Your perecpective on perspective

My point is that there is little virtue in discussing definitions in abstract. When it comes to a definition its value should be based on does it offer utility in terms of throwing some light upon the conundrums that photographers (in this context) find themselves in.
I listed five.
Please remind me.
Here (they are actually four):
I can't see how it is useful for those situations. I'm willing to be convinced.
(i) When taking panoramas, to avoid the parallax error, you want to shoot from the same, well, perspective (point). (ii) Some people think that 50mm on crop has different perspective than 80mm on FF. (iii) One can convert a fisheye image to a rectilinear one, taken from the same point. (iv) Standing at the same point and rotating (a bit) the axis of the camera will not give you are shot that you cannot get by software distortion correction.
Yes, I commented on them at the time. I can't see those as an expression of 'utility'. Yes. making a panorama, you need to shoot all the shots from the same point. I suppose that is a consequence of perspective theory, but not specifically of any version.
Each shot comes with a different projection,
Yes
since you rotate the camera but since they are shot from the same point, you can transform each shot to achieve any projection of the stitched image you want.
Sure. And so?
(ii) is an observation about what you think many people think, not an expression of any utility,
It dispels a myth.
Sure, but it doesn't relate solely to your new theory of perspective. So you count it as a unique virtue of your definition over, say, mine, which would lead to the same conclusion (and in fact my definition leads to all of your four virtues also, so is equally virtuous)
(iii) is another observation which does not depend on your definition of perspective and as is (iv).
Every logical conclusion can be called an observation. Some people use fisheye lenses to take panoramas. It is not a priori obvious that you can get the same result as with rectilinear lenses.
But they don't result from your definition, that is the point.
More (those are actually derivatives of what I listed above but they are all connected):

(v) My subject has a big nose. Should I change the FL? - Not necessarily, you just have to change the perspective (the distance). Taking "environmental portraits" with WA lenses, for example, works.

(vi) You can correct a face in a WA shot to look as you expect it to look (remove the WA "distortion"). You can make it look as if is it taken with the lens pointing directly to that face, as long as your shot and the hypothetical one have the same perspective. You can correct "distortion" in buildings, too - you may not need that TSE lens after all except for better resolution/different AOV.

(vii) I love my truck and I want to make it bigger than the background (with a rectilinear zoom). - Get close and shoot at the wide end if necessarily but the important part is to change the perspective.
All the same, they are all useful things to know about how to manipulate perspective, but they none of them derive from your definition.
I suspect that what photographers are looking for in a discussion on perspective is a clue on how to manipulate the variables at their disposal to achieve a desire perspective effect.
Or what factors are "written in stone" and cannot be manipulated. Understanding that helps you understand in (v) and (vii), for example, that you need to change the perspective.
I'm not sure how a definition of perspective that says equal perspective means the same point of view helps people understand any of that.
 
Some people would have it that the perspective in these two images is the same.

77b833f581e941ff837b8c2b2ee308c4.jpg

2e7bdccfbc10470c8c6516fe114408b6.jpg

So, the question I would ask is "is a definition of 'the same perspective' that makes these two the same likely to be useful in the context of general photographic practice"?
For in the #1 camp I mention up thread, the two images would be "different perspectives" (using assumption the images are displayed at same size in viewer's FOV).

https://www.dpreview.com/forums/post/62787459

People in #2 would argue the images show different FOV, but the "same perspective" because you can crop the first image and get an image that looks the same (ignoring other non-perspective differences like DOF, different lens distortion. lighting etc).

Here's a quick and dirty crop:

Left: Crop of 1st image, Right: 2nd Image; looks almost identical.
Left: Crop of 1st image, Right: 2nd Image; looks almost identical.

For people in the #2 camp, the most important thing is relative sizes/proportion of subjects in the image remain the same (as it does in example above). It's an useful concept for people that like to crop their images afterwards, but be ensured their subjects still look the "same" afterwards.

It's also an important concept to understand for lens selection. A lot of people have the misconception that it's the choice of lens that changes how a subject's face looks, but when reality it's the subject distance they chose (which is only indirectly influenced by the lens).

