Morse Description and Morphological Encoding of Continuous Data

A geometric representation for images is studied in this work. This is based on two complementary geometric structures for the topographic representation of an image. The first one computes a description of the Morse structure, while the second one computes a simplified version of drainage structures. The topographic significance of the Morse and drainage structures of digital elevation maps (DEMs) suggests that they can been used as the basis of an efficient encoding scheme. As an application we then combine this geometric representation with a consistent interpolation algorithm and lossless data compression schemes to develop an efficient compression algorithm for DEMs. This coding scheme controls the $L^{\infty}$ error in the decoded elevation map, a property that is necessary for the majority of applications dealing with DEMs. We present the underlying theory and some compression results for standard DEM data.

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