The Ansel Adams Fallacy: "True perspective depends only on the camera-to-subject distance"

Human vision doesn't maintain relative size and scale when viewing the real world, in terms of human vision it is unimportant.

Because that relationship is not preserved in human vision in the real 3D world it can't be (and isn't) a constant and so is not used in human vision in the way that you envision.

You continue to assume that what you see through your own eyes is absolute and directly equivalent to pure geometry and then apply pure geometry directly to to describe not only what you see, but also provide the explanation of why you see it. And a theory based on such a fundamental error of assumption will turn to mush pretty quickly. Which it does, you contradict known science, simple repeatable observation, even pure geometry and yet fail to notice. I could show you a dozen more images that demonstrate beyond any question that absolute angular size is not preserved in human vision. But it won't make any difference as you will still fail to question your assumptions and still treat the absolute angular size as proven fact. I've raised a reasonable doubt and shown you proof that confirms this doubt, real science would've looked at this objectively, (and did a long while ago).

To everybody else:

Perspective is the distortion of shape caused by a single and unique point of observation, pure geometry dictates that distortion should also be in constant motion relative to movement of the observer. Which it is. This is all obvious if you follow the maths of pure geometry.

But it is a really confusing place for us so we have developed through empirical means a way of cancelling it:

Constancy scaling.

Constancy scaling is a weird but wonderful trait of vision. What this means in practice is that constancy scaling allows us, in the world we see immediately around us and into the middle distance, to subtract that distortion that pure geometry dictates and with it the way shape and relative scale changes as we move. What it allows us is a far more accurate and stable understanding of the true shape and relationships between objects in our immediate environment. Our understanding of the shape of a book, for instance, remains constant no matter what distance or angle you view it. It may be really tempting to relate this directly to pure geometry, only constancy scaling is a proven fact, and it means that your consistent understanding of shape is because the brain is actually altering things like absolute angular size as you move.

It also means that it is impossible to apply pure geometry to human vision because human vision is actively subtracting the effects of pure geometry even as you look at your computer screen reading this. If anybody is actually reading this...

Because pure geometry is relative to distance, constancy scaling is also relative to distance, they wouldn't cancel effectively if they weren't. And so this has an odd effect when we view things out of context, like a photograph of a 3D scene where the relationships are fixed by rendering to a 2D surface and so don't move as we view at different distances.

If you view a photo of a distant object from a distance relative to the camera position (centre of perspective) then you find that constancy scaling has roughly the same effect in both the real world and the photo. But if you stand really close to the image then the brain assumes a closer distance and doesn't apply that constancy scaling, and so you begin to see the true pure geometric perspective as captured by the camera. Do the maths, work out what pure geometry dictates the image should be.

Similarly if you look at a photo of a near object from a distance behind the centre of perspective you brain assumes it is further away and so fails to subtract the distortion caused by viewing at a close distance and again you see something closer to the true pure geometric perspective as captured by the camera. Do the maths, work out what pure geometry dictates the image should be.

Of course the rub is that we learn through experience, and the whole point of constancy scaling is to give us a consistent understanding, so we even learn how to cancel the effect when viewing images. Basically even in images absolute angular size is not preserved.

It also means that mathematically and perceptually Ansel Adams is correct, distortion is primarily and fundamentally a function of camera position, wide angle distortion and telephoto compression are determined by camera position alone as they cannot be reversed by print viewing distance.

With reference to the highlighted text from Tom's OP: Until you move to a point where the brain finally says hang on, that constancy scaling doesn't describe what I am seeing.

The geometric concept of centre of perspective describes the only TRUE central point of perspective. What the brain does in it's shape and spatial recognition is indeed a good thing so we are not confused by projection. What you are talking about is what the mind perceives. I am quite capable of disconnecting from my constancy scaling and seeing, for example. the trapezoid outlined by my screen because I am not perpendicular to it. Just because my mind knows it is actually a rectangle doesn't mean I can't see it as it is truly projected.

Earlier in the thread Tom posted the pics of the man walking along the train line with a train in the distance. It took a bit of careful observation from up close and far away, but eventually I saw both telephoto compression and wide angle distortion.

