Descriptors of topographical depressions: A dimension reducing approach

We consider unsupervised learning of three-dimensional shapes (values) from topographical method. We propose the method based on direct analysis of three dimensional valleys and hills in a topographical region. The first step of this proposed approach is to extract the outer contour of the depression for normalization and description. A dimension reduction approach is then used to examine the three-dimensional depressions as a function of two-dimensional contour lines at given values of a function representing the elevation at a given point. Taking into consideration the shapes of the outer contour, the inner contours, the normalized height, and possible additional contours, we quantify the similarity between topographical features.