This talk introduces geometric representations for two important imaging modalities: elevation maps and point cloud data.
In the first part of the talk, we describe two complementary geometric structures for the topographic representation of elevation maps. 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, and this is demonstrated. This is joint work with A. Sole, V. Caselles, and F. Arandiga.
The second part of the talk describes ongoing work with C. Moenning, F. Memoli, and N. Dyn on mulstiscale representation of point cloud data. This is based on geometric meshless subdivision ideas that we will present.
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