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

Hmmm...

Which is why, when I need my car fixed, I go to the mechanic, not the one who wrote the manuals.

You are missing my point.

Say at some zoom on my screen, the train subtends x rad from my eye and the man y rad ... the ratio between them is x/y of the train relative to the man. If I zoom out X2 then the train now subtends x/2 rad and the man y/2 ... since x/y = (x/2)/(y/2) nothing has changed in the ratio betwixt the train and the man. Similarly if I zoom in nX, nx/ny still = x/y.

Same if I crop and same if I re-sample and same for all reasonable viewing distances.

[edit]The business of insets is a red herring ...[/edit]

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I am confused by the use of the term "center of perspective" in the above, which elsewhere in the world of AI simply means "vanishing point" and:

a) can be anywhere on an image or even outside of it and:

b) there can be more that one vanishing point (often three) associated with a single image.

If only I understood that, the OP might make some sense ...

It is simply a matter of terminology. Some people misuse the term "centre of perspective" to mean the vanishing point. I used centre of perspective in its original meaning. It does not mean the vanishing point.

If you find it confusing, then use the term "centre of projection" instead of centre of perspective. Bruce MacEvoy does this in his article, probably because centre of perspective has been so widely misused.

As I defined the term (following classical usage) centre of perspective is not synonymous with vanishing point. They are two entirely different concepts.

Thank you for clarifying your usage of the term. As to "centre of projection", does the following transcript from my AI buddy apply to the pin-hole in your earlier illustrations?

*Optics - Center of Projection:

In optics, particularly in the context of perspective projection, the term "origin" may refer to the center of projection. **This is the point in space (often located at the center of the camera lens) from which rays of light are considered to emanate.** It plays a crucial role in determining how a three-dimensional scene is projected onto a two-dimensional image.*

Pardon the clip format ....

Yes, that is precisely the centre of perspective (or centre of projection).

I think you're wrong, and it's not a matter of science, it's a matter of language.

"Perspective" in this context means "point of view", namely the "point of view" of the camera.

Viewing condition is another important concept, but one that shouldn't be combined with "perspective", it should be kept separate, most particularly because they are, in fact, separate. The place the camera is placed is controlled by the photographer, the place the viewer views the image is controlled by the viewer. Obviously, it makes more sense to keep these things separate. Further, "telephoto compression" and related terms are driven solely by camera position simply because that term refers to relative sizes of objects in the image, not the way the entire image is viewed. The viewer's viewpoint cannot change relative sizes in a 2D image.

Then you should be able to give a formula for working out how much telephoto compression will be present in a photograph taken from a known position.

Whenever I have asked the question "what is this formula?" it is met with a deafening silence!

It's simple trig to determine the relative sizes of things. You need the size in real life and the distance from the camera to the object plus SOH CAH TOA. Nothing to it.

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.

As I expected, a reply that completely dodges the question! Not even a mention of telephoto compression.

Mine does. But then you chose to ignore me:

Yes, of course. I think we can all agree on that.

Again, I think we all agree that it is not the same as our perception. And, we assume a distance and a scale that is not contained within the photograph, but is based on our experience of reality.

I agree.

I agree that it is a guess, assumed by the viewer. We only see perspective when we see (or think we see) familiar objects or familiar scenes in the image.

I think, so far, we are almost completely in agreement.

Yet you still haven't attempted to give a formula to work out whether or not telephoto compression occurs in a photo taken from a known position.

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.

"Telephoto compression" is nothing but an odd description of the relative sizes of things in an image. And I did answer it.

You will get exactly the same relative sizes of objects in an image with any focal length taken from the same location. In other words, "telephoto compression" is another way of saying "I took the picture from far away". So, back to Ansel being exactly right - location is all that matters in this context.

If you want to work on a myth, work on what I call "the 50mm myth". It's much more related to what you are talking about than Ansel's absolutely correct statement.

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.