Critical loci for projective reconstruction from multiple views in higher dimension: A comprehensive theoretical approach

A class of determinantal varieties, arising as critical loci for a natural generalization of a classical problem in computer vision, is introduced. Their ideals are investigated. These varieties are the critical loci for projective reconstruction from multiple views in higher dimension and, under suitable genericity assumptions, turn out to be hypersurfaces of degree r in P2r−1 or varieties of codimension 2 and degree (r+2)(r+1)2 in P2r.