Computing stable resultant-based minimal solvers by hiding a variable

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F21%3A00354781" target="_blank" >RIV/68407700:21230/21:00354781 - isvavai.cz</a>

Result on the web

<a href="https://doi.org/10.1109/ICPR48806.2021.9411957" target="_blank" >https://doi.org/10.1109/ICPR48806.2021.9411957</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1109/ICPR48806.2021.9411957" target="_blank" >10.1109/ICPR48806.2021.9411957</a>

Result language

angličtina

Original language name

Computing stable resultant-based minimal solvers by hiding a variable

Original language description

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.

Czech name

—

Czech description

—

Type

D - Article in proceedings

CEP classification

—

OECD FORD branch

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Project

<a href="/en/project/EF16_019%2F0000765" target="_blank" >EF16_019/0000765: Research Center for Informatics</a><br>

Continuities

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year

2021

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Article name in the collection

2020 25th International Conference on Pattern Recognition (ICPR)

ISBN

978-1-7281-8808-9

ISSN

1051-4651

e-ISSN

1051-4651

Number of pages

8

Pages from-to

6104-6111

Publisher name

IEEE Computer Society

Place of publication

Los Alamitos

Event location

Milan

Event date

Jan 10, 2021

Type of event by nationality

WRD - Celosvětová akce

UT code for WoS article

000678409206032