Calculate the tilt angle of a camera given the distance of a point in an image and knowing the camera's height and FOV

Jan 2020
1
0
Valencia
Hi all,
I'm trying to determine the tilt angle of a camera (α) given the distance from the camera to the base of an object present in the image (d). I also know the height of the camera, the horizontal field of view (FOVh), the size of the image in pixels and the position of the object in the image (X,Y). Could somebody help me to find the formula to do so?

Thanks!

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Jun 2016
1,364
694
England
I think that there is some additional information required.
Your problem is equivalent to judging distance with only one eye.
We seem to be able to do this, but only by using several tricks;

1) we sense the focal length of the lens in the eye (actually we sense how tightly the muscles around the lens are pulling)
2) we judge the distance based on the known size of the object being looked at (or the objects around it).

But our main method of judging distance is the difference between the images in our two eyes.
 
Jun 2016
1,364
694
England
To expand on my previous answer
If you know the height of the tree, you can work out the distance
If you know the distance, you can work out the height
However with just one camera , giving just one angle, you can't determine both.
With two cameras, giving you two angles, you get the additional information to allow you to work out both height and distance.