An Iterative Black Top Hat Transform Algorithm for the Volume Estimation of Lunar Impact Craters

Abstract

Volume estimation is a fundamental problem in the morphometric study of impact craters. The Top Hat Transform function (TH), a gray-level image processing technique has already been applied to gray-level Digital Elevation Model (DEM) to extract peaks and pits in a nonuniform background. In this study, an updated Black Top Hat Transform function (BTH) was applied to quantify the volume of lunar impact craters on the Moon. We proposed an iterative BTH (IBTH) where the window size and slope factor were linearly increased to extract craters of different sizes, along with a novel application of automatically adjusted threshold to remove noise. Volume was calculated as the sum of the crater depth multiplied by the cell area. When tested against the simulated dataset, IBTH achieved an overall relative accuracy of 95%, in comparison with only 65% for BTH. When applied to the Chang'E DEM and LOLA DEM, IBTH not only minimized the relative error of the total volume estimates, but also revealed the detailed spatial distribution of the crater depth. Therefore, the highly automated IBTH algorithm with few input parameters is ideally suited for estimating the volume of craters on the Moon on a global scale, which is important for understanding the early processes of impact erosion.

Keywords: Iterative Black Top Hat Transform (IBTH), crater volume, Moon, DEM