The Quadrifocal Variety

Multi-view Geometry is reviewed from an Algebraic Geometry perspective and multi-focal tensors are constructed as equivariant projections of the Grassmannian. A connection to the principal minor assignment problem is made by considering several flatlander cameras. The ideal of the quadrifocal variety is computed up to degree 8 (and partially in degree 9) using the representations of operatornameGL(3)× 4 in the polynomial ring on the space of 3 × 3 × 3 × 3 tensors. Further representation-theoretic analysis gives a lower bound for the number of minimal generators.