Uncovering symmetries in polynomial systems
Larsson, Viktor; Åström, Kalle (2016). Uncovering symmetries in polynomial systems. Leibe, Bastian; Matas, Jiri; Sebe, Nicu; Welling, Max (Eds.). Computer Vision – ECCV 2016 14th European Conference, Amsterdam, The Netherlands, October 11-14, 2016, Proceedings, Part III, 9907,, 252 - 267: Springer
Conference Proceeding/Paper
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Published
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English
Authors:
Larsson, Viktor
;
Åström, Kalle
Editors:
Leibe, Bastian
;
Matas, Jiri
;
Sebe, Nicu
;
Welling, Max
Department:
Mathematics (Faculty of Engineering)
Mathematical Imaging Group
Centre for Mathematical Sciences
ELLIIT: the Linköping-Lund initiative on IT and mobile communication
eSSENCE: The e-Science Collaboration
Research Group:
Mathematical Imaging Group
Abstract:
In this paper we study symmetries in polynomial equation systems and how they can be integrated into the action matrix method. The main contribution is a generalization of the partial p-fold symmetry and we provide new theoretical insights as to why these methods work. We show several examples of how to use this symmetry to construct more compact polynomial solvers. As a second contribution we present a simple and automatic method for finding these symmetries for a given problem. Finally we show two examples where these symmetries occur in real applications.
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