A sparse resultant based method for efficient minimal solvers

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F20%3A00345986" target="_blank" >RIV/68407700:21230/20:00345986 - isvavai.cz</a>

Result on the web

<a href="https://doi.org/10.1109/CVPR42600.2020.00184" target="_blank" >https://doi.org/10.1109/CVPR42600.2020.00184</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1109/CVPR42600.2020.00184" target="_blank" >10.1109/CVPR42600.2020.00184</a>

Result language

angličtina

Original language name

A sparse resultant based method for efficient minimal solvers

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 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 Groebner 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 Groebner 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 Groebner 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 Groebner basis methods for minimal problems in computer vision

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

Result was created during the realization of more than one project. More information in the Projects tab.

Continuities

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

Publication year

2020

Confidentiality

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

Article name in the collection

2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition

ISBN

978-1-7281-7169-2

ISSN

1063-6919

e-ISSN

2575-7075

Number of pages

10

Pages from-to

1767-1776

Publisher name

IEEE Computer Society

Place of publication

USA

Event location

Seattle

Event date

Jun 13, 2020

Type of event by nationality

WRD - Celosvětová akce

UT code for WoS article

000620679502003