If you view those thumbnails from 1m away, it is totally obvious that the 135mm shot shows compression relative to the 24mm shot (i.e. the background looks closer in the 135mm shot).
However, at that viewing distance it does not show compression relative to reality (i.e. to what you would see if you were standing at the camera position when the shot was taken). If you took your laptop to where the photographer stood when she took that shot and you viewed the thumbnails at 1m distance, with the actual Washington State Capitol Building visible across the lake at the same time, then it would be obvious to you that the Capitol Building looks further away in the 135mm thumbnail than it does in reality (when viewed from the camera position when the shot was taken).
When viewed from further away than the centre of perspective, distances appear extended, when viewed from closer than the centre of perspective, distances appear compressed (in comparison to what was seen from the camera position).
Try it sometime, it is instructive to do it for yourself.
You can even check it out with the photo displayed on your phone.
If you view each shot at a point relative to the centre of perspective the distortion disappears and the view is similar to what you actually see in front of you.
But all 4 images in that example were taken from different camera positions keeping the subject at the same variable size. So there are two variables, camera distance an viewing distance.
Now there is no distance at which you can view the image taken with the 24mm lens and it will look similar to the image taken with the 135mm lens. So the difference shown in the linked photos can't be attributed to the viewing distance of the photo and must be a function of camera distance.
Ansel Adams was correct? This is exactly what he was talking about.
@JACS This is the interesting part. The wide angle distortion as seen (at least partly) in the 24mm shot is the absolute fact of correct mathematical geometry forming an image from that camera position.
So why does that distortion disappear when we view that image from the centre of perspective?
If pure geometry is the constant and we are using machines as per @TomAxford then it must work the other way around. The image should remain constant and of a fixed perspective whilst the perspective in the real world changes until we reach a spot where they are the same. This is the function of pure geometry and exactly how it works on a camera sensor.
So why does that distortion disappear when we view that image from the centre of perspective as seen with human eyes?
What would happen if we found that world of pure geometry a confusing place, where perspective did actually change as we walked between the spots and took the photos in the link and so learnt how to cancel it?
Well, the world would become a much more stable place and your relative understanding about the size scale and distances between the objects wouldn't change. Your understanding about the size of the subject, the building behind and the distance between the two would remain constant.
It would be interesting to try it sometime, see if it proved instructive. 😀
So what would happen if we viewed a photo?
Well, if human vision did compensate for the way pure geometry dictates that relative shape and scale must alter as we change position (like the differences between the linked photos which are machine proven to represent correct geometry), then you'd expect it to do the opposite when you presented it with a fixed geometry that didn't change as you moved. You'd expect it to create variations in the perspective but in reverse. So if pure geometry dictates that "wide angle distortion" was the mathematical fact of a close camera position and the above is true: You'd expect the same cancellation at a point relative to the position the photo was taken, and as that cancellation would be relative to close distance you''d expect it to lessen as you moved further away. So if "wide angle distortion" was a pure geometrical fact of a close camera position you'd expect it to be a perceptual effect of viewing from too far away. And that would reverse for "telephoto compression" which is the geometrical fact of moving the cmaera further away and the perceptual effect of moving closer to view the image.
It would be interesting to try it sometime, see if it proved instructive. 😀
Andrew, there is a fundamental error in your logic. Consider this section of your argument:
Everything there is correct except the conclusion stated in the final sentence (which I have put in italics). To be logically correct, the sentence shown in italics needs to be qualified as follows (changes in bold):
So the difference shown in the linked photos can't be attributed to the viewing distancealoneand must be a function of camera distanceas well.
It is not logically possible to conclude that the viewing distance plays no part. All that can be said is that the difference in the photos must be due to either the camera distance alone or a combination of camera distance and viewing distance.
That logical error invalidates the rest of your argument.
This logical error is possibly the same one that Ansel Adams made in reaching his fallacious conclusion. It has been repeated many, many times since.
Oh dear. So you pick a hole in one sentence and with it find an excuse to dismiss a whole opinion?
That's not good science.
The mathematical fact of pure image geometry is that the differences between the four 2D images linked to is entirely due to camera/viewer position and they must be rendered on the back of the retina as an exact copy.
Therefore the forming of a 3D understanding when viewing images and the apparent variation of perspective with viewing distance is down to human perception/cognitive function. It simply doesn't exist in the pure geometry.
So you can’t then explain it only in terms of pure geometry. You must also include the nature of human vision in that description. Why do you have such a problem with this? Your failure to see it is really causing some unsound logic and unsupportable conclusions.
In the four images linked above the geometry of the images with the relative sizes between the Capitol and the subject is fixed in the image by camera position alone. It is entirely a function of human perception that we misinterpret those separate perspectives when we view those images. But there is no distance you can view the 135mm shot and see the Capitol as being half the size relative to the subject, you simply misinterpret the depth of the building and the space in between.
