Terminologies
Focal length = The distance between image plane and projection center on the lens (optical center).
Horizon – Parallel lines in 3d coordinates converge in image due to perspective transformation. Horizon is defined as the line connecting two vanishing points. If the horizon is above the center of the image, then the camera is tilted towards the ground.
In the below example, vanishing point A and B are created by intersection of 2 parallel lines and the line AB is a horizon.
Calculating the Image Center
In the Figure 1, point A, B and C are the vanishing points created at the intersection of parallel lines. A and B are created from horizontal lines and C is created from vertical lines. Therefore ABC spans a triangle. The intersection point of all heights or orthocenter of ABC gives the center of the image.
Calculating the Focal Length
In a pinhole model, the center of the image plane is positioned on the optical axis OH. This is the focal length. Using geometry and Pythagoras theorem in triangle OAB and OhH, we can obtain the focal length as follows:
The values of d1, d2 and d3 can be measured in pixels in the image plane.
Conclusion
This method is not precise. In practical case, the vanishing point will have large x,y values. This causes huge errors and cannot be reliable.
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