Trifocal tensor

In computer vision, the trifocal tensor can be considered as the generalization of the
fundamental matrix in three views. It is a tensor thatincorporates all projective geometric relationships between three views andis independent of the scene structure, depending only on the relative motion (i.e. pose) among theviews and their intrinsic calibration parameters. Thus, the tensor can be calculated in closed formfrom the projection matrices of the three views. However, in practice the tensor is estimated frompoint and line matches across the three views.

One of the most important properties of the tensor is that it can be used to transfer correspondingpoints or lines in two views to the corresponding point or line in the third view.

References

*cite book
author=Richard Hartley and Andrew Zisserman
title=Multiple View Geometry in computer vision
publisher=Cambridge University Press
year=2003
id=ISBN 0-521-54051-8 Chapter on tensor is online [http://www.robots.ox.ac.uk/~vgg/hzbook/hzbook2/HZtrifocal.pdf]

*cite journal
author=Richard I. Hartley
title=Lines and Points in Three Views and the Trifocal Tensor
journal=International Journal of Computer Vision
volume=22(2)
pages=125-140
year=1997

*cite journal
author=Philip Torr and Andrew Zisserman
title=Robust Parameterization and Computation of the Trifocal Tensor
journal=Image and Vision Computing
volume=15(8)
pages=591-607
year=1997

External links

* [http://www.informatik.hu-berlin.de/~blaschek/diplvortrag/learn_epi/EpipolarGeo.html Visualization of trifocal geometry] (originally by Sylvain Bougnoux of INRIA Robotvis, requires Internet Explorer)