When we look at a two-dimensional image of a three-dimensional scene, our brains imagine the third dimension even though it is not present. We are extremely good at depth perception and use a wide variety of cues in the 2-D image to construct in our brains an imaginary third dimension, or depth in the image.
Perspective compression (often called telephoto compression) occurs when our brains are fooled into thinking that the depth in the scene is much less than it was in reality. Distances to or from the viewer appear compressed. This is purely an optical illusion, as is all depth perception.
Compression in our perception of depth occurs when a photographic image is seen with an angle of view that is much greater than the angle of view seen by the camera when the photograph was taken. The angle of view seen by the viewer depends on the distance between the viewer's eye and the photograph (relative to the size of the photograph). The angle of view of the camera depends on the focal length of the lens relative to the size of the sensor.
One of the cues that our brain uses when perceiving depth is the size of the image of a familiar object on the retina of the eye. For example, our brains know from the size of the image in our eyes whether a person is a few metres away or a few hundred metres away. If that image is suddenly magnified ten times by looking through a 10x telescope, we think that the person looks ten times closer. In reality, all that has happened to the image in our eyes is that it is ten times larger. Yet our brains know that people do not suddenly grow ten times larger, so, instead, our brain interprets the image as if they are ten times closer.
So, looking through a 10x telescope, a person 100m away appears to be 10m away, while a person 200m away appears to be 20m away. The distances away from the viewer appear compressed by a factor of ten. The second person appears to be only 10m further away than the first, instead of 100m further away.
The same thing can happen when viewing photographs. If I take a shot with a 500mm lens on a camera with a sensor size of 36x24mm, then the camera lens is effectively 500mm from the image on the sensor. If I want to see the image with exactly the same perspective as the camera saw it, I need to view the image from relatively the same position as the camera lens.
Suppose I print the image at 36x24cm (14x9 inches) which is ten times the sensor size, then I need to view the image at a distance of ten times the focal length of the lens (i.e. 5m) to see it with the same perspective as the camera saw it.
Suppose instead that I view it from a more normal distance of 0.5m, then the image will appear ten times larger in my eye than the original scene appeared from the camera position. If the scene contains familiar objects, then my brain will probably imagine them to be ten times closer than they were to the camera position. This is perspective compression or telephoto compression. It depends on the viewing distance relative to the size of the image.
Anamorphosis is the creation of distorted images that appear natural only under certain viewing conditions, such as when viewed at a raking angle or reflected in a curved mirror. This is another phenomenon in which changing the way an image is viewed changes the viewer's perpective quite dramatically.
Example Images
It is important that you view these images approximately "normally", which means viewing them so that the distance between your eye and the centre of the image is equal to the length of the image diagonal. Enlarge them sufficiently so that you can do this comfortably.
The first image is a wide-angle view of a building (28mm FFequivalent).
The second image is a view with a 200mm FFe lens, taken from the same camera position. It is effectively the same as a small crop from the first picture, enlarged about 7 times.
The third image is a small crop from the centre of the second image. It is equivalent to an image taken with a 570mm FFe lens from the same position.
If all images are viewed normally, the first image shows the scene with magnification of 0.65x (i.e. it's like looking through a telescope with magnification of 0.65x). The second image has about 4.6x magnification. The third image has about 13x magnification (compared to what the eye would see from the camera position).
People differ somewhat in their ability to judge depth in a 2-D photograph. We see so many photographs, both wide-angle and telephoto, that we tend to discount the distorted perspective and see what we expect to see rather than what the photo shows us.
However, the third image (viewed normally) will probably show strong perspective compression to most people. The brain is familiar with the usual size of house bricks and the brain then works out that the viewer is probably between 2 and 3 metres away from the building. Starting from that assumption, the whole scene looks very flat because the size of the bricks varies very little from one part of the wall to another. So the brain deduces that the two sides of the building are both nearly perpendicular to our line of sight. Hence the two sides of the building are not at 90 degrees as might be expected, but at a much flatter angle to each other. Also, the angle of the railing doesn't look quite right either.
All this happens subconsciously in our brains because the image is highly magnified compared to what we would see if we stood at the camera position. Our brains interpret this as meaning that we are much closer than was actually the case. The first image allows a much better judgement of distances because we can view it with an almost natural perspective (meaning that the image on the retina of our eyes is about the same size as when viewing the real scene from the camera position).
An experiment to do yourself to test your depth perception
Enlarge the third image above so that you can view it normally (at a distance equal to the length of the diagonal). While viewing the image, gradually move further and further away. Do you notice your perception of depth in the image changing? At a distance of about 13 times the length of the diagonal you will see the image with the natural perspective (i.e. the image will appear exactly as if you were standing in the camera position and viewing the scene with the naked eye, except that you see only a tiny part of the whole scene). At this viewing distance, the image looks much more natural than it does close up.
Dolly Zoom Effect
It is sometimes claimed that the dolly zoom effect proves that changing the camera position causes telephoto compression. That is not so.
The dolly zoom effect is when the lens is zoomed in and simultaneously the camera is moved away from the subject. The two actions are coordinated so that the subject remains the same size in the frame. There is a very nice computer animation of the effect in the Wikipedia article on dolly zoom. Notice that on zooming in, the background appears to move closer to the subject while the foreground also appears to move closer to the subject. In other words, everything becomes compressed closer together. The camera movement is carefully worked out so that the subject remains the same size in the frame and hence it appears to remain the same distance from the camera. Everything else appears to move.
If there was no camera movement and the lens was zoomed in, then everything in the scene would appear to move closer to the camera.
Apparent Speeds in Video Images
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.
If the train takes, say, 10 seconds to reach a point on the line that is 1km away, then if the image is magnified 10 times by using a long lens, that point on the line may appear to be only 100m away and so the train will then appear to be travelling only 100m in 10 seconds.
The apparent reduction in speed when using longer focal lengths is due to the apparent compression of distances when using longer focal lengths. It is, of course, assumed that the viewer is viewing the images from approximately the normal viewing distance (equal to the length of the image diagonal) and that the viewing distance remains the same as the focal length is changed.
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