A geometric approach to the trifocal tensor

In geometric computer vision the trifocal tensors are 3x3x3 tensors T by whose means three different camera views of the same scene are related to each other. In this paper we find two different sets of constraints, in the entries of T, that must be satisfied by trifocal tensors. The first set gives exactly the (closure of the) trifocal locus, i.e. all trifocal tensors, but it is very big. The second set, although not complete and still very big, has the property that it is possible to extract from it a set of only eight equations that are generically complete, i.e. for a generic choice of T, they suffice to decide whether T is indeed trifocal. Note that 8 is the codimension of the trifocal locus in its ambient space.