Caselles, VicentSapiro, GuillermoSolé, Andres2007-08-162007-08-162002-10https://hdl.handle.net/11299/3834In this paper we develop and analyze basic geometric structures for the topographic representation of images. One component of the geometric description is based on the Morse structure of the image, while a second one is connected to its drainage structure. These fundamental descriptors could be used as building blocks for a geometric multiscale representation of images in general and Digital Elevation Models (DEM) in particular. The topographic significance of the Morse and drainage structures of DEMs suggests that they can be used as the basis of an efficient encoding scheme. Therefore, we combine this geometric representation with partial differential equations based interpolation algorithms and lossless data compression techniques to develop a compression scheme for DEM. This algorithm permits to obtain compression results 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.