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