Effiziente Modellierung geometrischer Strukturen in digitalen Bildern Entwurf und Analyse neuer Algorithmen

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The Institute of Biomathematics and Biometry has recently developed new fast algorithms for the rapid computation of geometry-based adaptive image approximation schemes such as wedgelets, resulting in a speedup for wedgelet approximation of the order 103. Besides speed, an attractive new feature of our implementation is the fact that the algorithms provide instantaneous access to a whole scale of such approximations, from coarse to fine, allowing the development of a new generation of algorithms that use the multiscale information inherent in the scale of approximations. The proposed project has two aims: One is the further development and extension of our techniques to include more diverse local approximation models and geometries. The result will be approximation schemes that rely on a combination of geometric partitioning of the image domain and local regression. The project addresses the specification and mathematical analysis of such algorithms for the adaptive approximation of geometrical image features. The second aim is the development and mathematical analysis of multiscale algorithms that exploit the instantaneous access to the full scale of minimizers. As possible application of these methods we mention image-processing problems such as feature-oriented denoising, compression, pattern recognition or interpolation/resampling problems. Applications to real-life problems dealing with biomedical data and images will also be addressed.