There's another example in the article linked below (before and after using 400mm vs 24mm cropped from an image of "same perspective").

https://fstoppers.com/architecture/how-lens-compression-and-perspective-distortion-work-251737

Here's what those in the #2 camp would consider a "different perspective":

707bf987d39e421d9a5bcdf279777c39.jpg
That's a nice summary. The basic problem here is that we have two camps, talking past each other. The nub of it is whether you think perspective is scene relative of image relative. I think clickbait mantras like 'Lens Compression Doesn't Exist' are unhelpful. People use 'lens compression' as a shorthand whereby they understand if you take a photo from a distance and achieve the framing they want with a narrow AOV lens, they'll get a 'compressed' rather than 'exaggerated' perspective effect. What's actually being argued is not that it 'doesn't exist' but that it's a misnomer. I'm not even sure that's right.

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263, look deader.
 
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Some people would have it that the perspective in these two images is the same.

77b833f581e941ff837b8c2b2ee308c4.jpg

2e7bdccfbc10470c8c6516fe114408b6.jpg

So, the question I would ask is "is a definition of 'the same perspective' that makes these two the same likely to be useful in the context of general photographic practice"?
Is this a rhetorical question?
No. I'd quite like an answer for someone who says that the perspective of these two images is 'the same'. On both why they think it's 'the same' and as to why that's useful.
I don't want to assume anything...are they taken from the same exact point?
That would be something of a giveaway. If perspective is a 'thing' you should be able to work it out without additional information to allow you to decide which definition you choose to adopt. The images conform with some peoples' definition of 'the same perspective', which is why some people would say they have the same perspective.

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263, look deader.
 
Perspective is not a distortion. It is a product of how large objects appear relative to each other when viewed from a particular point. It is entirely governed by the position of the viewer relative to the objects being viewed and has nothing to do with the lens an image is viewed through. . .
You might have too limited a view of perspective. By changing both position and focal length (or perhaps more particularly, angle of view), you can alter the apparent distance between objects as well as their relative size. By just changing focal length, you can make distant items seem smaller and farther away or larger and closer. The short article linked to below touches briefly not only on linear perspective, but also on rectilinear perspective, vanishing point perspective, height perspective, overlap perspective, dwindling size perspective, volume perspective, and atmospheric perspective.

http://photoinf.com/General/NAVY/Perspective.htm
The key thing is changing angle of view, not focal length. We tend to use focal length as a synonym of angle of view, but it isn't. Angle of view can also be changed by cropping.
Which is why I included the comment in parentheses above. Admittedly, I often think of focal length as a synonym for angle of view, possibly due to my long use of slide film and getting pre-mounted slides back from the lab, or because with most digital cameras I prefer using JPEG images just as they come from the camera, with no cropping or other post-processing involved.
There's a school of thought that cropping doesn't change perspective, which would also mean that changing the focal length doesn't change perspective. (It's not a school of thought that I agree with)
 
I'm not going for cheap shots. You criticised my earlier definition for being incomplete, and you were right. When trying to work out the applicable definition, you need to be clear about all of the conditions. Maybe you can be excused for being a bit sloppier thereafter, but for clarity you need your definition to encompass the whole problem.
Here is what I said:
I could try, now. How about defining perspective (of a photo of a scene, relating both) as being the same (or eq. classes, if you want to make it more precise) when the points of the scene mapped to the same on the image are always the same? This basically means the same - well - point of perspective (the term used in panorama stitching, I believe).
It is not really so incomplete.
It is. Try reading it carefully, and see if it makes sense. For instance, what does 'the points of the scene mapped to the same on the image are always the same?'
Points along the same ray in the 3D scene are mapped to one point on the 2D image (the 1st "the same"). You do not want that relation to change (the second "the same"). In other words, you want those non-uniqueness sets to be the same (well, the common ones - not the ones one image would crop and the other would not).

