A progressive black top hat transformation algorithm for estimating valley volumes on Mars

Abstract

a b s t r a c tThe depth of valley incision and valley volume are important parameters in understanding the geologic history of early Mars, because they are related to the amount sediments eroded and the quantity of water needed to create the valley networks (VNs). With readily available digital elevation model (DEM) data, the Black Top Hat (BTH) transformation, an image processing technique for extracting dark features on a variable background, has been applied to DEM data to extract valley depth and estimate valley volume. Previous studies typically use a single window size for extracting the valley features and a single threshold value for removing noise, resulting in finer features such as tributaries not being extracted and underestimation of valley volume. Inspired by similar algorithms used in LiDAR data analysis to remove above-ground features to obtain bare-earth topography, here we propose a progressive BTH (PBTH) transformation algorithm, where the window size is progressively increased to extract valleys of different orders. In addition, a slope factor is introduced so that the noise threshold can be automatically adjusted for windows with different sizes. Independently derived VN lines were used to select mask polygons that spatially overlap the VN lines. Volume is calculated as the sum of valley depth within the selected mask multiplied by cell area. Application of the PBTH to a simulated landform (for which the amount of erosion is known) achieved an overall relative accuracy of 96%, in comparison with only 78% for BTH. Application of PBTH to Ma'adim Vallies on Mars not only produced total volume estimates consistent with previous studies, but also revealed the detailed spatial distribution of valley depth. The highly automated PBTH algorithm shows great promise for estimating the volume of VN on Mars on global scale, which is important for understanding its early hydrologic cycle.

Global Map of Martian Fluvial Systems: Age and Total Eroded Volume Estimations

“…With the development of many morphological image processing techniques, other estimations of valleys' volume have been obtained (Jung et al, 2012;Luo et al, 2011Luo et al, , 2015Luo et al, , 2017Rodriguez et al, 2002). Luo et al (2017) developed a technique called progressive black top hat transformation method.…”

New Martian valley network volume estimate consistent with ancient ocean and warm and wet climate

“…However, their volume of VN excavation was based on eight largest VNs analysed in a previous study 28 , not on all the VNs mapped globally, even though they claimed that the rest of the VNs were small and had negligible contribution to the total global volume. Here we employed an innovative progressive black top hat (PBTH) transformation method to estimate the depth of each valley pixel 29 , the minimum volume of material that would have been excavated to form the global VNs 16 30 and the minimum cumulative volume of water required to do that.…”

How image-processing parameters can influence the assessment of dental materials using micro-CT

“…Black top-hat transformation is an image-processing technique for extracting dark features on a variable background that offers more accurate volume estimations. 40 The smallest possible voxel size should preferably be used for scans of small structures in order to maximize the accuracy of the measurements. 18,21,41,42 However, higher-resolution scans require longer acquisition times, because they must collect more projections and generate large datasets.…”