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Pose estimation with SIFT and homography

Hello guys,

I am doing an application of object recognition using SIFT technique.
Now I would be able to estimate its 3d pose. Basically I would like to draw X,Y,Z axis.

Using homography i believe i have already its X and Y axis (by drawing the bounding box with homography and perspectiveTrasform i choose the first and second line to be X and Y axis)

Now what I need is the Z axis. Do you have any hint?
I was thinking I just need to find the line orthogonal at the plane formed by the first 2 line that i have already found with homography.

Basically in this pic the first 2 green line could be the X and Y axis, at this point i just need to draw its Z axis..