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Smooth determinantal varieties and critical loci in multiview geometry
- Source :
- Collectanea Mathematica. 73:457-475
- Publication Year :
- 2021
- Publisher :
- Springer Science and Business Media LLC, 2021.
-
Abstract
- Linear projections from $$\mathbb {P}^k$$ P k to $$\mathbb {P}^h$$ P h appear in computer vision as models of images of dynamic or segmented scenes. Given multiple projections of the same scene, the identification of sufficiently many correspondences between the images allows, in principle, to reconstruct the position of the projected objects. A critical locus for the reconstruction problem is a variety in $$\mathbb {P}^k$$ P k containing the set of points for which the reconstruction fails. Critical loci turn out to be determinantal varieties. In this paper we determine and classify all the smooth critical loci, showing that they are classical projective varieties.
- Subjects :
- Applied Mathematics
General Mathematics
0211 other engineering and technologies
021107 urban & regional planning
Locus (genetics)
02 engineering and technology
010501 environmental sciences
01 natural sciences
Combinatorics
Set (abstract data type)
Mathematics - Algebraic Geometry
Reconstruction problem
Position (vector)
FOS: Mathematics
Algebra over a field
Variety (universal algebra)
Algebraic Geometry (math.AG)
Determinantal varieties · Minimal degree varieties · Multiview geometry · Critical loci
0105 earth and related environmental sciences
Mathematics
Subjects
Details
- ISSN :
- 20384815 and 00100757
- Volume :
- 73
- Database :
- OpenAIRE
- Journal :
- Collectanea Mathematica
- Accession number :
- edsair.doi.dedup.....d42986bafeb32770aa205ec5e8b74a44