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.
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Correlation slices
The tensor can also be seen as a collection of three rank-two 3 x 3 matrices
Trilinear constraints
One of the most important properties of the trifocal tensor is that it gives rise to linear relationships between lines and points in three images. More specifically, for triplets of corresponding points
where
Transfer
Given the trifocal tensor of three views and a pair of matched points in two views, it is possible to determine the location of the point in the third view without any further information. This is known as point transfer and a similar result holds for lines.