Camera Pose Estimation from Vanishing Points
You can use the vanishing points to calibrate the camera. 
I recommend reading  Chapter 8.6 of Multiple View Geometry in Computer Vision [ http://www.cambridge.org/9780521540513 ]

Even better, if you have those points on a known sized plane, then you can compute an homography H and the it is possible to compute both intrinsic and extrinsic camera matrices [K],[R|T] respectively.

The size of the object helps determining the scene scale, or more precisely the scale of the column vector t in the extrinsic matrix.
(Zhang's calibration method)[ https://www.microsoft.com/en-us/research/wp-content/uploads/2016/02/tr98-71.pdf ]