🤖 AI Summary
This study addresses the computational challenges posed by high-resolution digital elevation models (DEMs) in calculating topographic prominence at a global scale. The authors propose an approximately linear-time algorithm that efficiently computes the prominence of all peaks worldwide. The key insight is that the prominence of the vast majority of peaks is determined solely by local terrain, with only a small fraction influenced by distant higher summits. Leveraging this observation, the method refines classical algorithms and incorporates memoization to drastically reduce redundant computations and memory usage. Validation on real-world 3-arcsecond SRTM data demonstrates that the approach achieves substantial gains in computational efficiency while preserving the correctness of prominence values, enabling scalable prominence analysis across massive DEM datasets.
📝 Abstract
Prominence is one of the most important measurements in topography and mountaineering. This paper describes an efficient, almost linear time algorithm for computing mountain prominence for all peaks on Earth using digital elevation models (DEMs). It builds on top of a classic algorithm and leverages the observation that only a few peaks have their prominence determined by a relatively distant other mountain. Thus, the classic algorithm can be adapted to memorize and use less information without the loss of correctness. The algorithm is demonstrated using 3 arcsecond real-life data from SRTM datasets. Its importance is underscored by the increasing accuracy of Earth mapping methods and the corresponding growth in the amount of data that must be processed to compute prominence.