Perspective Revisited

[Ray]

The rules of projective geometry are not a theory, they are based on axioms.
If you don't agree, well, how about ignoring the 'theory of gravity'. I wish you a speedy recovery

Cheers,
Bart

C'mon Bart,
You haven't thought that through, have you!  One doesn't need to know anything about the theory of gravity in order to negotiate the problems of gravity on a personal level. There were circus performers long before Isaac Newton came on the scene with his theory of gravity, who were able to perform amazing balancing acts without any theoretical knowledge of gravity whatsoever.

More likely, I would probably need a speedy recovery if I were to spend too much time contemplating the mystery of the gravitational force as I walked down the street. I might fall into a pot-hole through not paying attention to what I was doing. 

As regards axioms, it's axiomatic to me that all theories are a construct of the human brain and imagination.They represent models of reality which are usually found to be, eventually, either a bit wrong or completely wrong.

Astrophysicists are currently having a hard time explaining why 95% of the matter and energy in the universe is invisible and undetectable. The euphemistic term is Dark Matter.

There's a consensus of opinion amongst Astronomers and Astrophysicists that Dark Matter and Dark Energy really does exist, despite the fact that not one particle has been discovered so far. On the other hand, there's a growing number of impatient scientists who think our theories of gravity may be wrong, and who have attempted to modify Newton's theories. The acronym for the alternative theory to Dark Matter is MOND (Modification Of Newtonian Dynamics).

Cheers!

[John Camp]

Ray, you're essentially arguing nonsense, and I think you know it.

Of course the perception of perspective may differ from person to person, but the fact that my vision is 20-40 and you wear glasses to correct an astigmatism and the third guy is blind has nothing to do with the way a camera operates. All three of us could push the button on a camera, one after the the other, and we'd get the same photo. I doesn't depend on how we feel or what we think. The fact that there is fog in the valley doesn't change the lens. Perspective is determined by position, period. Perspective is not a philosophical concept, or an artificial construct, or negotiated in any way, it just is. (Unless, of course, you're a Republican, in which case we may need a new thread.)

What you're arguing is basically semantics. You're saying that because somebody somewhere may have misused the word "perspective," and their culture is as good as ours, then it's okay to say that perspective changes. No.

[Isaac]

(5) Those who claim adamantly that perspective can only be changed by a change in distance to subject should make clear that they are referring to a mathematically and geometrically abstract defintion which does not necessarily encompass the human experience which is plain and simply, and unavoidably, biased in accordance with its own sense of brain-wired perspective.

Why should they? Why isn't the burden on you to make clear what you are referring to when you talk of perspective? Why is it that you own the definition of that word?

[Isaac]

One doesn't need to know anything about the theory of gravity in order to negotiate the problems of gravity on a personal level.

One doesn't need to know because someone else does know, and has used their knowledge to magically provide us with technology we don't understand (communications satellites).

Astrophysicists are currently having a hard time explaining why 95% of the matter and energy in the universe is invisible and undetectable.

And that has relevance to theories about the nature of the physical universe but nothing to do with axioms.

[Eric Myrvaagnes]

Why should they? Why isn't the burden on you to make clear what you are referring to when you talk of perspective? Why is it that you own the definition of that word?

Because Ray is an ardent follower of that eminent philosopher Humpty Dumpty: “When I use a word,’ Humpty Dumpty said in rather a scornful tone, ‘it means just what I choose it to mean — neither more nor less.’" (Lewis Carroll)

Eric 

[mouse]

Because Ray is an ardent follower of that eminent philosopher Humpty Dumpty: “When I use a word,’ Humpty Dumpty said in rather a scornful tone, ‘it means just what I choose it to mean — neither more nor less.’" (Lewis Carroll)

Eric 

In response to Ray, in another thread, I wrote:

I think I finally understand Ray's problem.

