Figure 5. An example of the calibration of MBARS with manual
analysis (a) and how the MBARS-interpreted boulder changes with carrying
running conditions (b). MBARS results are denoted “##_B”, where the
## represents the boundary parameter chosen for that run (Section 3.1)
clipped to test area B (Fig. 9).
4. Model Verification
Due to accompanying manual analysis, the accuracy of MARS results is
quantified for each image. However, further testing is warranted to
ensure the accuracy of MBARS outside of the test areas and compare MBARS
to other methods of boulder quantification. Three avenues are pursued
here to demonstrate the accuracy MBARS and compare it to other methods:
(1) measuring objects of known size, (2) comparing results to previous
manual analysis, and (3) comparing results to existing algorithms. In
the plots below, error bars are smaller than the symbols on the plot.
4.1. Measuring Known
Objects
Robotic landers represent one of the few objects on the martian surface
with fully known shape and size, making them the ideal target to ground
truth MBARS. Here, these act as well-defined objects that can be
measured with MBARS to test the accuracy of shadow-based measures. Six
images of the Viking 1 (VL1) and 2 (VL2) landers (Table 1) are used to
test MBARS and allow comparison with the G-H method, which was also used
to measure these landers (Golombek et al., 2008). Manual calibration
areas were chosen in each image far from the vicinity of the landers to
further demonstrate the generality of the solution generated in each
image. In the case of the VL1 images, a suitably rocky area could not be
identified for calibration, so a selection of widespread, individual
boulders was used to calibrate MBARS instead using the same techniques.
HiRISE images of VL1 and VL2 are shown in Fig. 6 with the two bright
spots showing the two wind covers on either side of these landers. In
these images, the landers cast a sharp, dark shadow, and MBARS always
succeeded in detecting and measuring the shadow. In general, the rock
diameters given by MBARS for the Viking landers are smaller than the
2.7m diameter of the landers (Table 1). Across the six images, MBARS
measures the VL1 lander between 2.0 m and 2.5 m, and VL2 between 2.3 m
and 2.6 m. Published analyses with the G-H method yielded similar
diameters as MBARS and similarly measured slightly higher dimensions for
VL2 than VL1 (Table 1). While there may be some role played by the local
topography or photometric properties of the two locales, the most likely
cause of difference between the VL1 and VL2 measurements is lander
orientation relative to the sun. The full 2.7 m width of the lander is
measured at its widest point, along the axis of the two RTG wind
screens, but this widest dimension is not necessarily captured by its
shadow. The orientation of VL1 and VL2 is well-constrained thanks to
correlation of rock populations from orbital and ground imagery
(Golombek et al., 2008).VL 1 is facing E-SE, with its long axis pointing
roughly NE-SW, and VL2 is facing NE, with its long axis pointing NW-SE.
In the VL1 images, the sun is oriented closer to the long-axis, making
the apparent diameter smaller, and in the VL2 images, the sun is
oriented more perpendicular to the long axis of the lander. In short,
their orientations relative to the sun reasonably explain the slightly
higher estimations for VL2, though neither are consistently measured at
their full width. For these observations, an extra step was taken to
calculate the actual height (Ha) of the landers (See Fig
1, Eq. 4). These correction amount to an ~20 cm increase
in height between Hm and Ha for all
observations, though the precise difference depends on the sun incidence
angle and boulder width. However, with this correction, all observations
are within 20cm of the known height of the lander, suggesting good
agreement between our spheroidal model and the landers.