Complete Singularity Analysis for the Perspective-Four-Point Problem - Ecole Centrale de Nantes Access content directly
Journal Articles International Journal of Computer Vision Year : 2021

Complete Singularity Analysis for the Perspective-Four-Point Problem


This paper is concerned with pose estimation and visual servoing from four points. We determine the configurations for which the corresponding Jacobian matrix becomes singular, leading to inaccurate and unstable results. Using an adequate representation and algebraic geometry, it is shown that, for any orientation between the camera and the object, there are always two to six singular locations of the camera in the generic case where the points are not coplanar, corresponding to the intersection of four cylinders. The particular case where the four points are coplanar is also characterized. Furthermore, some realistic example configurations are considered to substantiate the theory and to demonstrate failure cases in pose estimation and image-based visual servoing when the camera approaches a singularity.
Fichier principal
Vignette du fichier
main.pdf (976.86 Ko) Télécharger le fichier
Origin Files produced by the author(s)

Dates and versions

hal-03070525 , version 1 (15-12-2020)



Beatriz Pascual-Escudero, Abhilash Nayak, Sébastien Briot, Olivier Kermorgant, Philippe Martinet, et al.. Complete Singularity Analysis for the Perspective-Four-Point Problem. International Journal of Computer Vision, 2021, 129 (4), pp.1217-1237. ⟨10.1007/s11263-020-01420-0⟩. ⟨hal-03070525⟩
430 View
168 Download



Gmail Mastodon Facebook X LinkedIn More