Track Offset (degrees) 
  
  
2 4 6 8 19 12 14 16 18 20 22 
SCS Temperature (°C) 
  
Figure 7. Best-fit curves for the cross-track offset between the 
NAC-L to NAC-R. Red line is a best-fit curve (2"* order Fourier 
series). Y-axis units are 10? degrees. 
The relative offset correction was applied using a second order 
Fourier series with the following general form: 
f(x) 2 ag * a, cos(xw) * b, sin(xw) (1) 
*à» cos(2xw) * b5sin(2xw) 
where ay, a;, 42, b;, by, w= derived constants 
3.2 WAC Distortion Model and Pointing Correction 
Unlike the NAC, which can be directly tied to human artefacts 
on the lunar surface, the WAC in-flight geometric calibration 
was based on registration with map projected NAC images that 
have been processed with the latest calibration updates (see 
section 3.1). To limit topographic variation images were 
selected over the relatively flat Mare Imbrium region (Figure 8). 
In all, 729 WAC images (96 monochrome, 633 color) were co- 
registered to 1,212 NAC observations, thus collecting over 6.5 
million data points for deriving improved pointing and camera 
distortion models. 
  
Figure 8. Distribution of NAC images used for "ground truth" 
in calibrating the WAC instrument. The NAC observations are 
overlaid on the WAC derived topographic model, GLD100 
[Scholten et al., 2012]. 
3.2.1 Image Registration: To provide a "ground truth," 
NAC observation acquired over the Mare Imbrium region were 
map projected at 25 meters per pixel. WAC images, acquired 
under similar lighting conditions that overlapped these NAC 
images were oversampled and projected at the same pixel scale. 
Both images were map projected using the highest resolution 
digital terrain model, GLD100 [Scholten et al., 2012], and the 
latest ephemeris derived from radiometric data and altimetric 
crossovers [Mazarico et al., 2011]. 
Using a pattern-matching algorithm found in Integrated 
Software for Imagers and Spectrometers (ISIS) package 
compiled by the Astrogeology Research Group of the United 
States Geologic Survey (USGS) [Anderson et al., 2002] WAC 
images were registered to the NAC images (“Truth”) covering 
the same geographical region. Specifically, a region or pattern 
chip (in this case a 20 sample by 20 line region) was extracted 
from the map projected WAC image. The pattern chip was used 
to identify a matching region in the search chip. The search chip 
was a larger area found in the NAC image (in this case a 80 
sample by 80 line region). The pattern chip was scanned across 
and compared to sub regions of the search chip. A goodness of 
fit (GOF) was calculated for each point in the search chip by 
computing: 
GOF = | cov( pattern,subregion) | 
| var( pattern) x var(subregion ) 
(2) 
  
cov — covariance function 
var = variance function 
pattern = n x m pattern chip 
subregion =n x m sub-region of the search region 
where 
Upon walking the pattern chip through the search chip and 
calculating the corresponding goodness value for cach point, the 
pixel with the highest correlation value represents the position 
in the search chip that best matches the pattern chip. This result, 
however, was only good to one pixel accuracy. In most cases, 
the point may lie between a set of pixels. To match at the sub- 
pixel level, a surface model was generated over the matrix of 
GOF values. The maximum point of this surface estimates the 
true registration position of the pattern chip in the search chip. 
This process was repeated at multiple locations over each map- 
projected pair. Due to the large number of points (^ 6.5 M), any 
mis-registration has very little impact on the distortion 
modelling as a whole. 
The co-registration information was passed to a second ISIS 
program that identifies the location of the distorted and 
undistorted, or corrected, pixel. Due to the wide angle optics 
present on the WAC, images are distorted resulting in the 
location of pixels altered from their ideal point on the CCD. 
This effect increases the further the pixel is from the boresight, 
or where the optical axis of the lens intersects the focal plane. 
The program reads in the registration information and identifies 
where on the WAC focal plane the distorted (from the WAC 
image) and corrected (from the NAC image) pixel is located 
(Figure 9). This information can then be used to identify the 
distortion present in the WAC optics. 
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