3D reconstruction using the projection matrices from the trifocal tensor

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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.

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Chris On

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