Andrew564

@TomAxford Your theories on perspective contradict the traditional view of perspective, they contradict the maths of image geometry, they contradict what is clear by simple observation and they contradict current scientific theory.

You don't even seem to understand the maths of pure geometry to the point that you can't see the world it predicts, or how it differs from the world we see through human eyes. It's not hard to do this, any halfway competent mathematical can do it.

Instead you take an effect where we see distortion in the fixed perspective of a 2D image when we view it through human eyes and insist that it can be explained through pure geometry alone, even though pure geometry predicts something quite different.

You haven't even worked it out that "telephoto compression" and "wide angle distortion" are the true geometries of the respective images. Instead you take the one point when you view an image and don't see that perspective and use that as the point that you see perspective as described by pure geometry.

I've been trying all through this to prompt you to question your base assumptions and question that you are not looking at this whole thing back to front. But no, TomAxford alone has absolute vision and so what he sees is the absolute truth and this relates directly to pure geometry.

Even though that viewpoint even contradicts pure geometry, and everything else noted above.

It's a nonsense question.

FACT: We do not see the world of pure geometry through human eyes. The camera sees it, and we can glimpse it in images but only if we view them from a position outside the centre of perspective. That is the correct way around. And it's pointless discussing anything until you are able to see just a little way beyond your own opinion, even if it's just the true nature of the world that pure geometry predicts.

Yes.

LOL 😂😂😂

You sure about that?

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.

But I didn't say that, here's what I did say in the reply above:

dprevived.com/t/the-ansel-adams-fallacy-true-perspective-depends-only-on-the-camera-to-subject-distance/5326/post/71998/

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.

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.

The difference is clearly because the camera position has changed and not the viewing position of the print:

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]

Ansel Adams is still correct.

Yes, let's, in detail...

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. 😀

Ah, but I'm not the one trying to describe an effect that doesn't exist in pure geometry and only exists when we view images, entirely by the pure geometry that we don't see and the complete exclusion of human perception.

Besides, time was ticking before the start of the conversation and is pretty far along the road to being a judge already. But probably not so much on photo tutorial websites!

😀

So...

Involving 2D objects which will display no compression either geometrically or perceptually?

But:

And that includes your latest example, the relative sizes are not preserved in human vision, it's called size constancy scaling.

And:

So the effect of telephoto compression doesn't exist in the maths...

It's still not registering.

Is it just me?

No, I don't think I could make it simple enough to make any difference. There is enough information in this thread already.

There is nothing wrong with Ansel Adams' theory.

No.

Absolutely no by the maths of pure image geometry alone. When rendering 3D scenes on a camera sensor foreshortening is a function of distance alone and is completely independent of focal length. the object at 10x the distance will show far more foreshortening.

Your opening argument in the OP (your bold):

I will say this one more time, but I feel confident that you will still fail to grasp the meaning.

We do not see pure geometrical/mathematical perspective through human eyes.

So, what is the pure geometrical and mathematically correct appearance of a distant object?

Foreshortened

How that is rendered by pure geometry and correct maths onto a 2D plane?

Foreshortened

How is that 2D image rendered by pure geometry and correct maths to the back of the retina?

Exact copy of the original.

What we see when we view the image with a human eye?

Highly dependent on viewing position but generally accepted that we will normally see a distortion of the perspective.

Conclusion?

There is only one possible conclusion; we do not see the pure geometrical or correct mathematical perspective when we view images because if we did we would always see the same consistent foreshortened. The absolute truth is that the human visual system never sees pure geometrical or mathematically correct perspective

So it then becomes painfully obvious that you can't look at images and relate what you see to the pure geometry of image formation. If you did you would end up scrabbling around and making ever more nonsensical statements that contradict yourself, observation and pure geometry while still trying to bang that square peg in a round hole.

We see telephoto compression in images because we see those objects out of the context of their normal distance. We then make errors of judgement and misinterpret their perspective. The mathematically correct pure geometric perspective remains both constant and correct in an image, there is no misinterpretation in geometry, only in viewing. So you can't discuss it without including human perception.

This is getting so bizarre! All of the above must be plainly obvious??

Tom is actually very close, but is yet to make that conceptual leap and question the base assumptions we make without evidence.

A Brief History of Perspective..

We are born.

We learn to interpret and navigate the space we occupy, we have a lot of practice and become exceptionally good at it. The real world becomes a stable and constant place. We believe we have an absolute and complete understanding because it remains consistent.

