Exactly. However, there was another problem that developed with Renaissance Perspective, (not just linear but also the other 3 as well), it created a hell of a lot of extra work. Not just in assigning the correct spatial relationships for the main figures but now the whole of the spaces in between needed to be rendered with equal care.
[EDIT] I think the problem regarding rendering faces is an interesting one. Human faces are a special case with human perception because it's now believed that we may actually be born with the ability to recognise one, it doesn't seem to be learned behavior. And I think, though I'm not sure, the problem is also with the foreshortening as dictated by linear perspective and how that alters a face in a 2D image. Then when you view that image from a point other than the centre of perspective the distortion this causes is not so easily resolved as say a geometric shape like a barn that simply appears deeper or shallower, the distortion always looks unnatural. [EDIT]
It also reminds us that the point of taking a picture is for it to be viewed so the idea that devising a system of perspective that's independent of of the way we perceive it seems quite pointless. Though not quite as ludicrous as describing how perspective works in a picture when you're standing there with your eyes closed, it can still only ever be a partial theory if it does transform or change when you open your eyes and include the human visual system.
Besides the OP is mixing both. He is very much including both the act of viewing images and what we see when we do whilst insisting that it's purely about the geometry. It's a pointless discussion.
I understood Tom's post perfectly. I never needed to include my binocular viewing system rendered magically as one image in my mind, to understand the concept. My mind makes the necessary calculations / adjustments and I perceive an image as x units of distance away. As far as I can tell, my eyes / mind are functioning just the same as the vast majority of other people.
May I quote myself from the second post of the thread?
It's a very relevant discussion for those that wish to understand the effects of viewing an image at different angles of view than that of the camera at capture time, and that there is a viewing point where the perspective is equivalent. Just because you don't get it doesn't make it pointless...
It is not dogmatic it is just a concept. We are free to view from wherever we like. What empirical evidence contradicting?
It is about any viewing system. The same applies to a machine viewing components for faults. It will have it's sample in memory and compare what it's "eye" sees with that. That would be the classic case where, if the perspective was too far off, it's going to fail a lot more items than it should.
It's all a matter of degree. Sometimes I adjust my screen to be perpendicular when I am concentrating on an image. Mostly I don't because it's not too far off. But I see the trapezoid right now although it's only a few degrees. The other thing is our mind will do a pretty good job of adjusting the image to what it believes is necessary. It already knows the screen is a rectangle and if we don't need to know otherwise, no need to draw attention to it.
I do get it. I'm fully conversant with the principal of the centre of perspective of an image. I agree completely with the definition as written in The Manual Of Photography. Perspective is the function of position and that position also applies to when you view a photograph. There is a mathematical relationship between the position the photograph was taken and the position at which it is viewed, view a photo at that distance and the apparent spacial relationships between objects are preserved and you get the most natural perspecive, generally the one closest to what you see from the point at which the image was taken, and if you view from a position other than it creates an apparent distortion of the perspective in that image. I see nothing wrong and have no argument or misunderstanding of the principal.
I also agree entirely with the geometry of image formation and everything entailed in it.
I also agree with sound scientific method against pseudo science. And sound scientific method really dictates that if you're going to measure something then you have to consider the limitations of the device you use to measure when you form your conclusions. And the human eye is a notoriously unreliable scientific instrument mainly because it is empirical by nature and not logical or mathematical. Not really anything to do with binocular vision which is ineffective at mid to long distances, (effectively parallel) and 2D images.
The theories of centre of perspective as outlined in all the journals do exactly this when discussing only the the maths and geometry. They talk about preserving the spacial relationships and the point of natural perspective.
Tom is talking about a centre of perspective as a point where the perspective in the print matches exactly that you see with the naked eye when standing in the same spot. And there are two issues with this:
It contradicts observational data which is that although you can get close you can never seem to find a point where the two match exactly.
If you are going to predict a specific result you must also consider the device you use and whether it has any limitations that affect the result. To do otherwise would be bad science.
So we reach a point, that's universally accepted, where the problem in point 1 can be attributed entirely to there being a limitation in the human visual system that does affect the result, the maths is fine. I find it quite simple, and I don't think it's me that's not getting the point here.
The trouble with Tom's interpretation is by creating a false observation that there is a point where the maths of how a 3D scene is rendered on a 2D plane and our interpretation of that is exactly the same, we also create is a point where the maths of image formation can be applied directly to predict human perception.
Which it can't, not precisely. This is well researched, well documented and well understood.