I can make it more formal - call the projection F, then you want the sets F^{-1} to be the same; and even better - call them F_1 and F_2, you want the sets of their inverses to be the same on their intersection, etc., but that would make it too formal. A trick we often use in our papers is to formulate an equivalent but a simpler to state property, and then to state what we really wanted to say without being too formal because that would be just a comment never used in the proofs. In this case, "the same view point" is that simplification.
I can't work that one at all, apart from making it a threeway tautology. The problem is, that middle 'same', and also, what you mean by 'same'. I assume that you mean by the middle same the same points or features. So it would expand to 'the points on the scene mapped to the same features on the image are always at the same location on the image' That might be what you meant to say, but in that case, the two shots in my example don't have the same perspective by your definition. So, it's still not clear what it is you meant, which is why it's incomplete.
It postulates that you are shooting a scene. "A" means one scene. If you turn 360 degrees the second time, you shot a different scene.
So, it isn't 'same point of view', it's 'same point of view and direction', if that's what you meant. Though it looks as though you have in mind that the images could be allowed to have a different direction so long as there are some objects in common....
Yes, there could be overlapping (different directions) but it is not necessary to require that there is.
Or, you can extend it to non-intersecting scenes - you can move and shoot a completely different scene, then the corresponding points would form an empty set, and that empty set would be in perspective, which is OK
...or not. That is equivalent to saying that any number multiplied by zero is the same as any other number multiplied by zero.
Is that wrong?
What it means is that any two imaged covering disjoint sets of objects are 'in the same perspective'. OK, but again not what I guess people think of when they evaluate perspective. Nor do I think that it covers the situation you are thinking of.
It is a convenient assumption which would not bother anybody who is not deeply into math. Such a person would never ask himself if two different scenes are in perspective or not.
Back to your panorama. Say I'm taking a panorama of five images, A, B, C, D and F left to right. I take image A first. Then I move 10 metres to my right and take C. It has no objects in common with A, so by your definition they are in perspective.
The scene is wider that the scene for each shot. You need to apply the definition with the final scene in mind.
Now I another 10 metres to my right and take E. Again, no common features so in perspective with A and C. We now have A, C and E, all apparently in the same perspective. Now I move five metres to my left and take D. D has common features with C and F, so is not in perspective with them, but it has no common features with A, s it is in perspective with them. So now we have P(A) = P(C) = P(E) and P(A) = P(D) but P(D) != P(C) and != P(E). It doesn't work as an equality relation.
It does not have to be. Of course, all that is fixable by the simplified definition.
- empty sets are usually assumed to satisfy all you want for convenience. None of this makes it a bad definition.
Nor does it make it a good one. See the above.
Back to your experiment -
Not an experiment. Just a pair of images to pose a question.
if you shot from the same point but in different directions, this could serve as two shots for a wide angle or a 360 degrees panorama... if they have the same perspective.
By your original definition shots from the same point will always have the same perspective. Your additional thoughts don't seem to be consistent with what seems to be an interpretation of your original definition.
I used the simplified version now. Remember I said "basically", leaving room for oddities like non-intersecting scenes.
Your camera has a special mark at the nodal point, and there are some not so cheap devices allowing you to shoot in different directions from the same, well perspective. If you shot in the same direction, the zoomed image could be used in a panorama as well. Finally - they do not have to have a specific usage to have the same perspective. Two random f/5.6 images, for example, would not help each other much.
But, your definition says they would, see the case given above.
Not by its simple version or the long one but applied to the scene you really want to image.
Now what, you are going to go back to the same place tomorrow, shoot from the same spot and demonstrate that the shots would be different because the weather changed? And I have to amend my definition to include the time?
I'm not aware that weather conditions affect perspective, unless your definition says otherwise.
They may affect the scene and what was in perspective before not to be anymore.
I suspect the construction of a meaningless sentence means that you haven't worked this out clearly. I't hard to think of weather conditions apart from a hurricane or tornado which will change the geometry of the scene. I suppose the scene might all be made of chocolate and the sun melts it all and does the trick. It's a good idea when considering this kind of problem not to let yourself get sidetracked by irrelevancies.
Wind could change the geometry. This is why HDR landscapes can be problematic. Lighting changes all the time. Clouds move, etc.
 