While the majority of photographers, painters, and others involved in creating or interpreting 2D images have adopted the standard, mathematically defined concept of (linear) perspective, Ray has created his own personal definition of perspective..  He has every right to do so, but it is neither legitimate nor rational for him to argue that the consensus definition is wrong while his is correct.  While Ray may continue to submit any amount of evidence in support of his personal definition, nothing he has written calls into question the legitimacy of standard definition nor suggests that his definition is more useful or appropriate.

But Humpty Dumpty said it better.

[Ray]

Ray, you're essentially arguing nonsense, and I think you know it.

Of course the perception of perspective may differ from person to person, but the fact that my vision is 20-40 and you wear glasses to correct an astigmatism and the third guy is blind has nothing to do with the way a camera operates. All three of us could push the button on a camera, one after the the other, and we'd get the same photo. I doesn't depend on how we feel or what we think. The fact that there is fog in the valley doesn't change the lens. Perspective is determined by position, period. Perspective is not a philosophical concept, or an artificial construct, or negotiated in any way, it just is. (Unless, of course, you're a Republican, in which case we may need a new thread.)

What you're arguing is basically semantics. You're saying that because somebody somewhere may have misused the word "perspective," and their culture is as good as ours, then it's okay to say that perspective changes. No.

Not at all! You seem to have missed my point entirely, John. What I'm arguing makes total sense. I'm simply stating that using a different focal length of lens from the same position changes what's included or excluded in the scene and that exclusion or inclusion changes the sense of distance from the viewer to the various objects in the scene.

How anyone  could deny that fact beats me. Of course it's also true that, irrespective of lens used, if one crops or successfully stitches images so that the scenes do not differ with respect to what's included or excluded, in other words one arranges for the images to have the same angle of view, then perspective will broadly be the same, apart from the more subtle influences of greater resolution and clarity, or differences in Dof that one of the images may have.

Now the usual proof offered to support the theory that lens focal length has no bearing on perspective, is the above example of cropping a wide angle shot so that it has the same FoV as a longer focal length. This where the nonsense lies.

The fact that perspective is the same when one makes the angle of view the same, demostrates the principle of equivalent or effective focal length, which is why one of those threads that Bart linked to began with a confusion about lens FL equivalents on different camera formats and subsequently drifted into the issue of perspective because the equality of perspective evident at equal FoV and distance to subject, is the proof of the concept of equivalent or effective focal length, not proof that any focal length used, which is not effectively the same, provides equal perspective.

In other  words, a 30mm lens on an APS-C format really is equivalent to a 50mm lens on full-frame 35mm format, which really is equivalent to an 80mm lens on MF format, which really is equivalent to a 360mm lens on 8'x10' format (approximately, taking into account differences in resolution and DoF)).

How do we know that these different focal lengths of lens are all effectively the same, when used from the same position and direction with the appropriate format of camera? Because the perspective is the same.

How do we know perspective is the same using the same 'effective' focal length of lens?

Because our eyes tell us it's the same, when we compare the photos.

How do we know that changing the 'effective' FL of lens, at the same position, changes our sense of perspective?  Because our eyes tell us it has changed. Wide-angle shots make close objects appear closer, and distant object more distant. Didn't you know that?

Goodness gracious me!  

[mouse]

Wide-angle shots make close objects appear closer, and distant object more distant. Didn't you know that?

Goodness gracious me!  

Ray, Since you are so interested in what our eyes have to tell us,  I have an experiment for you to perform.  Secure the cardboard tube from the center of a roll of paper towels.  Go outside and find a distant object and a close object.  Hold the cardboard tube up to your eye and look at those two objects.  Now remove the tube (thus converting your narrow angle vision thru the tube to a wide angle vision).  Did the close object suddenly appear closer; or the distant object more distant?  If they did, you need to visit your ophthalmologist.

[Ray]

Ray, Since you are so interested in what our eyes have to tell us,  I have an experiment for you to perform.  Secure the cardboard tube from the center of a roll of paper towels.  Go outside and find a distant object and a close object.  Hold the cardboard tube up to your eye and look at those two objects.  Now remove the tube (thus converting your narrow angle vision thru the tube to a wide angle vision).  Did the close object suddenly appear closer; or the distant object more distant?  If they did, you need to visit your ophthalmologist.

