Algebraic Characterization of Essential Matrices and Their Averaging in Multiview Settings

Yoni Kasten, Amnon Geifman, Meirav Galun, Ronen Basri; The IEEE International Conference on Computer Vision (ICCV), 2019, pp. 5895-5903

Abstract


Essential matrix averaging, i.e., the task of recovering camera locations and orientations in calibrated, multiview settings, is a first step in global approaches to Euclidean structure from motion. A common approach to essential matrix averaging is to separately solve for camera orientations and subsequently for camera positions. This paper presents a novel approach that solves simultaneously for both camera orientations and positions. We offer a complete characterization of the algebraic conditions that enable a unique Euclidean reconstruction of n cameras from a collection of (^n_2) essential matrices. We next use these conditions to formulate essential matrix averaging as a constrained optimization problem, allowing us to recover a consistent set of essential matrices given a (possibly partial) set of measured essential matrices computed independently for pairs of images. We finally use the recovered essential matrices to determine the global positions and orientations of the n cameras. We test our method on common SfM datasets, demonstrating high accuracy while maintaining efficiency and robustness, compared to existing methods.

Related Material


[pdf] [supp]
[bibtex]
@InProceedings{Kasten_2019_ICCV,
author = {Kasten, Yoni and Geifman, Amnon and Galun, Meirav and Basri, Ronen},
title = {Algebraic Characterization of Essential Matrices and Their Averaging in Multiview Settings},
booktitle = {The IEEE International Conference on Computer Vision (ICCV)},
month = {October},
year = {2019}
}