I think Andrew546 likes to keep his position unclear as otherwise it might become obvious that the emperor has no clothes. I have had no success in trying to ascertain more precisely what he thinks.
If he was prepared to make his position clear, then we could start a rational scientific discussion.
As can be seen from his recent posts, he seems to prefer sneers to rational argument.
What's this a tag team?
I've tried discussing it with you, its all in the history, but you dismiss opinion that counters your own, then make comments like the ones above. I pointed out valid flaws in your argument and supported that opinion with a link to a very respected peer. But you ignore all of it. There is no discussion with you Tom, I must agree or be dismissed. To be frank I find you to be far from scientific, you do not question or doubt your own views but rather have the same view which you try to prove correct with ever more fantastic and absurd examples such as in this thread. I am familiar with a lot of the examples you use from the early Renaissance and I have to say that you completely misunderstand and misrepresent their meaning, which in some cases is virtually the opposite of what you say. Instead you bend them to support your own preconceived opinion. Sorry, but the whole premise of this thread is ludicrous, absolute nonsense. You formulate a mathematical relationship about 3D perspective by considering a case where there is A COMPLETE ABSENCE OF 3D PERSPECTIVE. Then rather than examining real data regarding the difference in your title we are DISCUSSING EXACTLY HOW WE NEED TO MOVE MOUNTAINS AND TREES AROUND THE LANDSCAPE (ALSO HOW WE NEED TO STRETCH AND COMPRESS THEM) TO MAKE THE IMAGES THE SAME.
Sorry about the bold, but I have said the same many times before and yet you still don't see the absurdity, fuck it, I'm through, there is no scientific discussion here just frustration. 😬
I don't think either of you has exercised much concision in this thread so that specific points of disagreement can be easily scrutinized - and perhaps adjusted or recanted. I believe you both know all the same things about perspective, but prefer to avoid saying so. Maybe that's okay, considering this is essentially just one of the many pickle barrel discussions found here and in other places.
Well, found what seems to be a concise summary of human one-eyed depth perception
www.wtamu.edu/~cbaird/sq/mobile/2023/07/28/why-does-a-person-with-only-one-working-eye-have-zero-depth-perception/
Can you see the similarities to "telephoto compression"?
"Zooming with your feet"? As if there wouldn't be any parallax... 🍿🍻
Yes, that is a good summary of depth perception.
Section 6 Familiar Size is the relevant depth cue for understanding telephoto compression. People often assume that Section 5 Relative Size is all that matters. However, when you use a longer focal length to magnify the image, the relative sizes all remain the same.
What changes is the absolute size. Quoting from Baird's tutorial:
"If a certain object has a known size, then its perceived size corresponds to how far away it is, even if there are no other objects in the field of view to compare it to."
By perceived size, he means the angular size seen by the observer. For example, a person who is 170cm tall and standing 100 metres away, subtends an angle of about 1 degree, while the same person standing 200m away subtends an angle of approximately half a degree.
Of course, the perceived sizes of objects in a photograph will depend on both the size of the photograph and the viewing distance.
I like this: christophertyler.org/CWTyler/Art%20Investigations/Perspective/PerspectiveRules/PerspectiveRules.html
No math. I believe it is inline with everything Tom says.
With regard to variance in each individual's perspective, the mind is always re-calibrating itself. If it didn't, an athlete who requires some form of distance perspective wouldn't have much chance of success. A builder isn't going to keep hitting his thumb with his hammer for too long is he. A draughtsman who creates perspective drawings uses a set of rules that everyone can follow. If my mental perspective interprets it differently, is the draughtsman at fault?
Thanks for that link. Tyler's Section 7B describes telephoto distortion. It is perhaps not immediately obvious that what he is describing is the same as what I called telephoto compression, but it is essentially the same thing.
Here is a very comprehensive online article on perspective (again written primarily for artists rather than photographers):
Bruce MacEvoy "Elements of Perspective". The section entitled Display Geometry and Image Impact is particularly relevant to this thread.