We learn maths which describes the absolute nature of the space we occupy.

Because the maths describes the absolute nature of the space and we have an absolute understanding we believe that they are one and the same with an incredible amount of inertia and use our langauge of maths to quantify and label our understanding of the space we occupy.

But the space that pure mathematical perspective describes, as seen by the camera and projected on the back of the retina, is actually one of constant shifting distortion. Yes, it's an absolute description, but that doesn't make it an absolute space.

The reason we have a constant understanding of the space we occupy is simply because the brain maintains consistency of understanding over the absolute maths. It basically means it distorts things so our understanding remains consistent. This is the nature of optical illusion, as you say deliberately introducing a conflict, and so the cracks become visible and the difference between the absolute world and our consistent understanding become obvious.

But which is better? The real world of pure mathematical geometry is a stable place for numbers but an ever shifting and confusing place for humans. Our understanding actually represents a far more accurate and stable overview of the true shapes of objects, but we get there purely by empirical means, without numbers.

Comparing angles and sizes in images with a human eye and relating that to geometry to explain how we see perspective in images is, to be blunt, nonsense. If you could see the difference between the perspective geometry describes and our actual perception of that space you'd realise immediately that is more than just trying to bang a square peg in a round hole.

Actually I didn't, I quite categorically remember stating that I agreed completely with them. But don't take my word, it's in black and white on this very site...

What I disagreed with was your interpretation that used the term exact same.

It's not about how realistic the table is. This is highlighting a very real and observable difference between the pure and mathematically correct geometry as projected on the back of your retina and what you actually see. And to do this in a way that's obvious and uncluttered.

With the simple addition of legs the 2D shape transforms to a 3D understanding.

So if a 2D shape does have near and far sides that are the same length then as a 3D table top one must in reality be longer. And this is what the brain is doing, it scales up the further edge and changes the angle to fit (mathematical relationships are not preserved in human vision). In effect it is subtracting the distortion caused by perspective (viewing from a single point in space) and showing you the perceived true shape of the object.

I could do this with a the correct perspective for a rectangular table top, or indeed I could use the examples of the sugar bowl and mugs in my wide angle shot from my burger bar mentioned above. But the problem is that you would just assume that that correct perspective is directly linked to the correct maths of image geometry. You wouldn't even think to question it. By starting with a symmetrical shape that is easy to understand it's easy to show that distortion precisely because it goes against your expectation for the 3D table top.

The fact remains that the pure mathematical relationships of the object are not preserved by human vision, the angles and lengths are noticably different.

Absolutely for the second bit, no for the first.

No, we don't. As I have said in far earlier posts there still seems to be a basic assumption you don't seem to be able to see beyond. A few posts ago you said:

None of the absolute mathematical relationships that you are treating as constant are actually perserved by the human visual system when you look at an image, or even the real world. And yet you are still treating the perspective you see in the image as an absolute truth and constant and assuming that there is no difference between the absolute linear geometry as rendered in the camera image and the assumed 3D perspective you see when you look at that image. It doesn't seem to occur to you to even question 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."

The front and back of our table here are exactly the same size, and so the two side are exactly parallel, and so the opposite angels are also exactly the same. This is the geometrical truth of the image and the truth of the photo and how it is mapped to the back of the retina.

But it is not what you see.

In fact very little of the geometry you actually see in the above image relates to it's true geometry. That the sides no longer look parallel is a clear indication that relative sizes as in the true geometry is not preserved in human vision. So:

Is proved to be incorrect as soon as we include human vision, the relationship is not maintained.

I keep saying that you can't relate what you see through human eyes directly to the geometry of image formation without taking into account the very nature of human perception because they are different. To fully understand telephoto compression it is necessary to fully understand the true nature of mathematically correct linear perspective and just how your view through human eyes differs from that. They are a long way from being one and the same.

P.s. I just posted an image and said the opposite, "it's not the same, see for yourself."

The absolute geometry of image formation and the perspective from the camera position is also a fact regardless of whether we know it or not.

We're talking about an effect that is quite distinct from normal vision here, and normal perspective. To create it you must hold the image plane at a fairly obtuse angle to the axis of the lens (or pinhole). This produces a unique distortion in an object that is never seen in normal vision and is as such undecipherable. Until, that is, you view it from exactly that angle that is the axis of the lens/pinhole. Then the transformation can be quite remarkable, almost 3D. Pavement artists use the same technique with their 3D chasms.

