University of Oulu

S. Bhayani, Z. Kukelova and J. Heikkilä, "A Sparse Resultant Based Method for Efficient Minimal Solvers," 2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), Seattle, WA, USA, 2020, pp. 1767-1776, doi: 10.1109/CVPR42600.2020.00184

A sparse resultant based method for efficient minimal solvers

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Author: Bhayani, Snehal1; Kukelova, Zuzana2; Heikkilä, Janne1
Organizations: 1Center for Machine Vision and Signal Analysis, University of Oulu, Finland
2Center for Machine Perception Czech Technical University, Prague
Format: article
Version: accepted version
Access: open
Online Access: PDF Full Text (PDF, 3.6 MB)
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Language: English
Published: Institute of Electrical and Electronics Engineers, 2020
Publish Date: 2021-02-18


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 framework. Minimal problems often result in complex systems of polynomial equations. Many state-of-the-art efficient polynomial solvers to these problems are based on Gröbner basis and the action-matrix method that has been automatized and highly optimized in recent years. In this paper we study an alternative algebraic method for solving systems of polynomial equations, i.e., the sparse resultant-based method and propose a novel approach to convert the resultant constraint to an eigenvalue problem. This technique can significantly improve the efficiency and stability of existing resultant-based solvers. We applied our new resultant-based method to a large variety of computer vision problems and show that for most of the considered problems, the new method leads to solvers that are the same size as the the best available Gröbner basis solvers and of similar accuracy. For some problems the new sparse-resultant based method leads to even smaller and more stable solvers than the state-of-the-art Gröbner basis solvers. Our new method can be fully automatized and incorporated into existing tools for automatic generation of efficient polynomial solvers and as such it represents a competitive alternative to popular Gröbner basis methods for minimal problems in computer vision.

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Series: Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition
ISSN: 1063-6919
ISSN-E: 2575-7075
ISSN-L: 1063-6919
ISBN: 978-1-7281-7168-5
ISBN Print: 978-1-7281-7169-2
Pages: 1767 - 1776
DOI: 10.1109/CVPR42600.2020.00184
Host publication: 2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), 13-19 June 2020, Seattle, WA, USA
Conference: IEEE Computer Society Conference on Computer Vision and Pattern Recognition
Type of Publication: A4 Article in conference proceedings
Field of Science: 113 Computer and information sciences
111 Mathematics
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