Figure 2. A flowchart of the MBARS algorithm. The blue box shows the required input data, all of which are available on the PDS. The image is specified manually, but the image metadata are automatically fetched by MBARS locally. The green box shows the processing steps of MBARS, described in detail in Section 3. The algorithm generally works with a single image panel at a time and carries out analyses with different shadow boundaries in sequence. The final product, the GIS-ready list of boulder objects and attributes, compiles all image panels into a single file for import to a GIS software. The user compares the results of the different boundary parameter settings to the manually counted boulders within the test areas (purple box) choosing the best-fit solution as the final MBARS output.

3.1. Image Preparation and Shadow Boundary Selection

Prior to MBARS processing, several steps are taken to prepare the image for analysis. First, the HiRISE image is broken into panels, which we carry out with the Split Raster tool in ArcMap This provides crucial map orientation information to MBARS (as .pgw world files, which are required for later steps) and splits the HiRISE image into manageable sizes for processing. The size of each panel can be controlled by the user, though 500-1000 pixel square image panels (~125-250 m) are used in this work. The individual panel size is only limited by computer hardware and MBARS can receive panels of any size.
Previous shadow segmentation methods have relied on maximum entropy thresholding (Golombek et al., 2008) or range filtering (Nagle-McNaughton et al., 2020) to define shadow boundaries. The maximum entropy thresholding approach used in the G-H method creates two classes within the image, shadows and non-shadows, and modifies the brightness boundary between those two classes to maximize the inter-class entropy. MBARS takes a different approach, predicting a shadow boundary, i.e., the expected maximum brightness to be considered a part of a shadow, for each image by forward modeling (Fig. 3). To predict a shadow boundary, three key components are used: the darkness of shadows, the brightness of non-shadow pixels, and the PSF of the HiRISE instrument. The interior of shadows larger than ~5 pixels are not perfectly dark but are generally dark enough to register as Digital Number (DN, corresponds to pixel brightness in the image) =1 in HiRISE images. The brightness of non-shadow pixels varies among images due to changing surface properties (e.g., albedo) and photometric conditions. Instead of predicting these changes, the brightness distribution in the target HiRISE image is statistically sampled and used in the shadow model. Note that this calculation is done on the entire image, not on individual image panels, making the shadow boundary calculation consistent across image panels. Finally, the HiRISE PSF is well-quantified from in-flight imaging of on-board targets and stars (McEwen et al., 2007), though other factors (spacecraft jitter, atmospheric conditions, etc.) are more difficult to constrain. Following previous HiRISE work (Kirk et al., 2008), a Lorentzian function with λ (half-width at half-maximum) = 0.77 is used here for the HiRISE PSF. Other factors that may influence the effective PSF are assumed to be accounted for within this PSF. To predict how a dark shadow will be blurred with the surrounding, brighter non-shadow pixels, we construct a model image with a dark (DN=1) shadow and convolve it with a background (non-shadowed area, Fig. 3) which is randomly sampled from the image pixel brightness distribution. After convolution, the shadow interior becomes brighter due to blurring with the nearby background. The DN of pixels within the constructed shadow are recorded, and this process is repeated 100 times for each HiRISE image. From the 100 results, the average of a user-chosen percentile of each shadow is taken as the shadow boundary. The choice of boundary parameter is the only point of user influence. User selected boundary parameters between 40-70 (i.e., 40th and 70th percentile) produce MBARS results consistent with manual observations (Table S1).
MBARS segments each image panel based on the shadow boundary DN value, below which the pixels are considered to be part of a shadowed area. During this step, MBARS also retrieves relevant metadata (sub-solar latitude/longitude, resolution, incidence angle, etc.) from the RDRCUMINDEX file provided by the PDS. The image is also rotated according to the sun direction calculated from the sub-solar and sub-spacecraft coordinates provided in the HiRISE image metadata. This first collection of functions results in one primary product: the original image rotated and filtered such that pixel intensities above the shadow boundary are set to a fixed value. This segmented image is passed onto the next major function, Boulder Segmentation.