Curvature analysis and geometric description of landforms using MATLAB

This paper suggests a differential geometry algorithm to objectively characterize the shape of 3-D land surfaces. Differential geometry is a mathematical framework for the quantitative description of curves and surfaces. The curvature defines the shape and orientation of points on the surface. By using differential geometry to calculate surface curvatures, mathematically rigorous geometric descriptions of land surfaces can be obtained, including determining if the surface at a given point is upwardly convex or concave. One MATLAB program is build to calculate the surface curvatures of land surfaces and visualize the results. Based on the visualization image of surface curvatures, we can perform a terrain shape classification and then use the classification for recognition of particular regions of the landforms and in estimating relative positions of these regions in the terrain.