Vol. 29 (2020):
Abstracts and Contents of Papers
Machine GRAPHICS & VISION, Vol. 29 (2020), No. 1/4
This number is not closed yet. The papers are published within the Accepted papers online policy.
- Bertolini M., Magri L.:
Critical hypersurfaces and instability for reconstruction of scenes in high dimensional projective spaces
MGV vol. 29, no. 1/4, 2020, pp. 3-20.
Accepted paper online
In the context of multiple view geometry, images of static scenes are modeled as linear projections from a projective space to a projective plane and, similarly, videos or images of suitable dynamic or segmented scenes can be modeled as linear projections from to , with . In those settings, the projective reconstruction of a scene consists in recovering the position of the projected objects and the projections themselves from their images, after identifying many enough correspondences between the images. A critical locus for the reconstruction problem is a configuration of points and of centers of projections, in the ambient space, where the reconstruction of a scene fails. Critical loci turn out to be suitable algebraic varieties. In this paper we investigate those critical loci which are hypersurfaces in high dimension complex projective spaces, and we determine their equations. Moreover, to give evidence of some practical implications of the existence of these critical loci, we perform a simulated experiment to test the instability phenomena for the reconstruction of a scene, near a critical hypersurface.
critical loci, projective reconstruction, computer vision, multiview geometry.
Last updated August 19, 2020