Determining the Singularities for the Observation of Three Image Lines

Sébastien Briot 1 Philippe Martinet 1 Francois Chaumette 2
2 Lagadic - Visual servoing in robotics, computer vision, and augmented reality
CRISAM - Inria Sophia Antipolis - Méditerranée , Inria Rennes – Bretagne Atlantique , IRISA_D5 - SIGNAUX ET IMAGES NUMÉRIQUES, ROBOTIQUE
Abstract : The determination of the singularity cases in the observation of image features is a complicated problem which is still open, apart from image points. For the first time, we provide the singularity cases in the observation of three image lines. We show that a concept named the “hidden robot”, which was formerly used for understanding the singularities of a vision- based controller dedicated to parallel robots and, more recently which proved to be efficient for finding the singularity cases in the observation of image points, can be used for interpreting the singularities in the observation of three image lines. The hidden robot concept considerably simplifies the analysis by using geometric interpretations of the mapping degeneracy and tools provided by the mechanical engineering community. We prove that in the most complicated case where three general lines in space are observed, singularities appear when the origin of the observed object frame is either on a quadric or a cubic surface whose location in space depends on the configuration of the observed lines. In simpler cases where at least two lines belong to the same plane, these two surfaces can degenerate into simpler geometrical loci (e.g. planes, cylinders, lines).
Type de document :
Article dans une revue
IEEE Robotics and Automation Letters, IEEE 2017, 2 (2), pp.412-419
Liste complète des métadonnées


https://hal.archives-ouvertes.fr/hal-01398925
Contributeur : Sébastien Briot <>
Soumis le : jeudi 1 décembre 2016 - 21:06:51
Dernière modification le : mardi 22 août 2017 - 14:56:31
Document(s) archivé(s) le : mardi 21 mars 2017 - 14:19:29

Fichier

2016_ral_briot.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

  • HAL Id : hal-01398925, version 1

Citation

Sébastien Briot, Philippe Martinet, Francois Chaumette. Determining the Singularities for the Observation of Three Image Lines. IEEE Robotics and Automation Letters, IEEE 2017, 2 (2), pp.412-419. <hal-01398925>

Partager

Métriques

Consultations de
la notice

775

Téléchargements du document

297