Exactly true! Good analogy! The perspective was the same because the focal length was the same, that is, the focal length of my eyes did not change simply because I was peering through a cardboard tube.

Camera lenses are not cardboard tubes. They are lenses, as our eyes are lenses, but different in some ways of course. If instead of using a cardboard tube, I'd used my D700 with a standard 50mm lens, I'd have got a similar effect, but not with a different focal length on my D700.

Let me try to explain what I think may be happening in this issue by providing additional clarification on this aspect of inclusion and exclusion.

One of the problems that scientific enquiry faces, which presents a problem in the formulation of theories and the confirmation or falsification of theories, is selection bias. One can collect a huge quantity of data on a particular subject, but the data one chooses to include or exclude will either confirm or refute the results one may hope to achieve, or the theory one is trying to either refute or substantiate

However, there's an additional problem because bias by its very nature is something we are not fully aware of. To be aware of one's biases is to be unbiased.
To  behave in a biased manner in science, despite being aware one is biased on a specific issue, is tantamount to scientific fraud. Through a process of careful exclusion of specific data which doesn't support one's hypothesis, and the inclusion only of the data which does support one's hypothesis, one can prove or disprove almost anything.

So let's apply the above principle to this issue of the sense of perspective that a viewer experiences, when viewing an image of a scene through different focal lengths of lenses, from the same position.

If one wishes to test this in a scientific manner, one should take a number of shots from the same position actually using different focal lengths of lenses, then compare the images.

When I do this it is clear to me that a wide angle shot produces a different sense of perspective to a telephoto shot. However, since I have a fair understanding of this principle of 'selection bias', I know that I can turn these results on their head by excluding data from the wide-angle shot that gives the impression that the perspective is different. I do this by cropping out the offending data.

If I have two sets of data which are different, one set being larger than the other, and I exclude from the larger set all the data that is different to the smaller set, then I'm obviously left with two identical sets of data.

Such is the proof that focal length has no bearing on perspective.

Really! Pull the other leg. 

[opgr]

It once occurred to me that the human eye is more akin to a fish-eye perspective than it is to a rectilinear perspective, even though we very much need the latter to interpret 2D images...

[Ray]

It once occurred to me that the human eye is more akin to a fish-eye perspective than it is to a rectilinear perspective, even though we very much need the latter to interpret 2D images...

My widest-angle lens is the rectilinear Nikkor 14mm (as in 14-24 zoom). When I raise that to my eyes, then compare the scene without camera, doing my best to stare at the same object in the centre of the scene, I find that there are peripheral, but broadly recognisable, objects in my vision which are outside the FoV shown in the 14mm lens, implying that my angle of vision is indeed wider than 14mm (full-frame 35mm equivalent).

The problem is in the definition of peripheral vision, which I suspect is the reason why there are so many variants on the true angle-of-view of human vision.

It seems very clear that the angle of focussed view in human vision is very narrow indeed. As the angle away from that very narrow focussed view increases, the objects lose more and more detail to the point where only sudden movement in the scene is detectable.

One of the problems in lens design of the wide angle, appears to be correcting for 'volume anamorphosis', as mentioned by Bart. This can make objects near the edges of the frame appear odd, distorted and larger in some way than the eye/brain perceives they should be.

However this is a separate issue from the general effect that wide-angle lenses make objects more distant, and telephoto lenses make objects appear closer.

[Guillermo Luijk]

How do we know that changing the 'effective' FL of lens, at the same position, changes our sense of perspective?  Because our eyes tell us it has changed. Wide-angle shots make close objects appear closer, and distant object more distant. Didn't you know that?

