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.
Highlights
The morphologic transition of impact craters with increasing size from simple to complex is the result of evolutions involving the interaction of depositional and erosional processes
In comparison to Black Top Hat Transform function (BTH), the the estimating accuracy of 45.9%, which demonstrates the superiority of the Iterative Black Top Hat Transform (IBTH) method on the IBTH method improved the estimating accuracy of 45.9%, which demonstrates the superiority of the simulated lunar surface
The advantage of IBTH was that it estimated crater volume with a higher accuracy by adopting iterative window sizes and slope factors: a series of window sizes covered the different size of craters, which guaranteed that the craters were extracted in full shape
Summary
The morphologic transition of impact craters with increasing size from simple to complex is the result of evolutions involving the interaction of depositional and erosional processes. The crater volume, one of the most important morphometric parameters of a crater, is a critical piece of information to better understand these processes. Estimates of cavity volume for lunar craters are difficult to derive due to the lack of a wealth of good data, few direct measurements, and the presence of complex crater shapes. The appearance of central peaks, terraces, an unknown true rim height above the pre-impact surface, the role of structural uplift, and the degree of crater infilling by fallback ejecta all make it difficult to calculate crater volume [1,2,3,4,5,6,7]. Use of lunar morphometric relationships for crater depth, rim height, and floor width versus diameter permit approximations of the crater volume. Several studies found a broad range in the ratio of Ve /Vi for fresh craters and suggested a significantly higher ratio for large complex craters based on the fact that the accuracy of the data used was not sufficient to yield explicit results [7,9,10]
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