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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.

takahashi
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1 Answers1

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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

Chris
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  • what I meant was the correct 3D structure up-to-scale, but in the meantime I have caught up on the theory. Yes I was using algorithm 16.2 (but without the iterative LM optimization). Thank you very much for the useful links, especially the nonlinear triangulation. Do you know any reference to this algorithm? In the book there is only a linear line triangulation method as far as I know.. – takahashi Dec 11 '15 at 08:17