I have computed the trifocal tensor and corresponding projection matrices P_0, P_1 and P_2 from line correspondences over 3 views, according to 'Multiple View Geometry by Hartley & Zisserman, 2nd edition', Chapter 16. The computed matrices are:
P_0 =
[1 0 0 0
0 1 0 0
0 0 1 0]
P_1 =
[-0.284955 -0.129918 -0.0276358 0.922516
0.122053 0.560496 0.061383 0.385913
0.00455229 -0.0114709 -0.607497 0.00589735]
P_2 =
[0.21558 -0.10182 0.00499782 0.998876
0.0079606 0.11325 0.0226247 0.047112
0.006613 -0.00260303 -0.130705 0.00512245]
Now I want to compute the 3D (plücker) lines from these projection matrices. I know the intrinsic camera matrix K. What I don't understand is, how to include the intrinsic matrix K with the normalized projection matrices from the trifocal tensor P_1, P_2 and P_3 in order to get correct 3D information. More specifically, I want to follow the triangulation procedure described by Bartoli and Sturm (Section 4, Triangulation).
I appreciate your help.
What do you mean with correct 3D information? The whole coordinate system is only computable up to a scale.
Which algorithm exactly did you use for the computation? Algorithm 16.2 in that chapter?
Why don't you use the triangulation algorithm here:
http://www.robots.ox.ac.uk/~vgg/hzbook/code/vgg_multiview/vgg_line3d_from_lP_lin.m http://www.robots.ox.ac.uk/~vgg/hzbook/code/vgg_multiview/vgg_line3d_from_lP_nonlin.m