No Tom he doesn't. Once again you apply the maths of how a lens forms an image on a sensor (mathematical perspective) as a framework to understand human cognitive function. He is quite clear:
5. Relative Size
If two objects in your field of view are the same type of object, then your brain assumes that their true physical sizes must be the same. Therefore, your brain assumes that the difference in their perceived sizes must be solely caused by perspective effects.
All through the description he uses words like, percieved, estimate, assumes, subconsciously understands, nowhere does he relate anything to a mathematical formula or any relationship to actual size. That is an assertion you added that without evidence to back it up, you continue to assume.
Our depth perception, or ability to understand the 3D world is really just memory modified by experience x 1 million and counting. The picture you see IS NOT the image projected directly on your retina but an AI generated by the brain. From the link I posted:
"...the brain didn’t actually evolve to see the world the way it is. We can’t. Instead, the brain evolved to see the world the way it was useful to see in the past. And how we see is by continually redefining normality."
The evidence for this is overwhelming. In his TED talk Beau Lotto concentrates on colour, because it is easier to see, and shows you comprehensively that we do not see the absolute values of the light our eyes detect. They are modified by both biological and cognitive process, the brain quite literally changes values in order to present an understanding that evolution defines, the one that was most useful in the past. The brain doesn't see perspective correctly either, it actively modifies it in order to present an understanding that makes more sense.
I said a long time ago (in a distant galaxy):
If you make a measurement you take into account the error in the device doing the measuring, if you use the human eye to compare you MUST take into account the way that human cognitive function modifies the data or your conclusions will be flawed. You cannot use visual examples as proof of mathematical fact or use the mathematical model as a framework for understanding why we see photos as we do. If you do your conclusions will be flawed.
The way the human brain perceives reality, or makes sense of the 3D world around us is a fascinating subject, but it has little to nothing to do with actual perspective. That what we see relates to the mathematical model is because we are good at it and not because there is any mathematical connection between the two, that is pure assumption.
No Tom it doesn't. He is describing how we view and make sense of the dynamics in the real 3D world where perspective changes with viewing distance, he is not describing the extra-ordinary example of a 2D image where the perspective is fixed and doesn't change with distance. We do not see telephoto compression in the real 3D world we only see it in 2D images when we view them out of context. If it doesn't exist in the 3D world and he's talking exclusively about the 3D world then... You can't keep bending fact to support your theory.
In the case of telephoto compression there is the the obvious: If your vision is absolute and relates to geometry then the way you see the 3D world would match exactly the way the camera sees the 3D world, everything you see in a photo would match exactly something we have memory of in the real 3D world. If your vision was absolute then the actual relationship of H x W x D being constant in the photo should also remain so when you view the image at any distance. But our understanding doesn't remain constant, our interpretations of H x W x D do not remain constant. There is a simple statement here:
When you view the photo you do not have an absolute understanding of it's correct mathematical perspective.
There are also underlying cognitive processes here, but fortunately there is a simpler explanation that's also correct:
We see the perspective incorrectly because we guess and we get it wrong. We use our memory and experience of the size of buildings to estimate their distance, but memory is fickle and we get it wrong. So we use our misunderstanding about the exact size of the building to misunderstand how far it is away and both those misunderstandings mean we completely misunderstand the absolute perspective and therefore we get the relationship between H x W x D wrong as well.
This is the actual meaning of the passages in the link. You cant equate them to actual maths, there is no 170cm and 1 degree of vision. One person may think 190cm and 40m away, another 190cm and 35m away. The same person may maker the first assumption on a Thursday and the other the following Monday and none of them represent the actual truth of the absolute size or distance (but our assumptions get progressively more accurate the closer we get and our binocular vision becomes more effective). There are also underlying cognitive functions.
You cannot keep using geometry as a framework to describe human perception, which the quote at the start of this response implicitly does. Any conclusions you draw from such observations are necessarily flawed.
Just letting you know I am still here 😊
Give it a rest, Andrew.
From earlier in this thread:
Well, you can see how well that went. 👎
No, Andrew, that is completely wrong. Baird's tutorial may not include any maths, but that does not mean that he doesn't think that the maths is relevant (although the only way we would know for sure would be to ask him).
