Critical loci for projective reconstruction from three views in four dimensional projective space are defined by an ideal generated by maximal minors of suitable 4×3 matrices, N, of linear forms. Such loci are classified in this paper, in the case in which N drops rank in codimension one, giving rise to reducible varieties. This rests on the complete classification of matrices of size (n+1)×n for n≤3, which drop rank in codimension one. Instability of reconstruction near non-linear components of critical loci is explored experimentally. The classification of special matrices as above is also leveraged to study degenerate critical loci for suitable projections from P3.

Critical loci in computer vision and matrices dropping rank in codimension one / M. Bertolini, G.M. Besana, R. Notari, C. Turrini. - In: JOURNAL OF PURE AND APPLIED ALGEBRA. - ISSN 0022-4049. - 224:12(2020 Dec).

Critical loci in computer vision and matrices dropping rank in codimension one

M. Bertolini
Primo
;
C. Turrini
Ultimo
2020

Abstract

Critical loci for projective reconstruction from three views in four dimensional projective space are defined by an ideal generated by maximal minors of suitable 4×3 matrices, N, of linear forms. Such loci are classified in this paper, in the case in which N drops rank in codimension one, giving rise to reducible varieties. This rests on the complete classification of matrices of size (n+1)×n for n≤3, which drop rank in codimension one. Instability of reconstruction near non-linear components of critical loci is explored experimentally. The classification of special matrices as above is also leveraged to study degenerate critical loci for suitable projections from P3.
Computer vision; Critical loci; Hilbert-Burch theorem; Multiview geometry; Projective reconstruction
Settore MAT/03 - Geometria
Settore INF/01 - Informatica
dic-2020
26-mag-2020
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/744927
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