What does "correct perspective" mean?

Whenever I have mentioned the term "correct perspective" it has caused a storm. I want to try to explain where the term came from and hopefully clarify its meaning to those who are not familiar with it.

Here is an extract from the "Manual of Photography" by RE Jacobson et al. (7th Edition, 1978) which defines the term:

I first read about the more technical aspects of photography in a 1937 Leica Manual owned by my father. It discusses perspective when comparing different focal length lenses. Here is a brief extract from page 64:

Notice that the Leica Manual uses the term "most natural perspective" to mean essentially the same as the term "correct perspective" means in the Manual of Photography. Personally, I am happy to use either.

I am willing to discuss this topic further and also to try to clarify anything that is unclear. Hopefully we can keep the conversion polite and on-topic and avoid personal comments.

The concept is clear to me.

I think we need to be aware that word usage changes over time. While it may have been appropriate to say "correct perspective", especially in the manner of scientific doctrine at that time, today, many infer that the opposite is somehow wrong and rail against it. Perhaps "Ideal Perspective - for reasons x,y,z" might be a better term for those who feel discomfort when they don't see the concept, allowing them to maintain their sense of self worth.

Once the concept is clear, we can lead onto the results of non-ideal perspective; telephoto compression and wide angle distortion.

Absolutely. Long post follows, as you can see, clearly. 😀

Or to put it another way:

Perspective is the distortion caused by viewing the 3D world from a unique point in space. Every unique point has it's own unique perspective, or it's own unique distortion caused by viewing from a single position.

To a point this also happens when we view a photo, or a 2D representation of a 3D space. Viewing an image from a unique point in space also causes us to see distortion in the perspective of that image. It also follows that there is a viewing position for a photo where the perspective, or unique distortion matches that or the original scene. This is said to be the "correct perspective" and is a point that can be worked out mathematically using the geometry of image formation. All very well explained above.

Tom, the problem I had with your post is that you inserted the term "exact same" when viewed where all descriptions use words like apparent and natural. You seem to make an assumption, or a leap, from working out the centre of perspective to find the point where the apparent relationships are the same, to this is the point where the perspective in the image will be "exactly' the same and "mathematically" correct.

There is a problem with this and it is in the nature of the viewer, or the nature of human vision.

There is a layer of processing between the back of the retina and the view you think comes from the back of your retina that is uniquely human and is "Relative, Historical and Empirical" rather than "Logical and Mathematical". This doesn't negate the maths of image formation, how a camera works or even how an image is formed on the back of the retina. But it does prevent you from trying to describe human perception of perspective in mathematical terms, or as the function of image geometry. It doesn't mean the maths is incorrect, it just means that there is a difference between how a camera sees and how the eye sees and that that difference is abstract, not logical.

Evolution has discovered that our chances of survival are better if we have a consistent understanding of our surroundings. This has very important consequences. It means that on the list of priority "consistent understanding" come above "absolute" and "mathematically correct". In short it means that the brain sacrifices, or fails to preserve, the mathematical relationship between objects in favor of retaining a consistent understanding.

I will relate this theory and apply it to a more comprehensive explanation of "telephoto compression", see how it fits.

In you previous post about "The Ansel Adams Fallacy" you branched into pictures with copies inserted as insets. I struggle to see your point, and frankly dismiss this as pseudo science as you seem to be cherry picking and applying conclusions that suit your narrative whilst ignoring the blatantly obvious. Yes if you line up converging parallels you inevitably scale the picture in accordance with a mathematical relationship and smaller objects look further away. Great, but you can't then work out the maths by measuring the relative sizes of the girls and then declare that she looks 7 times further away because that's the mathematical answer you arrived at. Yes, she looks smaller.

But those images also very convincingly show that perspective is indeed a function of position and not scaling. As @xpatUSA observed, all you did was align converging straight lines and the foreshortening, or complete perspective, doesn't fit.

The foreshortening of objects is a function of distance, it is a function of position, or it is a function of the distortion caused by a unique viewpoint, or it is a function of perspective. It is predicted by the maths of linear perspective and can also be entirely proved by the geometry of image formation. All objects are foreshortend by distance from a unique viewpoint and they are always foreshortened.

So the interesting question is not why we see it in shots taken with a telephoto lens, but why you don't see it in the normal landscape. And the answer is in the "Relative, Historical and Empirical" nature of human vision, and it does relate to viewing images from the "centre of perspective" so they are viewed with "correct perspective".

Perspective is the distortion caused by viewing from a unique position and each position creates a unique perspective. In other words things change as you move. But the human brain is very good at subtracting that distortion so the world [1] seems to be constant as you move through it. The side of a barn with its converging parallels doesn't elongate as you move towards it or shorten as you move away, your understanding of it's size remains constant. It's why we don't see distant barns as being foreshortened, because the brain is compensating and allowing you to see the real size of the barn. Also, and interestingly, we do not always estimate the distance of said barn correctly and my have assumed that it's further away. In this instance we will probably see the barn as being slightly longer than it actually is but we will never question this. We simply assume our vision is absolute and assume the barn is actually that distance away and is exactly the size we think it is. hen we approach our understanding modifies as our perception creates a more accurate picture, but again we never usually question this, just assume we always saw it correctly. It also why holding an image from a known camera position to prove yourself correct about perspective is not a foolproof method but may be subject to confirmation bias.