I don't want to assume anything...are they taken from the same exact point?
That would be something of a giveaway. If perspective is a 'thing' you should be able to work it out without additional information to allow you to decide which definition you choose to adopt. The images conform with some peoples' definition of 'the same perspective', which is why some people would say they have the same perspective.
If f-stop is a "thing", you should be able to tell it without the EXIF. Same for the shutter speed.
 
Perspective is not a distortion. It is a product of how large objects appear relative to each other when viewed from a particular point. It is entirely governed by the position of the viewer relative to the objects being viewed and has nothing to do with the lens an image is viewed through.

There are forms of distortion that may also be influenced by the position of the viewer and the lens (volume deformation would be one), but the extent of these distortions is influenced by the design of the formula of the lens rather than directly by the focal length of the lens.
Exatly!
 
Sure, but it doesn't relate solely to your new theory of perspective.
It is hardly new. Somebody in the other thread cited an old classical book with exactly the same definition (same point of view).
So you count it as a unique virtue of your definition over, say, mine, which would lead to the same conclusion (and in fact my definition leads to all of your four virtues also, so is equally virtuous)
(iii) is another observation which does not depend on your definition of perspective and as is (iv).
Every logical conclusion can be called an observation. Some people use fisheye lenses to take panoramas. It is not a priori obvious that you can get the same result as with rectilinear lenses.
But they don't result from your definition, that is the point.
No conclusions result from a definition. They may result from other conclusions.
More (those are actually derivatives of what I listed above but they are all connected):

(v) My subject has a big nose. Should I change the FL? - Not necessarily, you just have to change the perspective (the distance). Taking "environmental portraits" with WA lenses, for example, works.

(vi) You can correct a face in a WA shot to look as you expect it to look (remove the WA "distortion"). You can make it look as if is it taken with the lens pointing directly to that face, as long as your shot and the hypothetical one have the same perspective. You can correct "distortion" in buildings, too - you may not need that TSE lens after all except for better resolution/different AOV.

(vii) I love my truck and I want to make it bigger than the background (with a rectilinear zoom). - Get close and shoot at the wide end if necessarily but the important part is to change the perspective.
All the same, they are all useful things to know about how to manipulate perspective, but they none of them derive from your definition.
If you have the same perspective (by "my" definition), you can do it. If not, very often, you can't. Without going into specifics, often the same perspective is a necessary and sufficient condition for those to hold; and being just sufficient (and necessary at least sometimes) is enough to make it interesting enough.
I suspect that what photographers are looking for in a discussion on perspective is a clue on how to manipulate the variables at their disposal to achieve a desire perspective effect.
Or what factors are "written in stone" and cannot be manipulated. Understanding that helps you understand in (v) and (vii), for example, that you need to change the perspective.
I'm not sure how a definition of perspective that says equal perspective means the same point of view helps people understand any of that.
Well, they do not need to understand why, they just need to remember that it is true.
 
Some people would have it that the perspective in these two images is the same.

77b833f581e941ff837b8c2b2ee308c4.jpg

2e7bdccfbc10470c8c6516fe114408b6.jpg

So, the question I would ask is "is a definition of 'the same perspective' that makes these two the same likely to be useful in the context of general photographic practice"?
Is this a rhetorical question?
No. I'd quite like an answer for someone who says that the perspective of these two images is 'the same'. On both why they think it's 'the same' and as to why that's useful.
I don't want to assume anything...are they taken from the same exact point?
That would be something of a giveaway. If perspective is a 'thing' you should be able to work it out without additional information to allow you to decide which definition you choose to adopt.
I possibly could if I didn't have these lower resolution jpegs. Trying to work it out is difficult when I can't achieve the same framing without going to so much magnification on the wide shot that it essentially ruins the image.
The images conform with some peoples' definition of 'the same perspective', which is why some people would say they have the same perspective.
Those two shots are pretty extreme but could be used to illustrate a point.

The case I have usually encountered is a situation where a guy has an 85mm lens and a 28mm lens (for instance) and thinks that by choosing the 85mm lens, he will automatically get more "compression" in a certain scene. I would tell him that the compression isn't going to be "better" with the 85mm lens and that he will have to change his position to get that compression.

Or another case - when you see a scene from a certain place and it moves you, shoot it from that place. It's often the perspective from that position that contributes to the interest of the scene and it's a good idea to maintain that position.