If you were able to see the far distance you'd also notice that both mathematically and perceptually the distance between the camera positions makes very little difference. Even in pure perceptual terms the viewing distance only really changes our interpretation of what we assume to be closer objects, our understanding of the relationships of distant objects remains remarkably stable regardless of scale/viewing distance because in the real world this is precisely what happens.
As in the iphone image below there is no distance at which you can view it where the foreground will look like a distant object just a there is no distance you can view the background and it will have the perspective of a close object, even if you crop and isolate.
You only see "telephoto compression" when you view photos of distant objects and "wide angle distortion" only occurs when the camera to subject distance is short. This is not reversed with print viewing distance, you can stick your nose right against the print and the foreground will not foreshorten, and similarly as you back away from a close up shot of a distant object the compression reaches a point where it looks normal then it just stabilises the further you move away. [edited for clarity]
Really? I haven't dismissed your whole argument even though your opening statement clearly fails the simple test of observation:
Wide-angle perspective distortion is seen when the viewer views an image of an near object from further away than the centre of perspective. Telephoto compression is seen when the viewer views an image of an distant object from closer than the centre of perspective.
The two do not reverse with viewing position.
Not really, you do make some conceptual leaps in the right direction. There is some truth in what you say, but only partial truth. Some of it is flat out wrong, and it is because you have a massive blind spot demonstrated again in the reply to @JACS a few posts above.
I've tried again and again to show you with solid examples how the world of pure geometry differs from the one you see through human eyes. (and I'm sorry I must put this in bold, would've liked to use capitals as well such is my frustration that this simple point is still not sinking in) The simple fact that we do see different perspectives in the same fixed image is absolute proof that human vision differs from the world of pure geometry.
And yet you still keep doing this:
You insist we are talking only about the maths, that human vision doesn't enter into the equation, then "BOOM" - reality is what you see. And being reality it is of course subject to the rules of reality, i.e. pure geometry. You may think you're looking at the pure geometry in the real world and in images, but you still haven't sussed that you're doing it through human eyes, and so you randomly jump between one and the other as the same thing.
Eye and Brain - R L Gregory:
"When an artist employs strict geometrical perspective he does not draw what he sees-he represents his retinal image. As we know these are very different; for what is seen is affected by constancy scaling. A photograph, on the other hand, represents the retinal image but not how the scene appears... ...The camera gives true geometrical perspective; but because we do not see the world as it is projected on the retina, or in the camera, the photograph looks wrong."
[EDIT] Just to add that the above quote being true, that we never see the world as it appears in accordance with strict geometry, then it must logically follow that if we do stand in the same position as the camera and hold up a picture so to view it from the centre of perspective to achieve the same view then we absolutely can't be seeing the strict geometry in the image either. And if all other image viewing positions create a distortion...
You really need to consider the nature of human vision.
You keep repeating the same mistake. For each of the four images, the camera position changes. For each of the four images, the centre of perspective changes and hence the viewing position relative to the centre of perspective changes when all four images are viewed simultaneously.
It is irrational to claim that the change in viewing position relative to the centre of perspective has no effect and that the difference is solely because of the change in camera position.
You really need to do some experiments keeping the camera at the same place and just changing the viewing position (relative to the centre of perspective), but you seem unwilling to do that. It would quickly expose the fallacy in your argument.
It's also irrational to claim that changing the viewing position of the image changes the lighting angle in the scene. These are separate effects. Perspective is ONLY changed by changing camera position. Human perception of the image in relation to how the image is projected/displayed is a separate topic only peripherally related. Neither one controls the other.
I've already tried to show you where observation fails to support your theories but you seem so entrenched in your position that you seem also to be unable to see. You just assume I haven't checked or that I must be wrong. I don't need to ask if you have experimented as I know you have, but the trouble is you seem literally quite blind to anything that contradicts. And even though you accept that human perception differs form pure geometry you don't seem to apply that to your own vision. You still talk about reality being what you see and assume that you are looking at pure geometry.
You're wrong about the effect viewing distance has on perspective, your conclusions are not supported by observation. Basically all that happens is when you view images at the wrong distance you see a distortion that is similar to the truth of the pure geometry or perspective defined by camera position. As you change position towards the centre of perspective that distortion disappears. It doesn't reverse. "Wide angle distortion" and "telephoto compression" work in opposite directions and they are both defined by subject distance alone, this is not reversed by the distance you view the image.
Ansel Adams is not wrong, it's mathematically correct and it's a good way to visualise it. The full scientific explanation also involves human perception and so takes a perceptual leap that you are unwilling to entertain as even just a remote possibility.