As for telephoto compression Tom's description of viewing from the "correct perspective" is the answer, but without the "exactly the same" and "mathematically correct" additions. We see telephoto compression when we view an image from the wrong distance, too close, or in front of the center of perspective. The image has not changed, only our interpretation of it has. When we view an image of a barn foreshortened by perspective from the centre of perspective for that image then we see the correct perspective, or natural perspective. It is important to realise that we are seeing an image of a foreshortened barn and we are forming an understanding of it's actual size based on our experience of seeing distant barns, at this distance from the print we don't see it as foreshortened. Move closer to the print and your vision will fail to cancel the effect of foreshortening and it will become visible in the image, it is important to remember that the image has not changed only your interpretation of it has.

But vision is "Relative, Historical and Empirical", we rely on memory and do make mistakes, incorrect assumptions when viewing both images and the real world. The brain promotes consistent understanding over preserving absolute mathematical relationships so we don't really see perspective correctly in any image, we simply assume our vision is absolute and that what we see is an absolute truth that can be proved by maths.

[1] It is one of those strange abstract relationships that is the nature of human perception that we believe our vision to be absolute because it presents a consistent understanding, but that consistent understanding is achieved by disregarding the absolute truth when it conflicts with a consistent understanding. I find there to be many contradiction like this at the very centre of human perception. Odd.

Andrew,
Thank you for you very detailed response. I must confess that I do not understand much of what you say; we seem to be talking at cross purposes. However, I will try to comment on some key points.

1. What I said was not intended as a legal document and I am not going to try to defend my exact choice of words. I was trying to convey an idea in an easily understandable way. I apologise if it was not as understandable as I intended.

2. The nature of human vision does not come into my use of the term "correct perspective". My approach follows those references I gave and looks purely at the physics and mathematics of light rays before they enter the human eye. What happens inside the eye is not considered at all.

3. Viewing a photograph with the "correct perspective" simply means that the light rays from the various objects seen in the image enter the eye at exactly the same angles as did the light rays from the corresponding real objects when the eye was placed in the same position as the camera lens when the photo was taken. This is purely a statement of three-dimensional geometry and can be proved mathematically (making appropriate assumptions about how the camera creates the photograph). It says nothing about how the eye sees those light rays. It just says that when you look at a photo with "correct perspective", you see everything in the photo at exactly the same angular positions in space as the real objects had when viewed from the camera position when the photograph was taken.

I hope this helps to constrain the scope of what I meant by "correct perspective". I know there are very interesting things to talk about concerning how human vision works. I know much less about that and was not intending to start a discussion on that topic. Please start another thread on that subject if you would like to.

Tom.

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One of the issues when ever this subject matter comes up is the process of taking an image is a projective transform which all photons from a line in three space with the origin in the camera lens are focus to a single point on a plane (the sensor). By its very nature a projective transform does not preserve Euclidian metrics, e.g., angle, length, etc.

Therefore the appropriate geometric camera model to analyze this question is projective - not Euclidian - geometry. That is the perspective on the image is defined by the projective geometry. In human vision people use two eyes to feed the brain two distinct projective images which the brain then produces a 3 D representation which allows humans to determine relative sizes, locations, etc. The camera has only one "eye" which leaves an image of only one projective representation of 3 space in which neither relative sizes or locations can be derived.

courses.engr.illinois.edu/cs543/sp2011/lectures/Lecture%2002%20-%20Projective%20Geometry%20and%20Camera%20Models%20-%20Vision_Spring2011.pdf

Absolutely, I understand what you say here. But in your original post on DPR you did implicitly include human vision, quote, "A photograph is viewed with the correct perspective if it is seen with...". I don't know how to subtract the effect of human vision from that statement. The use of "exact" I have always though was more subconscious on your part, your translation, and have been trying to draw your attention to that rather than dismissing the whole.

But...

The raison d'etre of a photo is to be viewed, generally by a human, so maths of image formation can only ever be a partial theory of perspective in images. There is also a habit, yourself included, to use visual examples with images to back up those theories, "Go to the place from which you took the photo and hold the print up in front of you." How can any response to statements such as that be correct if it ignores the empirical nature of the human visual system that is looking at both the original scene and the photo and doing the comparison?

You see the problem here?

The biggest problem by far in these discussion is the assumption that our vision is absolute. Even if you could prove it isn't beyond any doubt then people would still fail to apply that knowledge to what they see, and so still use visual examples as proof of mathematical fact. "I see it so it is real and absolute, here is the proof, see for yourself..."