I've often seen something I liked from a road while driving and gone back and moved in closer only to realize that it was the perspective from my original vantage point that got my interest.

Is that what you're interested to know?
 
I'll just offer a very simple practical experiment that anyone can do. Look through a pair of binoculars at a distant scene with familiar objects in it (e.g. roads, cars, buildings, etc.). Does the scene look not look compressed? Does everything not look much closer to you? Try it!
Optical illusion, or misinterpretation, or both.

Take a picture of a scene containing adequate depth with a 600MM lens.

Without moving, take a picture of the same scene with a 40mm lens.

Yes, the objects in the picture taken with the telephoto do look closer than the same object sin the picture taken with the normal lens.

Do they look "compressed"? Not really.

Enlarge the portion of the picture from the normal lens to show the same objects with the same field of view as in the other picture.

Same picture, same perspective, right?
 
Some people would have it that the perspective in these two images is the same.

77b833f581e941ff837b8c2b2ee308c4.jpg

2e7bdccfbc10470c8c6516fe114408b6.jpg

So, the question I would ask is "is a definition of 'the same perspective' that makes these two the same likely to be useful in the context of general photographic practice"?
Is this a rhetorical question?
No. I'd quite like an answer for someone who says that the perspective of these two images is 'the same'. On both why they think it's 'the same' and as to why that's useful.
I don't want to assume anything...are they taken from the same exact point?
That would be something of a giveaway. If perspective is a 'thing' you should be able to work it out without additional information to allow you to decide which definition you choose to adopt.
I possibly could if I didn't have these lower resolution jpegs. Trying to work it out is difficult when I can't achieve the same framing without going to so much magnification on the wide shot that it essentially ruins the image.
I get the impression that you're trying to work back to a definition, rather than take a view just from what you see. If it requires detailed examination of a high resolution image to determine whether or not two images have the same perspective, then having the same perspective is not worth the average photographer getting too worried about, is it?
The images conform with some peoples' definition of 'the same perspective', which is why some people would say they have the same perspective.
Those two shots are pretty extreme but could be used to illustrate a point.
They were purposely extreme and are being used to illustrate the point.
The case I have usually encountered is a situation where a guy has an 85mm lens and a 28mm lens (for instance) and thinks that by choosing the 85mm lens, he will automatically get more "compression" in a certain scene. I would tell him that the compression isn't going to be "better" with the 85mm lens and that he will have to change his position to get that compression.
You probably don't have to tell him, because if he had a nicely framed image, fits the 85mm lens and looks through the viewfinder, he's going to find that the image isn't so nicely framed any more, so he's likely to move whether you tell him or not.
Or another case - when you see a scene from a certain place and it moves you, shoot it from that place. It's often the perspective from that position that contributes to the interest of the scene and it's a good idea to maintain that position.
You still have a choice of the framing, and strangely enough, the framing affects the perceived perspective, or at least it does the way I see it.
I've often seen something I liked from a road while driving and gone back and moved in closer only to realize that it was the perspective from my original vantage point that got my interest.

Is that what you're interested to know?
It concurs with my own take on the matter. What I was trying to find out is what the working definitions of 'perspective' that people seem to have adopted actually are.

And yes, the two images were taken from the same point, with the frame centred on the same tree. So it seems to me that perceived perspective in an image is not just to do with where you are and where you pint the camera, but also the framing (or if you like, angle of view).. I think you'd have a hard time convincing anyone other than a photographer who'd read a few 'perspective isn't what you think it is' tutorials that these tow shots had the same perspective.

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263, look deader.
 
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Perspective is not a distortion. It is a product of how large objects appear relative to each other when viewed from a particular point. It is entirely governed by the position of the viewer relative to the objects being viewed and has nothing to do with the lens an image is viewed through. . .
You might have too limited a view of perspective.
Not from my perspective:-D
By changing both position and focal length (or perhaps more particularly, angle of view), you can alter the apparent distance between objects as well as their relative size.
Of these, it is only changing position that alters perspective. If I take a photo of the end of my garden with a telephoto and with a fisheye and enlarge the centre of the fisheye shot so that it matches the Field of view of the telephoto they will share exactly the same perspective (providing I didn't move between shots).



