University of Oulu

S. Bhayani, Z. Kukelova and J. Heikkilä, "Computing stable resultant-based minimal solvers by hiding a variable," 2020 25th International Conference on Pattern Recognition (ICPR), 2021, pp. 6104-6111, doi: 10.1109/ICPR48806.2021.9411957

Computing stable resultant-based minimal solvers by hiding a variable

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Author: Bhayani, Snehal1; Kukelova, Zuzana2; Heikkilä, Janne1
Organizations: 1Center for Machine Vision and Signal Analysis, University of Oulu, Finland
2Visual Recognition Group, Faculty of Electrical Engineering, Czech Technical University in Prague
Format: article
Version: accepted version
Access: open
Online Access: PDF Full Text (PDF, 1 MB)
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Language: English
Published: IEEE Computer Society, 2021
Publish Date: 2022-03-21


Many computer vision applications require robust and efficient estimation of camera geometry. The robust estimation is usually based on solving camera geometry problems from a minimal number of input data measurements, i.e., solving minimal problems, in a RANSAC-style framework. Minimal problems often result in complex systems of polynomial equations. The existing state-of-the-art methods for solving such systems are either based on Gröbner bases and the action matrix method, which have been extensively studied and optimized in the recent years or recently proposed approach based on a resultant computation using an extra variable. In this paper, we study an interesting alternative resultant-based method for solving sparse systems of polynomial equations by hiding one variable. This approach results in a larger eigenvalue problem than the action matrix and extra variable resultant-based methods; however, it does not need to compute an inverse or elimination of large matrices that may be numerically unstable. The proposed approach includes several improvements to the standard sparse resultant algorithms, which significantly improves the efficiency and stability of the hidden variable resultant-based solvers as we demonstrate on several interesting computer vision problems. We show that for the studied problems, our sparse resultant based approach leads to more stable solvers than the state-of-the-art Gröbner basis as well as existing resultant-based solvers, especially in close to critical configurations. Our new method can be fully automated and incorporated into existing tools for the automatic generation of efficient minimal solvers.

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Series: International Conference on Pattern Recognition
ISSN: 1051-4651
ISSN-L: 1051-4651
ISBN: 978-1-7281-8808-9
ISBN Print: 978-1-7281-8809-6
Pages: 6104 - 6111
DOI: 10.1109/ICPR48806.2021.9411957
Host publication: 2020 25th International Conference on Pattern Recognition (ICPR)
Conference: International Conference on Pattern Recognition
Type of Publication: A4 Article in conference proceedings
Field of Science: 113 Computer and information sciences
Funding: The authors would like to thank Academy of Finland for the financial support of this research (grant no. 297732). Zuzana Kukelova was supported by OP VVV project Research Center for Informatics reg. no. CZ.02.1.01/0.0/0.0/16 019/0000765.
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