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 6 using the representations of GL(3) in the polynomial ring on the space of 3× 3× 3× 3 tensors. Further analysis gives a lower bound for the number of minimal generators. We conjecture that the ideal of the quadrifocal variety is minimally generated in degree at most 6.