A Progressive Black Top Hat Transformation Algorithm for Estimating Valley Volumes from DEM Data

The amount of valley incision and valley volume are important parameters in geomorphology and hydrology research, because they are related to the amount erosion (and thus the volume of sediments) and the amount of water needed to create the valley. This is not only the case for terrestrial research but also for planetary research as such figuring out how much water was on Mars. 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. However, previous studies typically use one single structuring element size for extracting the valley feature and one single threshold value for removing noise, resulting in some finer features such as tributaries not being extracted and underestimation of valley volume. Inspired by similar algorithms used in LiDAR data analysis to separate above ground features and bare earth topography, here we propose a progressive BTH (PBTH) transformation algorithm, where the structuring elements size is progressively increased to extract valleys of different orders. In addition, a slope based threshold was introduced to automatically adjust the threshold values for structuring elements with different sizes. Connectivity and shape parameters of the masked regions were used to keep the long linear valleys while removing other smaller non-connected regions. Preliminary application of the PBTH to Grand Canyon and two sites on Mars has produced promising results. More testing and fine-tuning is in progress. The ultimate goal of the project is to apply the algorithm to estimate the volume of valley networks on Mars and the volume of water needed to form the valleys we observe today and thus infer the nature of the hydrologic cycle on early Mars. The project is funded by NASA's Mars Data Analysis program.