Just because animal vision is shown to impose a non-geometric view to the mind, doesn't in anyway refute the concepts.

Even within constancy scaling, there is a point where the mind is not scaling at all. What might that point be?

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There are many variations of this optical illusion. Here is another that works in a similar way.

Yes, pretty much. Another way of saying it is that you reach a point and your brain goes, "hang on it makes more sense like this".

Almost certainly with distant objects, as they are also quite stable mathematically. But a very interesting question, certainly there is a point when viewing photos away from the centre of perspective where you are seeing more of the true perspective in that image so that does suggest it the very least not constant. I do not know for sure but would guess that there is some sort of hierarchy with the way we combine our binocular vision. As with a lot of these illusions, i.e. cafe wall illusion and the muller-lyer illusion, though the effect may be empirical the trigger points can be a precise function of pure geometry because that is the image projected on the back of the retina. So the concepts are still firmly rooted in maths, and even a basic working hypothesis is far more useful and easier to understand if you stick to the maths.

Pure geometry describes everything up to and including the back of the retina, then there's a layer of processing that's empirical in nature it prevents you from relating what you see directly to pure geometry without taking into account the nature of human vision. It is there precisely to provide you with a consistent understanding so you can believe that your vision is absolute and so act on it with complete confidence.

I'm just going to name them, if anybody wishes to google. The picture is The Ames Room, and the link (I think) is similar to the Ponzo illusion.

An image that I find relatively easy to see in both telephoto compression and normal perspective is this one:
The centre of perspective for this image is at a distance of just over 13 times the length of the diagonal.

I have put an approximately 10" x 8" print of this image on a convenient wall in my home so that I can view it from normal distance (34cm) or from further away up to the centre of perspective (450cm). At normal distance the corner of the building appears to be much greater than 90 degrees, but from 4m away, or thereabouts, it looks like the corner of a normal building (i.e. 90 degrees). I don't know if others will see the same, but even having looked at this picture many, many times, it is still very obvious to me that the corner looks to be 90 degrees when viewed from the centre of perspective (or anywhere around there), but it looks like a much more obtuse angle when viewed from less than a metre away.

Does anyone else see this too?

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I see a London (English) Bond with some fairly poor pointing work, but it was my trade and I'm not really seeing past it, (especially the poor pointing...) 😖

It's a good example.

Up close I see the obtuse angle. I can force my mind to see 90 degrees but it takes some effort.

It is interesting to watch the effect moving in from about half the cop to close. Even at 1/2, I see an angle > 90. It doesn't jump out but it's there.

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At full size I see an obtuse angle for the corner, downsized to a thumbnail I see a normal 90 degree corner. If you keep the same viewing position, then downsizing has the same effect as increasing your viewing distance when the size remains the same.

If you can't see it, that doesn't mean that others can't. Depth perception is something that we learn to do from long experience.

Now I have read the OP in which this photo was first posted, and skimmed through the article on geometry and perspective. I do not doubt the maths.

The photo is not a great example, as in I don't think that everybody will see what you are trying to demonstrate. When we view this from a distance in front of the centre of perspective we see an obtuse angle. This is the correct geometric perspective of the corner viewed from the camera position and the correct geometric representation of that on a 2D plane.
If we view from the centre of perspective we understand the true shape of the object as being 90 degrees, even through the actual angle in the image is still the same.

Now what I've been trying to explain all along is that the pure geometry of the image as projected on the back of the retina and the 3D understanding of actual real shape are not the same thing. It takes an extra layer of processing to get from one to the other. One of the processes the brain uses to convert that retinal image into a 90 degree corner (and form an understanding of correct 3D shape from 2D information) is not by maths but by actually changing the shape of the object. This prohibits you from reverse engineering the maths of image formation and using it as a direct explanation as to how we form a 3D understanding from a 2D image. It also shows that when we view the real world or an image from the centre of perspective we are at the one point where our vision fails to see the pure geometry and instead sees the understanding of actual shape.