Sorry Ray, but I am not able to understand the point of this entire thread. There are some facts that we'll all agree:

• If you have the same FOV, subject distance and orientation (no matter how you achieve it: by cropping a wide FL shot, by linearly stitching some narrower FL shots,...), you will have the same perspective and visual perception. Both images will be virtually the same.
• If you don't crop but the two shots were done from the same distance and orientation with different FL, you get the same geometrical perspective but you get more content (more things into your frame) the lower the focal length is, and hence you get a different visual perception.
• With linear geometrical manipulations (for example the so called 'perspective correction' in Photoshop), we can only change the orientation (direction of observation) of a given shot, never its perspective in terms of what is seen and what is hidden.

So, where is the discussion?   all this just seems a semantic discussion to me.

This is my kitchen shot from a tripod without changing the direction of observation. Of course the visual perception of the 10mm frame is different to that of the 17mm and 20mm shots, but nobody denies this, one picture shows more things than the other!. And of course the cropped content (geometrical perspective) is the same in all three shots. So?

Regards

[opgr]

However this is a separate issue from the general effect that wide-angle lenses make objects more distant, and telephoto lenses make objects appear closer.

Okay, got that. Sorry for reiterating.

[Ray]

.... we can only change the orientation (direction of observation) of a given shot, never its perspective in terms of what is seen and what is hidden.[/li]
[/list]

So, where is the discussion?   all this just seems a semantic discussion to me.

The perspective of what precisely is hidden?? This is the core of the nonsense. You are stating that the perspective of that which isn't there, which doesn't exist, which isn't in the photo, has not changed.

This is my kitchen shot from a tripod without changing the direction of observation. Of course the visual perception of the 10mm frame is different to that of the 17mm and 20mm shots, but nobody denies this, one picture shows more things than the other!. And of course the cropped content (geometrical perspective) is the same in all three shots. So?

So, if you make the stuff in your 10mm shot hidden (by cropping), your microwave looks closer to the viewer, whoever that viewer may be.

This is not semantics. It's an actual and real effect of human vision.

Now, if you wish to make the point that perspective has nothing to do with the observer and his sense of distance to objects, then we are getting into even greater nonsense. 

[Guillermo Luijk]

The perspective of what precisely is hidden?? This is the core of the nonsense. You are stating that the perspective of that which isn't there, which doesn't exist, which isn't in the photo, has not changed.

No Ray, not the perspective of what is hidden, the perspective of what is seen, which is the only perspective that can be judged on both images. All this seems so obvious to me that I wonder if you are just making a joke.

So, if you make the stuff in your 10mm shot hidden (by cropping), your microwave looks closer to the viewer, whoever that viewer may be.

Yes, you get an image where the microwave looks closer; in fact you get the same image as you got with the 22mm. Again: are you asking all these things seriously?  

I think you are not differentiating geometrical perspective (the result of a linear projection onto a plane, no matter how much is cropped) from the observer's image perception. Both concepts run in parallel, and are 100% compatible and explainable.

[Ray]

No Ray, not the perspective of what is hidden, the perspective of what is seen, which is the only perspective that can be judged on both images. All this seems so obvious to me that I wonder if you are just making a joke.


Yes, you get an image where the microwave looks closer; in fact you get the same image as you got with the 22mm. Again: are you asking all these things seriously?  

If what is seen in both images is different, how can the perspective be the same. It is you who is making a joke, right?  

Guillermo, you only get part of the same image, if you crop. Also, if you crop a 10mm shot to the FoV of a 22mm shot, you've effectively changed focal length of lens. That change in focal length has made your microwave look closer. I'm glad you agree.  

[Guillermo Luijk]

If what is seen in both images is different, how can the perspective be the same. It is you who is making a joke, right?  

As I said and you said no, this is all about semantics. The geometrical perspective is the same, because the linear projection is the same and takes place under the same conditions (distance, direction of observation...). The visual perception is not the same since both images are different.

The longer you insist in mixing both conceps (the geometrical perspective which solely depends on subject distance, vs the visual perception which depends both on subject distance and FOV), the longer it will take you to realize we are talking about the same thing and we all agree.

I'm glad you agree.  