It's ok to talk about perspective in general terms using a mathematical or geometric model to understand how it works. But you must also bear in mind that you cannot make a direct connection or apply that logic to exactly how we perceive images. You must allow that there will be instances where the two align very closely or less closely, where the difference in perception between two individuals is at a minimum or a maximum, and where what we see and perceive is in complete contradiction to the maths.
But by making this unsupported connection of exact Tom is also trying to expand image geometry to being a complete answer to things like telephoto compression. This is leading to some unsound logic, contradictions in the theory and visual examples that border on pseudo science. Good science means you don't just dig in and reinforce your position.
A good working knowledge of the centre of perspective can be outlined by the maths alone. But an exact one also includes elements of human perception, the non-linear way perspective is distorted as you move away from the centre of perspective, and certain elements of telephoto compression cannot be explained by the maths.
But the human eye is not a calibrated machine, images in the brain are not compared by pixel overlay where errors are calculated and defined by precise hierarchy. And if you were using such a machine to compare views and photos and assessing the results as calculated I would totally agree that we are talking only about the maths and geometry.
But you're not doing this, you're using the human eye, a notoriously unreliable observer, and just assuming what you see is absolute.
Andrew, I am very glad that we are now in full agreement on the concepts of "centre of perspective" and "correct perspective" or "most natural perspective". That is essentially all that I was trying to convey in my previous posts on this subject.
I was not intending to say anything profound about our visual perception and I am very surprised that what I said was interpreted in this way. I think you were reading into my comments a great deal more than was intended. I was thinking of perspective in purely mathematical terms.
In any event, I hope that we can end this discussion on an amicable agreement about the mathematical principles of perspective.
We can certainly end the discussion, and it's always been amicable. But I'm not sure we agree, or you even think so. 😀
Don't doubt it. We ourselves do learn most of it by trial and error in a single lifetime and I'm sure you can program AI to take a similar empirical approach. I think we do know enough about it to make this possible. I've only commented that it's beyond the scope of geometry and image formation.
LOL, I knew we'd have to get there, enter stage left - The Straw Man.
Well I shan't be attacking this one as I think I've been perfectly clear already. I thought you were just ending the deadlock politely calling the proverbial draw. I have no illusions that you've changed your point of view and expect to see you arguing the same narrative in another month or two. I doubt if I will have anything else to add so may just reach for the popcorn.
I have to admit that you do a good line in mockery and contempt. 😉 I do not wish to try to compete with you on that.
You insist on making this whole discussion very personal. You have frequently made statements like "Tom says ..." or "Tom thinks ..." You have paid a lot of attention to my use of the word "exactly", which I have used for emphasis, not with any precise scientific meaning. Yet you seem to think that it completely changes the meaning of what I have said, which I find bizarre.
My point of view and the words I use are essentially irrelevant. It is the science that matters.
I confess that I totally fail to understand what you really think. You disagree strongly with much (most?) of what I have said. Yet you agree with the Manual of Photography extract that I gave. I was trying to explain the same concept as in the Manual of Photography. How can you agree with one and disagree with the other?
I was too tired to reply last night and the internet has been blinking all day here...
I didn't read your earlier posts close enough to get your meaning but your last is clear. It is a fair enough point that two people may not perceive a similar perspective from the same location. That aside, as a starting point, I am happy with the original concept.
A straw man argument, basically where one party takes another out of context and forces them to defend an argument they did not make. It's as much mockery to try to catch another as it is to call one out. 😀
It's not personal, just frustrating that a simple point I find so easy to comprehend creates such a problem in photo forums.
It hinges on the basic assumption in humans that what they see is an absolute global truth, it's so deeply ingrained in some that they never think to question it. For example you think you are talking only about the geometry because you are only looking at the geometry. But you seem to completely fail to understand that you are making visual assessments by viewing photographs and still don't comprehend that you are including perceptual effects. To you you are looking only at the maths because that is all you are actually looking at.
You have this massive blind spot because it seems as if you fail to realise that you're using human vision to assess and prove this maths. You really need to re-visit your base assumptions.
I've tried to explain it directly to you, and obliquly and niether is working. So I will try again using quotes, and I didn't formulate this it is what I have read and understood from a variety of sources, and when I say you I do it automatically and generally mean the collective not you as an individual:
The importance of the terminology, or the real relevance of things not being exact.
There is your proof that there is an error introduced by the human visual system.
You never quite see exactly the same perspective in a photo even when you view it at the exact centre of perspective whilst you stand on the exact spot from which it was taken. This is entirely because of the error, if you like, introduced by the human visual system. Therefore a good scientific method would suggest that if you have irrefutable proof that the system you are using to verify the maths is introducing an error into the results...
The consequence of failing to examine base assumptions in scientific method.
