Can we prove that the object is not tilted from photo(s)?

Question

This is an image of Al-Masjid an-Nabawi. Can we from this image, or from combination of images available online say with a certain degree of confidence (prove?) that this red circled minaret is vertical, not tilted as it is claimed?

(Original bigger version is at commons.wikimedia)

I asked a question at Islam SE: Al-Masjid an-Nabawi tilted minaret?. So far it looks like there is no written evidence of that claim.

(Not sure what tags to use, feel free to edit/suggest)

Maybe a related post: Calculate camera tilt angle from 2D image

Note: I can't go there and retake shots, experiment, etc. Is it still possible to best guess if it is tilted based on available photos online?

Answer 1

The answer is maybe. It depends on whether the photos have required reference points to make the determination. If the required points exist on the photograph, yes.

Verticality (plumb) is established as the line between the zenith (point overhead) and the nadir (centre of the planet). Any eccentricity from that is considered "tilted."

The horizon is perpendicular to this imaginary line which can be established as the line joining the vanishing points (where receding parallel lines viewed in perspective appear to converge.) Any eccentricity from a line perpendicular to the horizon (level) is considered "tilted."

Any photograph used to define perpendicularity must have at least one dependable reference line (plumb and/or level) to use for linear construction and comparison.

You will need at least two of these photographic images taken from different orthogonal positions (90° with respect to the tower) to answer your question definitively. Additionally, it is handy for the camera axis to be "true." That is to be dead level with the subject centred horizontally and vertically in the viewfinder since, in effect, you are using the camera as a surveying (disambiguation) instrument.

Quite apart from the photographic evidence that may or may not exist, I'd tend to believe the popular claim. Any equipped and motivated land surveyor with a couple of hours off could provide the answer to a fraction of a degree.

Answer 2

No, not from one picture.
It could be tilted towards the camera (or away from it), and there is no way to see it in the shot.

Answer 3

I believe it's just a bad/distorted picture.

After correcting the pincushion lens distortion and camera angle (roll/tilt), it appears to me that the tower is straight. The horizontal lines I added reference to things that should be straight/level, and what I corrected for. The vertical lines are perpendicular to reference the straightness/verticality of the tower.

(this was a quick correction using photoshop's lens correction filter and could probably be refined)

Answer 4

Theoretically, you might be able to determine the tilt angle. However, more information besides the photos is necessary. You would need to know the exact coordinates of the camera and several other objects in the image (several points along the buildings in the foreground).

The next problem is that lenses are not perfectly rectilinear, straight lines will not necessarily appear straight. If you knew exactly which lens was used, you might be able to compensate.

It would be much easier for someone at the location to perform a simple experiment. Place a large shallow pan of water on the ground. Photograph the minaret and the reflection in the water in the same image. Gravity will level the water exactly to create a perfectly horizontal mirror. Put the minaret exactly in the center of the photo so you don't have to deal with lens rectilinear issues. From the image, you should be able to calculate any tilt of the minaret using geometry.

Answer 5

I hear that Microsoft has made 3D models of buildings just from using the huge corpus of photos available on the net so it is definitely possible. If you want to do that with 2 photos, just takes two pictures along two roughly orthogonal axes (for instance one from the North and one from the West), and if the minaret is vertical on both then it is vertical.

Now, the question is how you determine that the minaret is vertical on a specific picture. Several ways:

1. Take the picture with a camera which is known to be horizontal (bottom of the sensor horizontal) (likely requires tripod)
2. After correcting the picture for perspective (unless the lens axis was horizontal) compare with other known verticals in the picture (horizontals cannot be used, unless they were exactly parallel to the sensor plane).
3. Draw a long line on the ground, aiming at the minaret. Put yourself at the end of the line. Take a shot that includes the line and the minaret, centered. On the picture a vertical minaret would be aligned with the line. Note that this technique doesn't even require a camera, you can check the verticality on-site (from two directions of course).

Answer 6

Most normal camera lenses are rectilinear. That means that straight lines in the 3D scene should show up as straight lines in the photo.

If you photograph a scene with a rectilinear lens, then what you get is a perspective projection of the scene onto the image plane.

Lines that are truly parallel to each other in the scene will not necessarily appear as parallel lines in the photo, but what they will do is, they will all appear to intersect at a single point (a.k.a., a "vanishing point")

If you could extend all of the "vertical" lines in the picture to their vanishing point,* and if the "verticals" of the minaret converged on a different vanishing point from the other vertical lines, then that would prove that the real-life "vertical" lines of the minaret were not parallel to the other vertical lines in the scene (i.e., it would prove that the minaret was tilted.)

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* This could be hard to do because, depending on the viewpoint of the camera, the vanishing point could be far outside of the frame---like, miles outside of the frame.