13311e20dcfd4cdcb21ab284cef6ba65.jpg



dd3dcecc28144798a732c3d7eccd3bfe.jpg

(One of the above is from a 100mm lens, while the other is a crop from a 16mm fisheye - exif is intact for those who want to confirm which is which)
By just changing focal length, you can make distant items seem smaller and farther away or larger and closer.
It isn't changing the focal length that makes objects seen smaller or larger in relation to each other. Your linked article says "The use of different focal-length lenses in combination with different lens-to-subject distances helps you alter linear perspective in your pictures. " - which is slightly misleading - it is the different lens-to-subject distances that give a different perspective, the focal length merely enables you to highlight those differences in your pictures.
The short article linked to below touches briefly not only on linear perspective, but also on rectilinear perspective,
and it is at rectilinear perspective that the author of the piece starts to go off beam - rectilinear perspective is not what your eye sees, which is far closer to the view of a fisheye lens - your brain effectively de-fishes that image to create a rectilinear view that keeps lines straight - like your brain knows they must be. For example:

Imagine you are standing facing a twelve-foot brick wall which is about six feet in front of you. The wall extends at the same height and level for 100 yards either side of you. As you look directly ahead at the wall your peripheral vision sees a vanishing point for the wall on either side of you, about half way up your field of view - however the top of the wall (which is level with your eyeline on either side) is above your head at the mid-point of your view... so if the wall is straight and it there is no change of direction, the top of the wall must be tracing a curve in your vision - not the straight line that you get in a rectilinear view... (and that your brain constructs from the info it gets from your eyes).
vanishing point perspective, height perspective, overlap perspective, dwindling size perspective, volume perspective, and atmospheric perspective.

http://photoinf.com/General/NAVY/Perspective.htm
It is a reasonably good article, but the author tries to take it too far - perspective is only linked to where you are viewing from - that a digital zoom gives the same perspective as an optical zoom confirms this.

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https://bobjanes.smugmug.com/PoTB/
 
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I'll just offer a very simple practical experiment that anyone can do. Look through a pair of binoculars at a distant scene with familiar objects in it (e.g. roads, cars, buildings, etc.). Does the scene look not look compressed? Does everything not look much closer to you? Try it!
Optical illusion, or misinterpretation, or both.
Perspective is entirely an 'optical illusion' in the first place.
Take a picture of a scene containing adequate depth with a 600MM lens.

Without moving, take a picture of the same scene with a 40mm lens.
Did that further up the thread, but 14 and 500 mm.
Yes, the objects in the picture taken with the telephoto do look closer than the same object sin the picture taken with the normal lens.

Do they look "compressed"? Not really.
I think the 'perspective' looks 'compressed'.
Enlarge the portion of the picture from the normal lens to show the same objects with the same field of view as in the other picture.

Same picture, same perspective, right?
Sure, but those two are not the same picture as the 40mm shot. The perspective in the 40mm shot looks very different to that in the 600 mm or 600 mm(equiv) shot.
 
You are omitting the forms of distortion created by the way the image is viewed, rather than the way the image was captured.
Those forms of distortion are related to other factors than perspective.
They have been called perspective for a very long time. What would you call them?
If I stand in one position the perspective of what I see is the same regardless of what lens I view it through, or if I don't view it through a lens at all (ie with a pinhole) or with the mark 1 eyeball (binocular vision apart).
That is correct. The perspective seen by the camera depends on the camera position, not on the type of lens used or the type of camera used.

However, if you take a picture, the perspective you see in that picture also depends on how you view the picture.
 
I'll just offer a very simple practical experiment that anyone can do. Look through a pair of binoculars at a distant scene with familiar objects in it (e.g. roads, cars, buildings, etc.). Does the scene look not look compressed? Does everything not look much closer to you? Try it!
Optical illusion, or misinterpretation, or both.

Take a picture of a scene containing adequate depth with a 600MM lens.

Without moving, take a picture of the same scene with a 40mm lens.

