| 2. |
- Andrade-Loarca, Hector, et al.
(author)
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Shearlets as feature extractor for semantic edge detection : the model-based and data-driven realm
- 2020
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In: Proceedings of the Royal Society. Mathematical, Physical and Engineering Sciences. - : The Royal Society. - 1364-5021 .- 1471-2946. ; 476:2243
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Journal article (peer-reviewed)abstract
- Semantic edge detection has recently gained a lot of attention as an image-processing task, mainly because of its wide range of real-world applications. This is based on the fact that edges in images contain most of the semantic information. Semantic edge detection involves two tasks, namely pure edge detection and edge classification. Those are in fact fundamentally distinct in terms of the level of abstraction that each task requires. This fact is known as the distracted supervision paradox and limits the possible performance of a supervised model in semantic edge detection. In this work, we will present a novel hybrid method that is based on a combination of the model-based concept of shearlets, which provides probably optimally sparse approximations of a model class of images, and the data-driven method of a suitably designed convolutional neural network. We show that it avoids the distracted supervision paradox and achieves high performance in semantic edge detection. In addition, our approach requires significantly fewer parameters than a pure data-driven approach. Finally, we present several applications such as tomographic reconstruction and show that our approach significantly outperforms former methods, thereby also indicating the value of such hybrid methods for biomedical imaging.
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| 4. |
- Jorgensen, Palle, et al.
(author)
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Operator algebras and representation theory : frames, wavelets and fractals
- 2011
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In: Oberwolfach Reports. - 1660-8933 .- 1660-8941. ; 8:1, s. 901-978
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Journal article (peer-reviewed)abstract
- Operator Algebras and Representation Theory: Frames, Wavelets and Fractals Organized by: Palle E.T. Jorgensen (1), Gitta Kutyniok (2), Gestur Olafsson (3) and Sergei Silvestrov (4) (1) Department of Mathematics, University of Iowa, IA 52242-1466, IOWA CITY, UNITED STATES(2) Fachbereich Mathematik / Informatik, Universität Osnabrück, Albrechtstr. 28a, 49069, OSNABRÜCK, GERMANY(3) Department of Mathematics, Louisiana State University, LA 70803-4918, BATON ROUGE, UNITED STATES(4) Centre for Mathematical Sciences, Lund University, P.O. Box 118, 22100, LUND, SWEDEN The central focus of the workshop was Kadison-Singer conjecture and its connection to operator algebras, harmonic analysis, representation theory and the theory of fractals. The program was intrinsically interdisciplinary and represented areas with much recent progress. The workshop includes talks on operator theory, wavelets, shearlets, frames, fractals, representations theory and compressed sensing.
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