That's why I don't understand why you opened this thread, if we all agree, you must be kidding or something.

[Eric Myrvaagnes]

In Ray's earlier posts on this general topic he kept referring to "perspective" in a way that got many of us riled up. At some point he started using (occasionally, but I don't think consistently) the phrase "perception of perspective." It seems to me that he has been arguing for his own idea of "perception of perspective" all along and not talking about the generally understood mathematical notion of "perspective."

I will readily admit that certain very wide angle images can confuse the brain's interpretation of distances and sizes, but so can all the other optical illusions that Bernard posted a link to.

But none of that changes the generally understood meaning of "perspective," unless you take Humpty Dumpty's view of words.

Eric

[Isaac]

The longer you insist in mixing both conceps (the geometrical perspective which solely depends on subject distance, vs the visual perception which depends both on subject distance and FOV), the longer it will take you to realize we are talking about the same thing and we all agree.

Ray has been refusing to acknowledge that distinction and that agreement for days -

Now, what you pointed, the subjective factors that actually fool the eyes (atmosphere is one) and alter our perception of the perspective is correct. So both, what you are pointing, and the geometry  are correct and not in contradiction at all.

Ray is a great quarreller - he wishes to quarrel, he does not wish to understand - I dare say he would quarrel with Brunelleschi.

[Wayne Fox]

Exactly true! Good analogy! The perspective was the same because the focal length was the same, that is, the focal length of my eyes did not change simply because I was peering through a cardboard tube.

Camera lenses are not cardboard tubes. They are lenses, as our eyes are lenses, but different in some ways of course. If instead of using a cardboard tube, I'd used my D700 with a standard 50mm lens, I'd have got a similar effect, but not with a different focal length on my D700.

Let me try to explain what I think may be happening in this issue by providing additional clarification on this aspect of inclusion and exclusion.

One of the problems that scientific enquiry faces, which presents a problem in the formulation of theories and the confirmation or falsification of theories, is selection bias. One can collect a huge quantity of data on a particular subject, but the data one chooses to include or exclude will either confirm or refute the results one may hope to achieve, or the theory one is trying to either refute or substantiate

However, there's an additional problem because bias by its very nature is something we are not fully aware of. To be aware of one's biases is to be unbiased.
To  behave in a biased manner in science, despite being aware one is biased on a specific issue, is tantamount to scientific fraud. Through a process of careful exclusion of specific data which doesn't support one's hypothesis, and the inclusion only of the data which does support one's hypothesis, one can prove or disprove almost anything.

So let's apply the above principle to this issue of the sense of perspective that a viewer experiences, when viewing an image of a scene through different focal lengths of lenses, from the same position.

If one wishes to test this in a scientific manner, one should take a number of shots from the same position actually using different focal lengths of lenses, then compare the images.

When I do this it is clear to me that a wide angle shot produces a different sense of perspective to a telephoto shot. However, since I have a fair understanding of this principle of 'selection bias', I know that I can turn these results on their head by excluding data from the wide-angle shot that gives the impression that the perspective is different. I do this by cropping out the offending data.

If I have two sets of data which are different, one set being larger than the other, and I exclude from the larger set all the data that is different to the smaller set, then I'm obviously left with two identical sets of data.

Such is the proof that focal length has no bearing on perspective.

Really! Pull the other leg. 

Ray,

with apologies and please don't take any offense, but on this subject you really should leave it alone.  You just can't get past the idea that distortion is not perspective.  The point is when you remove the tube, you see more, but the perspective of the objects you saw with only the tube doesn't change.  The only way to change that is move your position in relation to those objects.  Make a framing guide from a piece of matt board and find a set of telephone poles receding in the distance.  Frame an image with the rectangle and note the perspective of the poles to each other.  When you remove the guide, that doesn't change.  You see more, and that's all focal length on a lens does.  Any other effect(distortion) is unintentional ( and now almost all of us correct it with software).

This insistence on this concept (you do realize that may be the ONLY one that believes this) reflects poorly on your credibility.