  The multiview variety of an arrangement of cameras is the Zariski closure of
the images of world points in the cameras. The prime vanishing ideal of this
complex projective variety is called the multiview ideal. We show that the
bifocal and trifocal polynomials from the cameras generate the multiview ideal
when the foci are distinct. In the computer vision literature, many sets of
(determinantal) polynomials have been proposed to describe the multiview
variety. We establish precise algebraic relationships between the multiview
ideal and these various ideals. When the camera foci are noncoplanar, we prove
that the ideal of bifocal polynomials saturate to give the multiview ideal.
Finally, we prove that all the ideals we consider coincide when dehomogenized,
to cut out the space of finite images.