As to the article. Well this thread has demonstrated very correctly that geometric perspective as displayed in photos is highly dependent on viewing distance, in fact to such an extent as to ensure that you almost never see the correct perspective in images. I'm not saying artists don't use linear perspective, just that they don't use it in the "pure" form. Just like artists don't go round bumping into walls (or become abstract impressionists) because they flunked maths and so can't see perspective very well, they do both generally because they are drunk. 😋

Also remember that though the Renaissance was the pinnacle of realism at the time it doesn't carry the same impact against the images that are now commonplace in the modern world.

Here is another image to test your depth perception. (Please view it from a distance of about 3 to 5 times the length of the diagonal)

Look at the nearer corner (on the right) of the building. Does the angle between the two walls appear to be (1) 90 degrees, (2) less than 90 degrees, or (3) greater than 90 degrees?

Another interesting question to consider: Think of the plane defined by the wall of the building that we can see. Can you estimate which point in that plane is closest to the camera? In other words, the point from which a line drawn to the camera is perpendicular to the plane. Where do you judge that point is located?

(The centre of perspective of the image above is at a distance of 0.42 times the diagonal)

Well, of course they are not the same thing. The geometry of the image as projected onto the 2D photograph is not the same as the 3D geometry of the object being photographed. The geometry of the image on the retina will be different yet again.

I'm not trying to explain how our depth perception works. I agree that it is a very interesting question, but it is not necessary to address that question when explaining perspective.

When we say that we look at an image from closer than the centre of perspective and see "telephoto compression", that simply means that what we see looks like a real scene in which everything has been compressed towards the viewer.

In other words, if you were able to wave a magic wand and suddenly compress the real scene, then what you would see from the camera position would be like what you see when viewing the original photo from closer than the CoP. Mathematics can easily show this to be the case. The maths tells you what directions the light rays come from. What the maths doesn't tell you is whether the viewer can perceive depth in that scene (when viewed from a single fixed point, the camera position). If the viewer can perceive depth in a monocular view of the real scene, then he or she can probably also perceive depth in a view of the photograph (although many people do seem to find it difficult to get beyond their knowledge that they are looking at a 2D photograph).

When we view a photograph from closer than the CoP, the light rays from a small object in the photograph enter your eye from the same direction as the light rays enter your eye from the real object if everything in the scene is compressed towards the viewer. The closer the viewer is to the photograph, the more the real scene must be compressed for it to look the same as the photograph.

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I still can't help thinking that we're still missing the fundamental and simple point here.

The image of the real world projected on the retina, like the one projected on a 2D sensor obeys the maths of pure geometry,

Is not the same as/does not equal

The image you see "with your eyes".

There is a layer of processing, lets call it "The Twilight Zone" because of the symmetrical meaning it conjurers, and call the one rule of TTZ "light does not travel in straight lines through TTZ.

Because that layer of processing includes things like Constancy Scaling it does in a very real sense mean that light doesn't travel in straight lines through TTZ.

So if you were to ray-trace from "what you see" through the centre of perspective to the real world it would fail to line up with the image projected on the back of the retina, and so would contradict the maths of geometry.

Telephoto compression only happens when we look at photos of distant objects, we never see it in other photos.

Foreshortening, or compression is the mathematical and geometrical fact of how distant objects are rendered on the retina/camera sensor.

Again you ray-trace directly from/to what you see, an imaginary space. And again the maths doesn't tell you anything of the sort. The maths only tells you what the retinal image should be, it fails to describe the "what you see" because of TTZ, so using geometry to describe "what you see" means that by very definition it must contradict the retinal image and therefore must also contradict geometry. And because you keep using "what you see" as the true baseline and relate that directly to geometry you are off base mathematically.

I think this is so wrong, telephoto compression and wide angle distortion are the function of camera to subject distance alone, the proof, and challenge, is simple:

If the above statement is correct then you will only see "telephoto compression" in photos of more distant objects viewed from the wrong distance.

And you will only see "wide angle distortion" in photos of close objects viewed from the wrong distance.

These two are not reversible with viewing distance.

If you are correct then you can show me a solid example where this is reversed with viewing distance.

My explanation is here:

dprevived.com/t/the-ansel-adams-fallacy-true-perspective-depends-only-on-the-camera-to-subject-distance/5326/post/72306/