  In Algebraic Vision, the projective reconstruction of the position of each
camera and scene point from the knowledge of many enough corresponding points
in the views is called the structure from motion problem. It is known that the
reconstruction is ambiguous if the scene points are contained in particular
algebraic varieties, called critical loci. To be more precise, from the
definition of criticality, for the same reconstruction problem, two critical
loci arise in a natural way. In the present paper, we investigate the relations
between these two critical loci, and we prove that, under some mild smoothness
hypotheses, (some of) their irreducible components are birational. To this end,
we introduce a unified critical locus that restores the symmetry between the
two critical loci, and a natural commutative diagram relating the unified
critical locus and the two single critical loci. For technical reasons, but of
interest in its own, we also consider how a critical locus change when one
increases the number of views.
