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Trifocal tensor : ウィキペディア英語版
Trifocal tensor
In computer vision, the trifocal tensor (also tritensor) is a 3×3×3 array of numbers
(i.e., a tensor) that incorporates all projective geometric relationships
among three views. It relates the coordinates of corresponding points or lines in three views, being
independent of the scene structure and depending only on the relative motion (i.e., pose) among the
three views and their intrinsic calibration parameters. Hence, the trifocal tensor can be considered as
the generalization of the fundamental matrix in three views.
It is noted that despite that the tensor is made up of 27 elements, only 18 of them are actually independent.
== Correlation slices ==
The tensor can also be seen as a collection of three rank-two 3 x 3 matrices
_1, \; _2, \; _3 known as its ''correlation slices''.
Assuming that the projection matrices of three views are
=( \; | \; ),
^'=( \; | \; _4 ) and \; | \; _4 ),
the correlation slices of the corresponding tensor can be expressed in closed form as
_i=_i _4^t - _4 _i^t, \; i=1 \ldots 3,
where
_i, \; _i
are respectively the ''i''th columns of the camera matrices.
In practice, however, the tensor is estimated from point and line matches across the three views.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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