Instead, let's look at the very comprehensive and reputable tutorial on perspective by Bruce MacEvoy. He does include the mathematics in very great detail. Read his section on "Distance and Size", which goes into a lot of detail on the very point I was trying to make. Then read his section on "Display Geometry and Image Impact" (note that his centre of projection is an alternative term for the centre of perspective).
It is also important to realise that understanding perspective does not depend on understanding human cognitive function. The theory of perspective is a mathematical theory that relates what we see when viewing a 2D image of a scene with what we see when viewing the scene directly. It is all about the geometry of the rays of light as they enter our eyes. It says nothing about how we interpret what we see.
I was having a discussion with a photographer about perspective when he stood up, went to the window, flung it open and said, "that is the real physical world out there and that is a real tree that has an absolute height and subtends an angle in my vision."
I say, "you still don't see it. Yes there is a real physical world out there that obeys all the physics and all the maths about perspective. But that is not it, that is just what you see."
You keep doing this. At one point you talk coherently about the maths and the nature of human vision and the next you treat what you see as the real physical world and so apply maths and physics directly to human perception while adamantly declaring that you are discussing "only the maths." Consequently you keep trying to include human cognitive function in your maths rather than allow for it. And as long as you continue to treat what you see as the real physical world your conclusions will be flawed.
Your statement earlier:
You then often expand that mathematical framework to predict how we would see a man standing 300m away and how that should look through a telescope, then suggest we should try looking for ourselves to prove the point. And still do not see that you have crossed the line from pure mathematical perspective to human perception of that perspective. You added this to the article about human cognitive function, it is not contained within it. It is your definition.
So why is "subtends an angle of" wrong when we treat what we see as though it's the real physical world? Please stick with this, it highlights the danger of assuming vision is absolute.
In his TED talk Beau Lotto uses this example to illustrate how we see colour. It is very revealing:
This is just what we are looking at, we are looking at two tiles on the floor both of which are exactly the same colour (bar jpeg compression). One is surrounded by a darker colour and one is surrounded by a lighter colour.
Now see what happens when we change the context, remember nothing has changed in the highlighted areas in the image above, all that's changed is the logic that explains the bright or dark backgrounds:
It is the law of physics that if you have two tiles of the same colour then they remain the same colour regardless of the surrounding colour. It is also a law of physics that if the two colours are the same and one is in shadow then in the real physical world it must be a lighter shade.
So we have absolute visual proof of scientific fact!
Or are we missing the point? What we have proved is the human vision has altered the image projected on the retina to match our knowledge gained from previous experience. It has literally changed the data. That it does this in line with the laws of physics is no surprise as the point of vision is to make sense of what we see, not nonsense.
Here's another one, involving perspective. It is a 2D image so everything in it the same distance from you the viewer, all the vans are exactly the same size, all the vans subtend exactly the same angle in your vision:
The biggest problem in these discussion is the assumption that our vision is absolute, that what we see is actually the real physical world rather than what it is, a projected image that has been processed by AI (Actual Intelligence). And because we often don't question our base assumptions about the nature of human vision we keep compounding these errors in our conclusions.
The article about how we perceive perspective is only correct without the maths, if you apply maths or the absolute data about actual size or angle subtended then it fails to explain human depth perception. It becomes incorrect. You assume too much and fail to question those assumptions.
As with the photo I bet that people will still try to formulate a rational reason why we see the vans the way we do and link that to the logic they know fit it within a framework they understand (maths) rather than expand that understanding to include new knowledge. And they will still miss the point, you do not see the image correctly because you brain has modified the perspective to fit previous experience. You would literally be trying to describe human cognitive function and not perspective.
Andrew,
what do you say to the above?
Sort of. And being a former builder/bricklayer I have to confess that I may, perhaps, be a very slow learner... We are all individual and so all have a unique view because we all view from a sightly different position, both philosophically and directly in what we see with our eyes. And what you learn, how you are taught (to classify, order and label) even how you understand physics does affect how your brain processes the information and forms the image you "see".
