  In two-view geometry, the essential matrix describes the relative position
and orientation of two calibrated images. In three views, a similar role is
assigned to the calibrated trifocal tensor. It is a particular case of the
(uncalibrated) trifocal tensor and thus it inherits all its properties but, due
to the smaller degrees of freedom, satisfies a number of additional algebraic
constraints. Some of them are described in this paper. More specifically, we
define a new notion --- the trifocal essential matrix. On the one hand, it is a
generalization of the ordinary (bifocal) essential matrix, and, on the other
hand, it is closely related to the calibrated trifocal tensor. We prove the two
necessary and sufficient conditions that characterize the set of trifocal
essential matrices. Based on these characterizations, we propose three
necessary conditions on a calibrated trifocal tensor. They have a form of 15
quartic and 99 quintic polynomial equations. We show that in the practically
significant real case the 15 quartic constraints are also sufficient.
