A standardized approach for quantitative characterization of impact crater topography

Historically, topographic profiles provided a quantitative means to investigate the morphology and formation processes for impact craters, although no generic mathematical framework was developed to reduce profiles to morphology descriptors. Only need-specific polynomial expressions were utilized in previous studies, thus no standardized automated comparison of craters exists. We employ a Chebyshev polynomial function approximation to describe crater forms in a quantitative and repeatable manner. We show that the Chebyshev polynomials return coefficients that are relatable to crater morphologic characteristics, thus providing a standardized mathematical means for describing crater forms.