There is a very well-established theory of perspective that explains mathematically what happens when we make a 2D photograph of a 3D scene from a given camera position. That theory also explains mathematically what we see when we look at that photograph from a given viewing position in comparison to what we saw when looking at the original scene. Any good mathematician has no problem understanding both of these.
As I understand it, you fully accept the first part (taking the photograph), but you do not accept the second part (viewing the photograph). Is that correct?
The "perceptual leap" that you refer to is simply an excuse to avoid a proper scientific explanation. Either you can explain clearly and logically what you mean or your theory is effectively nonsense.
If you assume that the absolute size of the image makes no difference then it is easy to prove that the viewing distance makes no difference.
But why do you assume that the absolute size is unimportant? I think this is probably the key to the whole of this discussion. I think Ansel Adams assumed that an image always looks exactly the same whether you look at it as a 4" x 5" print or as a 4' x 5' print.
If you view a 4" x 5" print alongside a 4' x 5' print of the same image, they will look like two prints of the same image. However, it is also obvious that one is much larger than the other. Why assume that the absolute size has no effect on how we "see" the two prints?
In other words, he thought that viewing distance does matter.
It puzzles me that so many photographers today are willing to assume that viewing distance does not matter and think that it is obvious that it doesn't matter.
It is obvious to me that it doesn't matter if you are purely seeing the photo as a 2D object. However, if you are viewing the photo in a situation where it is possible that you could imagine that you were looking at a real scene, then I think it is obvious that the angular size with which you see objects in the scene does matter and affects your perception of depth in the scene.
Suppose you are looking through a keyhole into a room containing two people. How do you judge depth in that situation? The keyhole is very small and prevents you from using binocular vision to judge depth. It also prevents you from moving your head from side to side to use parallax to help judge distance. Yet most people can easily tell if both people are standing close to the keyhole or if they are standing some distance away. How?
Let's try again. But I have no illusions that you will read this with an open mind, people can get so rooted in their own opinions that they can't see far enough beyond them even to see actual words right in front of them. Such is the nature of human vision 😀
Didn't you state in the OP?
And also you clearly said a short while ago:
Now call me old fashioned and a stickler for maths, but your statement from the OP clearly suggests that you are at a null point where you see neither "telephoto compression" nor "wide angle distortion". And your statement above clearly links the centre of perspective to a reality that is governed by pure geometry and that reality directly to what you see.
But pure geometry dictates that when I view an image of a distant object I should see foreshortened or "telephoto compression" at the centre of perspective because that is the pure geometrical reality of the perspective from that point.
The problem is, and always has been, that you think your vision is absolute and so just automatically relate what you see to pure geometry without even thinking. So let's cancel that assumption and look at what we see and the world as described by pure geometry side by side and see if they do line up.
When I view an image of a distant object from inside the centre of perspective I see the perspective as being roughly what pure geometry predicts, foreshortened. As I move away the perspective looks normal and then just stabilises. If I view an image of a close object from outside the centre of perspective I see the perspective as being roughly what pure geometry predicts until I reach a point where it look normal then I reach a point where my nose is against the print. It never looks foreshortened and my understanding of distant objects stays remarkably constant.
So if we view images of distant objects from too close, or images of near objects from too far, then we see something similar to the correct perspective as described by pure geometry. As we move towards the centre of perspective the perspective we see resembles what we see in the real 3D world.
That is it, that is the entirety of what observation shows us. This never reverses with viewing position so close objects never display "telephoto compression" and vice-versa.
The statement below is scientific fact, demonstrated and confirmed countless times, even the Renaissance painters understood this:
Eye and Brain - R L Gregory:
"When an artist employs strict geometrical perspective he does not draw what he sees-he represents his retinal image. As we know these are very different; for what is seen is affected by constancy scaling. A photograph, on the other hand, represents the retinal image but not how the scene appears... ...The camera gives true geometrical perspective; but because we do not see the world as it is projected on the retina, or in the camera, the photograph looks wrong."
Now your theories, assumptions and predictions directly contradict this. My observations in bold above don't.
The world of pure geometry describes a world where perspective is the distortion in the shape of objects caused by a single viewpoint, and that pure geometry must predict a world where perspective is in constant motion relative to viewpoint.
I think that they have also figured out that this isn't quite how the world appears to us. And I've already described in a previous post the effect of constancy scaling, and just how that would work if you applied something calibrated to cancel that motion to an object that displays a static perspective like a photo. Guess what? Yes, it also fits perfectly with the observations in bold above.
Really? I've already been through how you can't relate human vision directly to pure geometry, how constancy scaling prevents this, how we only ever see the front elevation and have no knowledge of the side elevation, etc... etc...
And what do you do? Try to force me to describe human vision in terms of pure maths and only in pure maths or be labelled evasive and dismissed by youself.
I don't fall for tricks like that, and I don't find them to be very objective or scientific.
