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arXiv · 1902.00376

Matrices dropping rank in codimension one and critical loci in computer vision

Marina Bertolini·GianMario Besana·Roberto Notari·Cristina Turrini
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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 $4 \times 3$ 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 leads to a complete classification of matrices of size $(n+1) \times n$ for $n \le 3,$ which drop rank in codimension one. Instability of reconstruction near non-linear components of critical loci is explored experimentally.

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Marina Bertolini, GianMario Besana, Roberto Notari, Cristina Turrini. 2019-02-01. Matrices dropping rank in codimension one and critical loci in computer vision. https://arxiv.org/abs/1902.00376

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