Algorithms for ridge and valley detections in terrain maps

We introduce "the steepest ascent method" and "the steepest descent method" to more effectively detects ridges and valleys in terrain maps, respectively. First, we propose algorithms by our methods. Next, we detect ridges and valleys in the entire Japan to compare our methods with the discrete Laplace transform method and show various advantages for our methods. And then, we claim that our algorithms can get sharper ridge and valley lines than the discrete Laplace transform method and makes it possible to generate terrain maps detected ridges and valleys in a huge area such as the entire Japan.