But in reality similar social/political groups have a similar shared environment and so true variance within that environment is very small, we all have roughly the same skills and the difference between beginner and expert is really just practice. You have to separate shared experience by a long distance before you see any significant change. However, if you start to encourage people only to glance rather than look, then we don't see correctly or completely. We then fill in the gaps from the only place we know, our own experience and memory. And if we are encouraged to do this emotively rather than rationally (something you see quite frequently on social media these days) then that perception, provided largely by our own memory and containing that bias, becomes physical proven fact supported by the evidence. Never underestimate the power of the human brain to ignore what it doesn't wish to see.
Perspective drawings are, or should be, mathematically correct. And any modern draughtsman will know that pure linear perspective always looks slightly odd. The reason is if human cognitive function prevents you seeing the world of pure mathematical perspective then that 2D representation is one you never see, it will look different (slightly) to the real world "as you perceive it". Because they are technical in nature they include lots of geometry and so it is more obvious that a photo of a landscape. But artists have known this since the Renaissance, that true linear perspective doesn't represent what we see and have been working their way around it since before Leonardo. BTW, it's quite easy to show that you never see perspective in a photo correctly either, and see the second paragraph above, it applies.
If I look out of the window and don't see the real world, what exactly do I see?
From that response:
With colour the composition of the light reflected from objects depends on the composition of light hitting the object. The scientific reality of the world is that colour constantly changes. Yet this is not the world you see. You see one where your understanding of colour remains remarkably consistent. There are many processes that evolution has promoted to do this, I showed you proof that it also actively changes data so it matches experience.
With perspective the mathematical model dictates that shape and relative distance must be in constant motion as you move through 3D space. Yet this is not the world you see. You see one where your understanding of shape and relative distance remains remarkable consistent. There are many processes that evolution has promoted to do this, I showed you proof that it also actively changes data so it matches experience.
Seeing depth in a 2D image is entirely a human cognitive process. Sorry but it isn't a mathematical function of the image, it exists only in how we process the data. The image projected on the retina of a 2D image is a facsimile, that is mathematical and geometrically a fact. There is no 3D information attached, only what we work out with our brains. That calculation only happens in the brain, if you discuss depth perception you are discussing that function and not perspective. That what we see in a 2D image relates to the maths of how it is rendered is only because we are very good at it. But it is not visual proof of scientific fact. See my previous response.
From your own definition, your bold:
The reality of geometry is that if you view from a single point in 3D space (the only thing we can physically do) then perspective effects distort what we see in a way that changes as we move through the space. It shows a far more confusing and unstable landscape than we see. In reality the image that our brains construct is far more representative of the real static nature of 3D space, a view that's made impossible for us to see because we can only ever view it from a single point in space, and so our view is always distorted by perspective (the way the 3D world is projected on the retina). We can do this because of human cognitive process.
But it also means that what you see is not directly representative of mathematical perspective. It is also true to say: Seeing depth in the real 3D world is entirely a human cognitive process.
Andrew, I think what you are saying here is so bloody obvious that I hadn't realised that you could be making such a fuss over something so obvious. Everyone with reasonable scientific understanding knows that when we look at anything our eyes are recording photons that hit our retinas, this is converted into electrical and chemical signals that get transmitted to our brain and go through very complex processing to interpret those signals, etc, etc.
So what? This does not mean that we are not looking at the real world! Of course there are situations in which we may be unable to interpret what we see or interpret it incorrectly. This does not negate the usefulness of having a mathematical model of perspective that works when we are able to correctly interpret what we see.
Your lack of understanding of how science works is seriously clouding your ability to talk rationally about these things. It is possible to discuss perspective without having to consider how the eye works, how the brain works, how depth perception works and all the other things that may be involved when we look at a photograph or when we look at a real scene. Science always works by the abstraction and separation of ideas so that we can consider one thing at a time. Real situations are always much more complicated than the idealised models that scientists consider. But those idealised models are an essential part of the scientific process.
