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.