The maths of image formation is fine, and you can use it to make general assumptions about how an image will be percieved, but you can't make absolute ones and you can't describe the nature of human vision in those terms.

😀

Andrew, I have absolutely no idea what you are trying to say. It makes no sense in terms of the usual theories of perspective. If you are trying to develop your own theory of perspective then I think a good deal more work is needed to make it intelligible and useful.

I'm at the end of my tether here.

You instruct me to use my human visual system to look at a photograph when standing a the same spot it was taken.

You instruct me to use my human visual system to look at the real scene.

You instruct me to use my human visual system to compare the two.

Then insist you have been talking exclusively about the maths of image formation all along and are not including the human visual system in your argument.

You need to understand the fallacy of your own proof. I really can't put it any clearer.

I'm sorry but I can't talk to you any more about this because you really do seem to have a block on something that's so plainly obvious to me.

I would say exactly the same about you. I don't understand why, but we are clearly on different wavelengths!

I have already given a couple of references for my point of view, both quite old. An article by Bruce MacEvoy on the theory of linear perspective as used by artists can be found here. It is very comprehensive, but written for artists with very little reference to photography. The theory is essentially the same, however.

Andrew, do you have any references for your point of view?

Yes! Yes! Yes!

OH THANK YOU !!!!!

And then you obviously will run into problems when you post visual examples to exclusively prove the maths of image formation alone correct becuse you have to use the human visual system to view them. and the simple act of viewing through human eyes will always distort the result simply because the the way the eye/brain works is empirical by nature (based on, concerned with, or verifiable by observation or experience rather than theory or pure logic).

If you wanted to make an accurate scientific measurement you would use a calibrated machine. But on photo forums we just post jpegs, view them on computer screens and just assume what we see with a human eye is an absolute and calibrated truth.

Sorry, but it just seems so simple to me. 😀

Tom, I am not talking theory any more. I'm saying that you REALLY need to see the fallacy of your own proof!

Tom- "Look at this image, it proves my point"

Andrew- "But if we observe then we really need to consider the limitations of the device we use to do the observation, i.e. the human visual system, when we form our conclusions."

Tom- "But I'm not talking about the human visual system, only about the maths of image formation."

Andrew- "But your proofs exclusively involve a visual examination through human eyes."

Tom- "Andrew, I have absolutely no idea what you are trying to say. It makes no sense in terms of the usual theories of perspective."

😫

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NO, they do not. Visual examination is the easy way to do it, but you could instead substitute measurements of the positions of points in the image and relate them to the positions of the real objects in 3-D space and this is the rigorous way to do it.

Theories of perspective actually have nothing to do with human eyes. They are all to do with light rays and how they are used to represent 3-D scenes as 2-D images.

I don't know, is it me? Is my point that obscure? The OP seems to be trying so hard to contain perspective to such a narrow definition that is no longer includes the viewer in a discussion that is essentially about how changing the distance at which you view a photo changes your perception of the perspective contained. Does a photo exist if it is not viewed? I'm beginning to wonder.

It reminds me of my friend who always declared the world to be flat. Anyway, one day he set of to prove it, and I've never seen him since. Does that mean he's correct or just raise doubts about his ability to navigate? Good job I decided not to go with him.

The article basically says what a history of art already shows, that pure mathematical perspective was abandoned even before the High Renaissance. Mainly because of the empirical nature of human vision and how that created differences between the way we perceive a real scene and the way we perceive a 2D representation of one. Linear perspective was still used, but in a modified form, abstracted from reality because it looked more natural. Even paintings in the Impressionist and Fauvist movements are created with a centre of perspective of sorts, an ideal viewing distance, but it's a long way from linear perspective.

I notice exactly has slipped back into your definition.

A very interesting link which I have bookmarked, for a deeper reading. But this closing paragraph struck a cord.

"Paolo Uccello would have been the most gracious and fanciful genius that was ever devoted to the art of painting, from Giotto's day to our own, if he had laboured as much at figures and animals as he laboured and lost time over the details of perspective; for although these are ingenious and beautiful, yet if a man pursues them beyond measure he does nothing but waste his time, exhausts his powers, fills his mind with difficulties, and often transforms its fertility and readiness into sterility and constraint, and renders his manner, by attending more to these details than to figures, dry and angular, which all comes from a wish to examine things too minutely; not to mention that he very often becomes solitary, eccentric, melancholy and poor, as did Paolo Uccello. This man, endowed by nature with a penetrating and subtle mind, knew no other delight than to investigate certain difficult, nay impossible problems of perspective, which, although they were fanciful and beautiful, yet hindered him so greatly in the painting of figures, that the older he grew the worse he did them. ... For the sake of these investigations he kept himself in seclusion and almost a hermit, having little intercourse with anyone, and staying weeks and months in his house without showing himself." [Lives of the Painters, Sculptors and Architects, 1550; "Paolo Uccello, Painter of Florence"]

Which reminds us that art is something beyond geometry and applied science.