Scaling up Window-Based Slope Computations for Geographic Information System

Slope computations in Geographic Information Systems are typically done over windows of sizes as small as $3\times 3$ pixels, and the algorithms that are used do not scale to very large windows. Considering the abundance of high-resolution Digital Elevation Model (DEM) data, these algorithms are inadequate for providing high-quality processed data efficiently. We propose an iterative aggregation strategy, in which four values are aggregated in each iteration, and aggregates from previous iterations are reused. Our approach, thereby, scales logarithmically in the size of the windows. It is enabled by the observation that all quantities that are needed for determining slope are linear in the number of data points considered, allowing reuse in the next iteration. We show the usefulness of the proposed strategy for artificial data as well as actual Digital Elevation Model data.