  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.
