Hundreds of thousands of lives were lost in the natural disasters such as geological earthquakes, floods, landslides and mud-rock flow in every year. Nowadays, with the rapid development in airborne LiDAR techniques, extraction of the multi-scale topographical features from high-resolution topographic data acquired via airborne LiDAR would lead to fundamentally new understandings of earth essential to mapping flood, landslide and mud-rock flow hazards for decision makers. In this paper, we define topographic features in a multi-scale manner using a center-surround operator on Gaussian-weighted mean curvatures. These multi-scale topographical features would allow improved detecting, understanding and prediction of flood inundation, landslide and mud-rock flow likelihood. For example, experimental results identify that proposed method can be employed for detecting landslide.