3D reconstruction using projection matrices from the trifocal tensor
I have computed the trifocal tensor and the corresponding projection matrices P_0
, P_1
and P_2
from the linear correspondences over 3 views according to Hartley and Zisserman's Multiple Gaze Geometry, 2nd Edition, Chapter 16. the matrices computed 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 calculate 3D (plücker) lines from these projection matrices. I know the internal matrix of the camera K
. I do not understand how to include the internal matrix K
with normalized projection matrices from the trifocal tensor P_1
, P_2
and P_3
to get the correct 3D information. In particular, I want to follow the triangulation procedure described by Bartoli and Sturm (section 4, triangulation).
I appreciate your help.
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What do you mean with correct 3D information? The entire coordinate system is calculated by the scale only.
Which algorithm did you use to calculate? Algorithm 16.2 in this 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
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