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

[摘要] 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 x 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) x 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 P-3. (C) 2020 Elsevier B.V. All rights reserved.

[发布日期] 2020-12-01

[关键词] Critical loci;Projective reconstruction;Computer vision;Multiview geometry;Hilbert-Burch theorem