A Bayesian Approach to Subkilometer Crater Shape Analysis Using Individual HiRISE Images

Abstract

The ages of terrains on other planetary bodies are chiefly determined using crater size–frequency distributions. However, primary impacts can generate numerous secondary craters that can affect the crater population. Classifying impact craters as primary or secondary is commonly done via time-consuming manual inspection, which limits the areas that can be analyzed at high resolution. We present a parametric model for characterizing small (100–600 m diameter) impact craters, where the model parameters have implications for describing the physical processes involved in their formation and modification. We infer these parameters from craters in images captured by the high-resolution imaging science experiment (HiRISE) camera onboard the Mars Reconnaissance Orbiter. For each crater within the appropriate size range, our algorithm creates a 3-D surface for a parametrically modeled crater and a 2-D rendering using illumination metadata, including emission, phase, and solar incidence angles at the time when the image was captured. A function describes the likelihood of each set of model parameters in terms of the geometry of craters in a given HiRISE image. These values are then optimized using a Metropolis–Hasting Markov chain Monte Carlo sampler. We evaluated three different prior probability distributions over the parameter space and two different likelihoods: one for digital terrain models and the other for images. We show that after applying t-distributed stochastic neighbor embedding (t-SNE) over the inferred crater parameters, t-SNE is able to project the multidimensional crater parameters into a 2-D space where secondary craters cluster together and are separable from primary craters.