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| 001 | 830151 | ||
| 005 | 20210129230431.0 | ||
| 020 | _ | _ | |a 978-3-319-57239-0 (print) |
| 020 | _ | _ | |a 978-3-319-57240-6 (electronic) |
| 024 | 7 | _ | |a 10.1007/978-3-319-57240-6_23 |2 doi |
| 024 | 7 | _ | |a 0302-9743 |2 ISSN |
| 024 | 7 | _ | |a 1611-3349 |2 ISSN |
| 024 | 7 | _ | |a WOS:000425356700023 |2 WOS |
| 037 | _ | _ | |a FZJ-2017-03728 |
| 041 | _ | _ | |a English |
| 082 | _ | _ | |a 004 |
| 100 | 1 | _ | |a Burgeth, Bernhard |0 P:(DE-HGF)0 |b 0 |e Corresponding author |
| 111 | 2 | _ | |a 13th International Symposium on Mathematical Morphology and Its Applications to Signal and Image Processing |g ISMM 2017 |c Fontainebleau |d 2017-05-15 - 2017-05-17 |w France |
| 245 | _ | _ | |a A Unified Approach to PDE-Driven Morphology for Fields of Orthogonal and Generalized Doubly-Stochastic Matrices |
| 260 | _ | _ | |a Cham |c 2017 |b Springer International Publishing |
| 295 | 1 | 0 | |a Mathematical Morphology and Its Applications to Signal and Image Processing / Angulo, Jesús (Editor) ; Cham : Springer International Publishing, 2017, Chapter 23 ; ISSN: 0302-9743=1611-3349 ; ISBN: 978-3-319-57239-0=978-3-319-57240-6 |
| 300 | _ | _ | |a 284 - 295 |
| 336 | 7 | _ | |a Contribution to a conference proceedings |0 PUB:(DE-HGF)8 |2 PUB:(DE-HGF) |m contrib |
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| 490 | 0 | _ | |a Lecture Notes in Computer Science |v 10225 |
| 520 | _ | _ | |a In continuous morphology two nonlinear partial differential equations (PDEs) together with specialized numerical solution schemes are employed to mimic the fundamental processes of dilation and erosion on a scalar valued image. Some attempts to tackle in a likewise manner the processing of higher order data, such as color images or even matrix valued images, so-called matrix fields, have been made. However, research has been focused almost exclusively on real symmetric matrices. Fields of non-symmetric matrices, for example rotation matrices, defy a unified approach. That is the goal of this article. First, the framework for symmetric matrices is extended to complex-valued Hermitian matrices. The later offer sufficient degrees of freedom within their structures such that, in principle, any class of real matrices may be mapped in a one-to-one manner onto a suitable subset of Hermitian matrices, where image processing may take place. Second, both the linear mapping and its inverse are provided. However, the non-linearity of dilation and erosion processes requires a backprojection onto the original class of matrices. Restricted by visualization shortcomings, the steps of this procedure are applied to the set of 3D-rotation matrices and the set of generalized doubly-stochastic matrices. |
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| 700 | 1 | _ | |a Kleefeld, Andreas |0 P:(DE-Juel1)169421 |b 1 |u fzj |
| 773 | _ | _ | |a 10.1007/978-3-319-57240-6_23 |
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