Morse description and geometric encoding of digital elevation maps

Abstract

Two complementary geometric structures for the topographic representation of an image are developed in this work. The first one computes a description of the Morse-topological structure of the image, while the second one computes a simplified version of its drainage structure. The topographic significance of the Morse and drainage structures of Digital Elevation Maps (DEM) suggests that they can been used as the basis of an efficient encoding scheme. As an application we combine this geometric representation with an interpolation algorithm and lossless data compression schemes to develop a compression scheme for DEM. This algorithm achieves high compression while controlling the maximum error in the decoded elevation map, a property that is necessary for the majority of applications dealing with DEM. We present the underlying theory and compression results for standard DEM data.