Perspective Distortion

Perspective, or why lenses don't compress things.

Prelude: The Hitchcock Zoom

The Hitchcock zoom, or dolly zoom, is a famous little bit of optical trickery from the world of cinema. If you can unlock how this trick works, then you have an understanding of perspective distortion.

So, before we get into exploring perspective distortion, take a look at this montage video of some famous shots that manipulate perspective.

There is no CGI or such trickery, this effect is done in-camera, and the underlying concepts that power this trick are used by photographers every single time we take a photo.

The short version is this: instead of animating along the effect, a photographer has the ability to choose how to stage the scene in terms of "compression", the effect being demonstrated in the dolly zoom.

A photographer might think with questions like the following:

Evolution of the Dolly Zoom from Vashi Nedomansky ACE on Vimeo.

Zoom Is Just Crop

All zooming in and out of our image does is crop it.

Zooming in on and image and cropping after the fact will produce images that (aside from resolution or sharpness) look the same. Objects will be positioned in the 2D frame similarly.

The only thing that changes the relative sizes of objects is distance.

Explore the toy below. Change the distance such that two objects are aligned in the 2D final camera image. Then adjusting the field of view (FOV) (AKA zooming in or out). Note how the alignment doesn't change.

Camera-Subject Distances

Measure your world in units of camera-to-subject distances. By definition, your subject is one camera-subject-distance unit away. How far away is the background?

Because of perspective, the size (in the resulting 2D image) of an object is determined by its distance to the camera. I don't keep a tape measure with in my camera bag, because everything is just relative.

If you want to make a hypothetical statue in the background larger, compared to the subject, then you need to make it closer... in terms of camera-subject distances. The easiest way to do this - far easier than moving the statue of liberty - is to step back away from your subject and zoom in.

Background is 0 camera-subject units away.
Background will appear 0 times as tall as the subject.
Background will take 0 times the area as the subject.

These numbers, despite their precision, are only loose estimates.

The statue of liberty, which was thousands of camera-subject distances away (when the camera is at arms-length) is now much closer, maybe only 100 camera-subject units away, thanks to you merely stepping back 10 feet.

100:1 is a much smaller ratio than 5000:1, and the statue of liberty just got 50 times larger. We decreased the camera-background distance when described in camera-subject units.

Not actually 50 times larger. We could do the math, but I don't want you to think that that matters. Remember, it's all relative.

The further away we are, the closer everything is to being about the same distance away from the camera, with the extreme being an orthographic camera, where the distance away from the camera has no effect on the perceived size of the object in the frame.