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

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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.

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In fact, depth perception is quite well understood. It depends on a large number of different cues in the image, but many of those cues behave in a mathematically predictable way when you enlarge the image.

If you observe two adult people, one 100m away and the second 200m away, the first person has a size of about 1 degree and the second a size of about 0.5 degree. If you look through a 10x telescope, then the size of the first person is 10 degrees and the second person is 5 degrees. Now, that is the same as you would see looking (with the naked eye) at a person 10m away and another 20m away. So your brain tends to perceive the distances as 10m and 20m when looking through the telescope and as 100m and 200m when looking without the telescope. The distance between the two people appears to be compressed from 100m to 10m by the telescope.

However, when we look at a photograph, we know it is a photo and we usually don't know what focal length was used or how much it has been cropped, so we tend to automatically reserve judgement on how far away things might be in the image. So, it is often only in the most extreme cases that we are confident in saying that the perspective looks compressed.

Because all depth perception is just an optical illusion, like most illusions thinking about them too much can sometimes make them harder to see. To see depth in an image you need to imagine that you are looking at a real scene rather than looking at a flat image.

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It's interesting that you don't think so. I see plenty of evidence for it myself. But, of course, it all depends on one's perception of depth in a two-dimensional image.

OK, what do we really see when looking at these two images at the same time?

The second image is simply the centre of the first image magnified 4 times.

Everything in the second image is 4 times larger than it is in the first image.

Hence every object in the second image appears 4 times closer than it appears in the first. In other words, it appears one quarter as far away. That applies to every individual object in the image.

All the distances in the first image appear to be compressed by a factor of 4, in comparison with the first image. That is telephoto compression.

Which step in this argument do you disagree with?

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I wish it was my theory! It's actually the classical theory of perspective that has been known for about 6 centuries or so.

You'll probably be in line for a Nobel Prize if you prove that it is wrong! (I'm not holding my breath!)

Depth perception is absolute, not relative!

The optical illusion is still there. You may not be very good at seeing it, but it is still there.

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I think your consciousness is probably overriding your instinctive depth perception, but I really don't know.

I would be interested to know what you see when you look at the videos in this article.

If your depth perception really isn't seeing any difference when the image is magnified, then you will not see the illusion of the train apparently moving more slowly when the image is magnified (by zooming the lens).

Do you see the illusion or not?

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