What is telephoto compression (perspective compression)? Tom Axford 2023

Agreed. I think you will find that 99% of people don't consider perspective (or compression) when taking an image. In the majority of cases (I include myself here) people are far more interested in capturing the scene or moment before them. Few people stop and consider how they want the image to look in respect to how the background relates to the subject before them, and when it comes to smartphone users its likely no one is considering these considerations, and there are far more smartphone images being taken than any other form these days.

For those of us who may well consider background to subject to foreground as part of our image process, most of us know that if we want bokeh in our images we can use short focal length lenses. If we want the perspective to be somewhat compressed, we can accomplish that with a telephoto lens or use this technique to create some nice background blur. "Zooming" with your feet can also do the trick.
At the end of the day, I'm not interested in doing complicated calculations in my head, I'm interested in taking a photo.

When I took the photo of the bird I was only interested in the bird, not how the background would look. In this case the bird was 20 meters from me, I was using me Fuji HS20EXR at 87mm focal length to "zoom in". I wanted the bird to fill the majority of the left side of the frame. The background was incidental to the intent of the image. The elderly couple in the background are a good 200 meters beyond the bird and the building in the background is a further 100 meters beyond the couple walking. Was I taking all this into consideration? No, I was interested in the pose of the bird, I intrinsically know that anything beyond the point of focus will be out of focus, more or less so depending upon F ratio used.

The point is had I been using a 40 mm lens I would have had to halve my distance to the bird to get the same effect, which would have made the bird fly away. This is what was demonstrated in the video I alluded to, however Its not something I ever truly worry about when taking photos unless I'm working off a tripod with a fixed subject, which I almost never do.

I have added a short section on dolly zoom to my first post in this thread. The Wikipedia article on dolly zoom contains a very nice computer animation of the effect, which is also a nice illustration of telephoto compression.

PetaPixel has published an article entitled "Why You Seem to Move Slower When Shooting at Longer Focal Length" which includes some nice driver's eye view videos from moving trains. In those taken with long focal lengths, the train appears to be moving more slowly than in those taken with wide-angle lenses. The train was actually travelling at the same speed all the time.

This is a simple consequence of telephoto compression. Suppose a 250mm lens is used and distances from the camera appear to be compressed by a factor of 5 (relative to a 50mm lens). Then if the train appears to be moving at 100mph in the video taken with the 50mm lens, it will appear to be moving at only 20mph in the video taken with the 250mm lens. Of course, the speed of the train is still the same, but the distance travelled appears to be much less than it really is.

It is just an optical illusion, but a surprisingly convincing illusion (watch the videos in the PetaPixel article).

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Exactly!

The scene that the eye sees when viewing a magnified image (i.e. a "zoomed in" image or one taken with a long focal length or an image viewed from closer than normal viewing distance) has a distorted perspective, a perspective that does not exist in reality (i.e. there is nowhere that we can stand to see the scene with this perspective with the naked eye).

It is not the same perspective as seen by moving closer to the subject ("zooming with your feet").

Our brains try to make sense of this magnified perspective. Typically, we get the illusion that the scene is compressed towards the viewer.

That is simply untrue. The geometry does change when you zoom in, i.e. when you magnify the image.

Consider this image:

This is a 4x zoom into the above image (i.e. the image has been cropped and magnified by a factor of 4):

The geometry and the perspective is obviously different in the two images (when viewed from the same distance). Although the perspective lines that converge to a vanishing point in the distance are at the same angle in the two images, shapes are different. Look at the shape of the blocks that make up the road surface along the bottom edge of the image. They are very obviously of different aspect ratios in the two images.

I find it astonishing that some people seem to be very unwilling to accept this. It has been understood as part of the theory of perspective for around 600 years!

"Know that a painted thing can never appear truthful where there is not a definite distance for seeing it." (Leon Battista Alberti, 1435)

Perspective in great paintings of that time (and later) was worked out on the basis of knowing how far away the viewer of the painting would be. Perspective depends on viewing distance.

HAND.

You are talking about the perspective seen by the camera and captured in the image.

I am talking about the perspective seen by the person viewing the image, which is not the same. It depends on the position of the viewer relative to the image.

Is that really so hard to understand? It has been understood by artists since the year dot. Takethe skull in Hans Holbein's famous painting "The Ambassadors". The skull can be properly seen as a skull by viewing the painting from an extreme angle, not from a normal viewing position.

The perspective seen by the viewer depends not only on the angle from which the picture is viewed, but also on the distance of the viewer from the image. When viewing an image straight on, it is that distance that determines whether you see wide-angle perspective distortion, correct perspective or telephoto compression.

Of course they are, the second image is an enlargement of just a small region of the first.

The point is that enlarging a small region of the first image produces a different image with a different perspective. That road surface uses bricks of identical size and shape all the way along, yet in the second image they appear to be different from those in the first image. As I said before, this is something that has been understood for centuries by those who have studied perspective in art.

Here is a very detailed and comprehensive article on classical perspective for artists:
"Elements of Perspective" by Bruce MacEvoy.
It is written for artists and is not an easy read for photographers, but it is essentially all there (Page 2 is the relevant section).

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HAND.

Yes, that is obvious; when you magnify an image, the shapes do not change.

However, the perspective does change because perspective depends on size as well as shape.

Perspective is what creates the impression of depth in a 2-D image. Depth perception depends on many factors, but one of the most important factors is size: the angular size of an object as seen by our eyes. That depends on the size of the image and the viewing distance.

Go back and read the first post in this thread. It is explained there.

For a more detailed explanation, see this section of Bruce MacEvoy's article. (You may need to read the earlier parts of his article to understand his terminology.)

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Indeed the second image is an enlarged crop from the first, as I originally stated.

The two images are seen with a different perspective exactly because they differ in size.

We get so used to seeing pictures at different sizes and from different distances that we tend to ignore the perspective differences and you possibly don't notice them here.

However, in some situations our depth perception is so automatic that it is hard to ignore. Have a look at the videos in this article and it should be obvious that the train appears to go more slowly when the lens is zoomed to a very long focal length (which is equivalent to enlarging the image).

Perspective is what creates the impression of depth in a 2-D image. Depth perception depends on many factors, but one of the most important factors is size: the angular size of an object as seen by our eyes. That depends on the size of the image and the viewing distance.

Go back and read the first post in this thread. It is explained there.

For a more detailed explanation, see this section of Bruce MacEvoy's article. (You may need to read the earlier parts of his article to understand his terminology.)

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Are you saying that when you look through a telescope or binoculars, things don't look any closer than they did without the telescope?

A telescope simply magnifies the scene in front of you, in just the same way as using a longer focal length does.

Why would people bother using a telescope or binoculars if they didn't make things look closer?

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I have seen no rational argument that explains perspective distortion in terms of cropping. I haven't tried it, but zooming into a gigapixel image would involve very little cropping and the perspective distortion will be the same.

After all, there is a precise mathematical formula for the amount of compression produced by a given amount of magnification. If you look through a telescope of magnification m, then distances to or from the viewer appear compressed by the same factor m, while the other two dimensions remain the same as they were. That formula does not depend on the amount of cropping.