  The fundamental matrix and trifocal tensor are convenient algebraic
representations of the epipolar geometry of two and three view configurations,
respectively. The estimation of these entities is central to most
reconstruction algorithms, and a solid understanding of their properties and
constraints is therefore very important. The fundamental matrix has 1 internal
constraint which is well understood, whereas the trifocal tensor has 8
independent algebraic constraints. The internal tensor constraints can be
represented in many ways, although there is only one minimal and sufficient set
of 8 constraints known. In this paper, we derive a second set of minimal and
sufficient constraints that is simpler. We also show how this can be used in a
new parameterization of the trifocal tensor. We hope that this increased
understanding of the internal constraints may lead to improved algorithms for
estimating the trifocal tensor, although the primary contribution is an
improved theoretical understanding.
