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

I am very pleased that you have come round to my way of thinking. This is supporting what I have been saying all along.

It is a little more than just misinterpreting the perspective in an image.

The perspective seen by our eyes changes when the viewing distance changes. The relative sizes of objects does not change, but the absolute size (i.e. angular size) does change. It is this change of angular size that causes us to misinterpret the perspective captured in the image.

If the image is moved closer to our eyes, then everything in the image looks larger (angular size) and hence everything looks closer by the usual rule of perspective: object size / object distance = image size / image distance. If we increase the image distance then the object distance appears to increase in proportion.

I am not having trouble with this and I never have. I thought you were having trouble with it!

I agree.

No, the perspective we see in a photo also depends on our viewpoint. It is a combination of the perspective captured in the photo and any perspective distortion produced by not viewing it from the centre of perspective. [Maybe this is a problem of terminology if you do not like using the word perspective for the distortions introduced by the viewing position.]

For example, take the skull in Hans Hobein's painting "The Ambassadors".
Viewed normally, the skull is seen with a highly distorted perspective. To see it with the correct perspective it must be viewed from a particular position to the right of the painting and at a very oblique angle. The perspective we see depends on our viewing position.

No it doesn't.

Glad you agree.

Which is not "perspective".

Humans are very insensitive to that effect, and in any case, it's not "perspective".

What changes when you change "perspective" is relative sizes of objects in the image. This is why the "dolly zoom" effect works - no change in field of view, but a change in relative sizes of the objects in the image, caused solely by moving the camera position.

No, it does not. The "perspective" is "in the photo". We can't change it after it has been captured. Viewpoint of the image is separate from the "perspective" (point of view) of the image, which is solely caused by the location from which the image was taken. This is effortless to prove. Take a picture of a wall. Now, take a picture from the other side of the wall. Now, look at the first picture from any location you want and see if you can see what's in the second picture.

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.

It seems that we agree on all the key points. Telephoto compression is something that we see when we view an image from closer than the centre of perspective.

The effect here is quite extreme, but it is not different in principle. As you say, the image plane must be at an extreme angle to the optical axis of the camera. To see the image correctly, it must be viewed from a similarly extreme angle (at the centre of perspective).

[deleted]

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."

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.

Why would I object to that? Obviously, our perception of what we are looking at depends greatly on the context. Depth perception depends on a very large number of cues that may (or may not) be present in the image. Many optical illusions (such as the three vans illusion that was discussed recently in dpreview) occur when different cues appear to be contradictory.

Perspective is just one cue that helps with depth perception (although often a very important one). I would never claim that depth perception depends on perspective alone, let alone just on the angular size of familiar objects which is the only thing that changes when just the viewing distance changes.

I am still very puzzled about what Andrew really thinks. He persistently avoids giving a precise description of what he thinks "telephoto compression" is and how it occurs, yet he very confidently claims that the explanations given in the Manual of Photography and elsewhere are all wrong.

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.

Suppose I take a photo of two objects against a completely uniform white background. Object A is at a distance of 10 (in whatever units you like) from the camera and object B is at a distance of 20 (in the same units). The photo is taken with a 500mm lens.

Then I take a second photo with object A at distance 1 and object B at distance 2; this time using a 50mm lens. The size of object A will be the same in both photos. The size of object B will also be the same in both. The positions of A and B relative to the camera are assumed to be consistent with their positions in the first photo.

So, our perception of depth in both photos will necessarily be the same (provided that the only thing in the photos from which we can judge depth is the size of the two objects).

In other words, the photo with a 500mm lens has the same apparent perspective as a photo with a 50mm lens and with all distances from the camera reduced to one tenth of their original values. This is another way of describing telephoto compression. It does not involve looking at the photos by eye. They could instead be analysed digitally with software. How our eyes work does not come into it..

[deleted]

The image of object A would not be the same size as in the 500mm lens. So the software perception would not be the same.

[deleted]

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??