I still think that you are missing the point here. How perspective is captured in a 2D image is not being questioned, we both agree here.

The maths of "ray tracing" a 2D image through a lens onto another 2D surface is also beyond doubt, you get an exact copy.

That we recognise a 2D surface as an abstract of the 3D world we inhabit and from a 3D understanding of that is entirely a human cognitive function, it is not a mathematical function of the image because we have never learnt how to interpret our surroundings in a mathematical way. It is the reverse, we learn maths and angles long after we learn to navigate and simply try to define our space by that language. Which works in that we can define the space and perspective in a way that's very advanced.

Perspective is the distortion of relative scale and shape caused by a unique viewpoint. It is what a camera captures with mathematical accuracy.

And you never see in real life.

If you stand next to a barn (again a shape with a perspective) and back away it completely fails firstly to look like wide angle distortion as you stand close, then fails to shrink to telephoto compression as you move further away.

But I tell you what, a 2D image with baked in perspective does something similar to the exact opposite. It looks compressed if you stand too close and stretches as you move further away.

So why does real 3D perspective that does change with viewing position appear consistent to our eyes, and perspective in images which is fixed and immutable appear to change as we move?

I think you are holding the wrong thing as a constant, perspective distorts - mathematical fact, that we don't see it and have a correct understanding- human cognitive function. We subtract the effects of perspective distortion as we move through the real world, our understanding of shape doesn't distort but remains constant. If we freeze that, say in an image and move around it we see the almost exact reverse of an effect that would cancel wide angle distortion/telephoto compression that we should see in the real 3D world.

I'm really not sure what relevance the "photo taken from a known position" has. That we see wide angle distortion or telephoto compression in images is completely independent of whether we know the camera position or not.

So if we look at the definition, that the term "telephoto compression" describes an effect where photos of distant objects appear to be compressed when we view them from a point in front of the centre of perspective.

It's an apparent effect that is fundamentally based on us misinterpreting the perspective in an image, apparent because there is no change in the perspective captured in the photo, it remains constant, all that changes is our interpretation of that perspective. So we see "telephoto compression" when we make an error of judgement that appears to change relative to our viewing distance.

Ok, we have a camera on a tripod and we take two pics, one with a 200mm lens one with a 24mm lens. We view both as A4 prints, so as to see two photos of exactly the same perspective (true perspective as defined by camera position) at different magnifications. We see the perspective in the magnfied image (200mm) as compressed and the perspective of distant objects in the wide angle shot as stretched.

This suggests there is a null point where our perception switches from compressed to stretched, but let's see if we can nail this definition of normal down a little further.

It just so happens that my photography career never took off and I'm actually taking these photos of a lovely country scene from my burger van at the side of a road. So my wide angle shot includes the counter of my burger bar where there are circular objects such as a sugar bowl and a few cups in the corner. They are distinctly oval in the shot, in fact their tru perspective as per the rules of geometry is for them to be rendered as oval.

But if I put my nose against my photo and view it from the centre of perspective that distortion disappears and I clearly see those shapes as being perfectly circular.

I think we should unpack that last statement because it suggests something that so far nobody is seeming to acknowledge. When we view our wide angle shot from the centre of perspective we do not see the objects at the edge in their true perspective, as the maths of image geometry predicts any object must be rendered on a 2D plane when viewed from a single point in space.

We form an understanding of the true and absolute shape of those objects.

Is that confined to the edges of wide angle shots, or does it apply to complete photos in general?

So we are at a point where we could also say that when we view an image from the centre of perspective we are viewing that image from the same relative position that we view the real 3D world, and from that position our ability to see through the distortion caused by the perspective dictated by a single viewpoint in the real 3D world aligns with that of the image, and so we see normal.

If you're still having trouble, try this:

The thing about a 2D photo is that the true perspective as defined by camera position is baked absolutely firm and unchanging within the image. So if our eyesight was absolute then we must see a photo exactly as it is, and always exactly as it is.

That we actually see different perspectives at different magnifications in images is a clear indication that human perception of perspective varies with the assumption of distance, the shape we see changes depending on the assumption of the distance at which it is viewed. Which is similar to an effect you would apply to say make objects appear to be constant in shape and scale in a world where perspective dictates they must be ever changing.

And there is no formula that really covers it, but I find Ansel Adams' to pretty close whist still being true to the maths of image geometry.