Yes, the objects in the picture taken with the telephoto do look closer than the same object sin the picture taken with the normal lens.

Do they look "compressed"? Not really.

Enlarge the portion of the picture from the normal lens to show the same objects with the same field of view as in the other picture.

Same picture, same perspective, right?
Wrong! You are viewing the picture in a different way and that changes the apparent perspective.

The perspective seen by the camera is exactly the same for a wide-angle shot and a telephoto shot from the same position. But when you view the two shots in the normal way, the perspective looks quite different. Any experienced photographer can distinguish between the wide-angle and the telephoto shot (provided they contain sufficient 3-D objects in the view and not just an expanse of blue sky or something very unfamiliar).
 
You are omitting the forms of distortion created by the way the image is viewed, rather than the way the image was captured.
Those forms of distortion are related to other factors than perspective.
They have been called perspective for a very long time.
The graphite and clay material in pencils is generally known as pencil lead... however it has nothing to do with the metallic element Lead (Pb).
What would you call them?
Volume distortion. rectilinear distortion...
If I stand in one position the perspective of what I see is the same regardless of what lens I view it through, or if I don't view it through a lens at all (ie with a pinhole) or with the mark 1 eyeball (binocular vision apart).
That is correct. The perspective seen by the camera depends on the camera position, not on the type of lens used or the type of camera used.

However, if you take a picture, the perspective you see in that picture also depends on how you view the picture.
 
Some people would have it that the perspective in these two images is the same.

77b833f581e941ff837b8c2b2ee308c4.jpg

2e7bdccfbc10470c8c6516fe114408b6.jpg

So, the question I would ask is "is a definition of 'the same perspective' that makes these two the same likely to be useful in the context of general photographic practice"?
Is this a rhetorical question?
No. I'd quite like an answer for someone who says that the perspective of these two images is 'the same'. On both why they think it's 'the same' and as to why that's useful.
I don't want to assume anything...are they taken from the same exact point?
That would be something of a giveaway. If perspective is a 'thing' you should be able to work it out without additional information to allow you to decide which definition you choose to adopt.
I possibly could if I didn't have these lower resolution jpegs. Trying to work it out is difficult when I can't achieve the same framing without going to so much magnification on the wide shot that it essentially ruins the image.
I get the impression that you're trying to work back to a definition
Not sure why you get that impression.
, rather than take a view just from what you see. If it requires detailed examination of a high resolution image to determine whether or not two images have the same perspective, then having the same perspective is not worth the average photographer getting too worried about, is it?
It could be - this would be a good example to illustrate the point if one could do the proper crop and still see something.
The images conform with some peoples' definition of 'the same perspective', which is why some people would say they have the same perspective.
Those two shots are pretty extreme but could be used to illustrate a point.
They were purposely extreme and are being used to illustrate the point.
Can't illustrate the point if the crop of the wide shot looks like three globs. Given the resolution you used, I suspect it could be done with the original images.
The case I have usually encountered is a situation where a guy has an 85mm lens and a 28mm lens (for instance) and thinks that by choosing the 85mm lens, he will automatically get more "compression" in a certain scene. I would tell him that the compression isn't going to be "better" with the 85mm lens and that he will have to change his position to get that compression.
You probably don't have to tell him, because if he had a nicely framed image, fits the 85mm lens and looks through the viewfinder, he's going to find that the image isn't so nicely framed any more, so he's likely to move whether you tell him or not.
Maybe, maybe not.
Or another case - when you see a scene from a certain place and it moves you, shoot it from that place. It's often the perspective from that position that contributes to the interest of the scene and it's a good idea to maintain that position.
You still have a choice of the framing, and strangely enough, the framing affects the perceived perspective, or at least it does the way I see it.
It does if you change position to get that framing. It doesn't if you crop to get it.
I've often seen something I liked from a road while driving and gone back and moved in closer only to realize that it was the perspective from my original vantage point that got my interest.