Well it can lead to some pretty dodgy conclusions. Because you have decided that you are only looking at the maths everything you see has become a maths problem and because you assume your vision is absolute everything you see in an image is also part of that maths problem. It's like it just hasn't occured to you to question this.
I entirely agree with the definition of a centre of perspective, and entirely agree that viewing an image at a point in front of this will create us to see a distortion in that perspective that is often referred to as "telephoto compression". But your maths also throws up an interesting point or two, and at what point does observation fail
Well observation always fails to confirm the maths, the proof is above so we must consider the perceptual effect when we describe why we see telephoto compression. Now the real trouble with this and why you think that there is an "Adams Fallacy" is that the complete answer requires a massive perceptual shift on the part of the reader. Also a description of the effect can only ever be a partial one if it doesn't include this. So you are correct in recognising that current explanations are not complete, but so wrong in trying to fill that gap with geometry.
One of the main problems with assuming your vision is a Global Overview that is absolute in nature is that you also fail to recognise that like perspective viewpoint is the unique distortion caused by looking at something from a specific point. In a way by thinking that you have a global overview it just doesn't occur to some that there are other viewpoints to consider before you do have a real global overview.
So to have a complete overview of "telephoto compression" we also need to see it from the viewpoint of human perception being the constant as well as the viewpoint of the geometry. And that's a perceptual leap that's possibly beyond the scope of a photo manual.
OK, so the interesting point about an image of a distant object showing telephoto compression viewed in front of the centre of perception is at what point it becomes an elongated one similar to a wide angle view. How far away from the image do you have to move to see the close up perspective?
There is another problem with the maths which is that optical geometry predicts that all distant objects are rendered on a 2D plane foreshortened and that this foreshortening is baked into the image.
So your statement from "The Ansel Adams Fallacy" isn't really a complete answer either:
Ansel Adams is entirely correct, perspective is a function of position alone, it's the distance alone that predicts telephoto compression not the centre of perspective.
Especially with the othe rpurely perceptual effect you touch on, and one I offered and explanation of purely because you touch on it:
My response:
It was in my original response, and you really need to let it sink in. What it says is that when we look at a photo we make an assumption about the scale and relative distances between objects. By the maths of the centre of perspective we must accept that we will generally see a distortion of perspective. But the first point we have already shown that the human eye adds another distortion. And the quote above suggests that because the brain values a consistent understanding over an absolute and logical one it will also preserve that distorted understanding over the over the logical and mathematically derived one.
In short when we view and image we will never see the correct perspective, and our (mis)understanding is perserved as we change our position relative to that image.
Or you can't use visual examples on a photo forum to explain the maths of image formation without taking into account human perception.
I have been saying the same thing over and over and really doubt that I can put int in a way that will be any clearer.
The original concept as far as photos you actually take, conditions they are actually viewed under, and the distortions you actually see, is a really sound and practical one. There is a centre of perspective when viewing images.
Tom, you have a real blind spot that really is preventing you seeing past your own opinion. As I said, I can't put it any plainer. The problem with perception is yours, and not because I don't question my assumptions but:
I did not say that, Though there is a typo I think the meaning is still clear enough: viewing an image at a point in front of this will create cause us to see a distortion in that perspective that is often referred to as "telephoto compression"
The affect is apparent, not real. I also said:
Or to reveal: How far away do you have to move to see close up perspective?
And:
So tell me where the null point is on your scale? At what point mathematically does a photo with baked in geometry that is foreshortened in exact accordance with the maths of image formation reach a correct perspective. What is the nature of that correct perspective? Is it when we see the object correctly foreshortened, or exactly as depicted in the photo, or the point where it no longer appears foreshortened as in at the point where it becomes elongated? Remembering that the foreshortening is baked into the 2D image as a function of distance alone.
Please explain this mathematically. Because I can explain how it's possible perceptually, and it's entirely a function of distance both in the taking of the original image and the viewing of the print.
No, it doesn't, perspective is a function of distance alone.
Your inability to see this stems from your own inability to question your base assumptions and the massive blind spot they are creating in your thinking. I've been as clear as I can be without actually dictating to you because to understand this you really need to work it out yourself because only then will you break out of your tunnel vision instead of trying to fit everything I say within it.
I dont think I am at all unusual in that I take no trouble at all to place my eyes in the “magic spot” with respect to any photos I look at: the fact that they are 2D and not 3D representations prevents them looking any different to me as I move them around in my central field of view. I would also note that, when I look up at a close building, my eye/brain combination prevents me from noticing the non parallel walls. Nor am I convinced by the apparent view that railway lines join at infinity, or that the world is flat.