Mine does. But then you chose to ignore me:

I get your meaning, and yes (ish).

Telephoto compression and wide angle distortion are not the opposites as in TomAxford's theory, and certainly not in Ansel Adam's book, (I've just checked mine and strangely it still smells strongly of darkroom chemicals...). Wide angle distortion occurs when we view images of close objects from behind the centre of perspective. Telephoto compression is when we view photos of distant objects from in front of the centre of perspective.

There are a couple of points here. Firstly that the two are not reversible. It is not possible to take a single photo say a head and shoulders with a 50mm lens (35mm equivalent) and just adjust your position to see the two different perspectives. There is no way that you can stand far enough away (what the "maths" predicts) and see that face distorted in the same way as taking a photo of same face with nose nearly touching the lens. Similarly you could stand with your nose against the head and shoulder shot and still not see it as a distant object. Though distant objects in wide angle shots viewed behind the centre of perspective do appear stretched as do the distances between them.

The perspective formed by the image geometry and baked in is a function of subject to camera distance as regards to near and far objects. It is set by the maths of image geometry and happens as fact completely independently of any viewing of the image.

Now as to your mnemonic, please demonstrate this in the mapping of a 2D image to the back of the retina. The maths is that the 2D image is copied exactly as is depicted, as a 2D image to a 2D image with simple changes of scale dependent on distance.

Honestly, I'm not kidding here, show me the maths.

So when we realise that a photo is basically a front elevation and can't be rebuilt accurately without the corresponding side elevation which is all the information that is lost in a 2D photo. Then we realise that the 3D projection is purely an assumption of the human viewer.

Further to that we must then realise that in order for our assumptions of relative distance and scale to change in an image that not a pixel moves as we change our viewing distance that we must therefore at least at every single distance but one be seeing that perspective incorrectly.

And given that we don't have the side elevation so are guessing based on a memory of relative sizes rather than any absolute scale...

Surely the amount of foreshortening present in a photograph taken from a know position is a matter of simple geometry?

This is not the same as our perception of perspective when we view the image and assume a distance and scale that is notr contained within that photograph.

Personally I think that the assumption of perspective in a 2D image is a human perception. It doesn't exists in the maths without the corresponding side elevation, it is a guess, assumed by the viewer. And if we never see perspective in images correctly, (we don't have the side elevation), then there is no way that the absolute maths of the real 3D scene will ever match what we see in a 2D image.

Couple of points here.

1. Binocular vision is only effective at near distance, and has no role when viewing 2D images. And telephoto compression is an effect we see in a 2D image, formed by a camera in regard to the isolated point quoted above.

2. it's quite a big leap to assume that our vision and robotic/computer vision is the same, and therefore the same maths applies. We are not equipped with a radar system for instance.

The maths of rendering a 2D image through a lens onto a 2D plane (retina) is quite simple, there is no 3D transformation involved. How does your robot (with radar) translate a 2D image, say a brick wall with a mural? Probably the same as us initially, as a wall with a mural. But would it be able to form an opinion of that mural and interpret the 3D space it represents (as a separate and abstract space that doesn't exist). How would it do that? As you quite correctly say in your post above it would involve a programmed "memory" of a variety of different 3D scenes with corresponding side elevations and measurements, it would also involve measuring and comparing absolute sizes of objects etc.

And it would fail to mimic human vision because in doing so it would also fail to see the optical illusions as we do.

Every time you look closely you find the observational data is quite clearly showing us that human vision doesn't match the mathematical model. Which is pretty much what I'm trying to highlight in the OP.

So to recap, the 3D understanding of a 2D image is not contained in the geometry of forming that image on another 2D plane (retina/camera sensor), it is purely a supposition of the human visual system/AI robot.

It is not rebuilt through pure maths but also requires a "memory" to reconstruct a "most likely/most probable" understanding.

There are still consistent, observable and predictalble differences between the mathematical model and what we see through our eyes. And so any theory that includes "look at this image with your own eyes it proves the maths," is flawed unless you also consider the nature of human vision.

Our human understanding of the 3D space we occupy is very remarkable in a number of ways. Of course it resembles the mathematical model, it wouldn't be very remarkable if it didn't. But it's a massive leap of assumption that we can describe human perception by the maths of image geometry. And yet we still insist, without evidence, that there must be a mathematical explanation. Another human trait perhaps?

😀