Is that what you're interested to know?
It concurs with my own take on the matter. What I was trying to find out is what the working definitions of 'perspective' that people seem to have adopted actually are.
And what do you think it is here?
And yes, the two images were taken from the same point, with the frame centred on the same tree.
I suspected so, but again, I can't enlarge the wide shot without turning everything into mush. So not as helpful at this resolution as otherwise would be.
So it seems to me that perceived perspective in an image is not just to do with where you are and where you pint the camera, but also the framing (or if you like, angle of view)..
So you're in the backcountry and you want to capture an old mining cabin that you saw last year from up on the continental divide, because the closer / wider shot didn't have the perspective and look you wanted. When you saw it from the continental divide with your bare eyes, it had a more compressed look that made it stand out better against the landscape. But when you first captured it, all you had was your 20mm and a 35mm. When you cropped the 35mm shot, it looked the way you wanted it to, but lost too much resolution to make a nice print.

This time, you have opted not to lug a 200mm telephoto for 6 nights / 55 miles. You opt instead for the 85mm, knowing that you can crop it and achieve the compressed look you're after and with enough resolution to make a nice print. That's one way I find it useful. If I could drive closer to the spot, it wouldn't be so bad to lug a number of lenses up there to get the best framing of the shot. But it's a two day hike from any direction and things get heavy and the air is thin at 13,000 feet.
I think you'd have a hard time convincing anyone other than a photographer who'd read a few 'perspective isn't what you think it is' tutorials that these tow shots had the same perspective.
It could be a very good example if you can get enough resolution to do a decent framing of the wide shot to compare. Not complaining, just assuming there are limitations for posting size and that limits that comparison.
 
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Only here could something so elemental be discussed so extensively!

I wonder if in math forums they have arguments over whether 1+1 really equals 2?
There are many papers and books on foundational theories of math that go back over 100 years that lay out the proof of the mathematical equation 1+1=2.

https://en.wikipedia.org/wiki/Principia_Mathematica



The book lays out the foundation for the logical constructs to prove 1+1=2

The book lays out the foundation for the logical constructs to prove 1+1=2
 
I'll just offer a very simple practical experiment that anyone can do. Look through a pair of binoculars at a distant scene with familiar objects in it (e.g. roads, cars, buildings, etc.). Does the scene look not look compressed? Does everything not look much closer to you? Try it!
Optical illusion, or misinterpretation, or both.

Take a picture of a scene containing adequate depth with a 600MM lens.

Without moving, take a picture of the same scene with a 40mm lens.

Yes, the objects in the picture taken with the telephoto do look closer than the same object sin the picture taken with the normal lens.

Do they look "compressed"? Not really.

Enlarge the portion of the picture from the normal lens to show the same objects with the same field of view as in the other picture.

Same picture, same perspective, right?
Wrong! You are viewing the picture in a different way and that changes the apparent perspective.

The perspective seen by the camera is exactly the same for a wide-angle shot and a telephoto shot from the same position. But when you view the two shots in the normal way, the perspective looks quite different. Any experienced photographer can distinguish between the wide-angle and the telephoto shot (provided they contain sufficient 3-D objects in the view and not just an expanse of blue sky or something very unfamiliar).
If you're implying what I think you're implying, that wide angle lenses can deform objects near their edges (for instance), I don't think it would be very apparent for every pairing of wide angle/telephoto lenses.
 
If you're implying what I think you're implying, that wide angle lenses can deform objects near their edges (for instance), I don't think it would be very apparent for every pairing of wide angle/telephoto lenses.
If you stood at the side of a busy street in a typical business district and took (i) a wide-angle shot looking down the street, and (ii) a telephoto shot at same spot and looked at those shots side by side, I think you could easily see the difference in perspective. The camera sees no difference in perspective, but the viewer of the image does. Some of that difference in perspective manifests itself as familiar objects appearing to be different in shape from what you expect them to be.

Call it distortion or call it something else, it is what you see. And it is caused by the viewer's perspective (not the camera's perspective, which was exactly the same in the two shots).

The camera's perspective depends on the position of the camera in relation to the various elements of the scene.

The viewer's perspective depends on the position of the viewer in relation to the image being viewed, primarily the distance between the viewer and the image (relative to the size of the image).

Those two types of perspective are exactly analogous to each other except that the latter is simpler because the image is only two dimensional (at least, for most photography).
 

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