What's more "normal"...

FHPhotographer · 10-22-2009, 11:00 AM

Charlie, I think I followed that, on the other, hand I might not have. But I'm working on the core idea you suggested "Whichever length lens is used to capture a photo, the sizes (and therefore apparent distances) of objects in the picture relative to each other will remain the same. However, their apparent sizes (and therefore distances) relative to the viewpoint will change" and it might come clear, eventually. Thanks,
Brian

Last edited by FHPhotographer; 10-22-2009 at 11:01 AM. Reason: typo

FHPhotographer · 10-22-2009, 11:04 AM

After reading the posts, I think it's time for a suitably ambiguous quote from Garry Winogrand, "Photography is not about the thing photographed. It is about how that thing looks photographed."
Brian

CFWhitman · 10-22-2009, 11:21 AM

Originally posted by audiobomber

Dammit Charlie, you're making me dizzy.

Sorry.

This subject has one hurdle for people to get over. They seem to have trouble resolving these two facts with each other.

1. Changing focal length does not change the relationship of the the sizes of objects in the photo compared to each other.

2. Changing focal lengths does change perspective distortion.

If you can resolve these two facts with each other, and understand that number one not only does not contradict number two, but is actually the cause of it, then you've got it made.

FHPhotographer · 10-22-2009, 11:34 AM

Dave, interesting stuff and you hit it spot on with "To me, like you I suspect, almost all landscapes are "too small" and almost all wide angles are "too wide". Following the "foveal-field rule" the most precisely focused part of the image is that central 1%, and using my messed-up math tells me that for a 13 x 8.5" print (always my abiding interest) a K20 image at 360 ppi reduced to the finest focus point would be .13 " x.08 " print, glad I got a 14.2MP camera to crop to that detail

Brian

Last edited by FHPhotographer; 10-22-2009 at 05:07 PM. Reason: clarity, I hope

Eruditass · 10-22-2009, 11:39 AM

"Perspective distortion" is not created by focal length, but by your feet, which you often use to create identical framing. Two images with radically different focal lengths taken from the same physical spot have the exact same perspective relationship between objects. Crop a wide angle and compare it to a telephoto. There is a luminous landscape article on it.

CFWhitman · 10-22-2009, 12:43 PM

Originally posted by Eruditass

"Perspective distortion" is not created by focal length, but by your feet, which you often use to create identical framing. Two images with radically different focal lengths taken from the same physical spot have the exact same perspective relationship between objects. Crop a wide angle and compare it to a telephoto. There is a luminous landscape article on it.

Perspective distortion is created by altering the angle of view, which is directly influenced by focal length as well as by cropping the photo, but not at all by distance (Changing distance alters the perspective, but not the distortion).

The author of the Luminous Landscape article (if that is the article I'm thinking of) is hung up on fact number one (Changing focal length does not change the relationship of the the sizes of objects in the photo compared to each other.) and fails to resolve it with fact number two (Changing focal lengths does change perspective distortion.) He mistakenly thinks that fact number one contradicts fact number two. He does not have a complete understanding of it.

The mistaken understanding goes like this:

1. First, people discover fact number two, that changing their focal length changes perspective distortion. This is perfectly true.

2. Then people (mistakenly) reason out that if changing focal lengths changes perspective distortion, then it must change the relationship of the sizes of objects compared to each other in the photo. This is completely false.

3. People then learn that (2) is completely false, and using the same mistaken reasoning that made them come up with (2) in the first place, but in reverse, decide that (1) must also be false.

4. Using the same false premise that perspective distortion is caused by changing the relationship of the sizes of objects in the photo (which is what causes normal perspective changes), they conclude that perspective distortion is caused by changing distances to objects.

A big problem with this reasoning is that if perspective distortion were caused by the same changes that normal perspective changes are caused by, then it would not be distortion, but would be normal. Perspective distortion is caused by apparently altering one aspect of perspective, the viewpoint, without making the other corresponding changes in perspective, thereby causing it to become distorted, or give a false perspective. It is akin to an optical illusion.

FHPhotographer · 10-22-2009, 01:40 PM

Charlie, this is starting to make more sense. Here's a link to what seems to me to be an excellent visual illustration,
Brian

Eruditass · 10-22-2009, 01:56 PM

Originally posted by CFWhitman

Perspective distortion is created by altering the angle of view, which is directly influenced by focal length as well as by cropping the photo, but not at all by distance (Changing distance alters the perspective, but not the distortion).

Quote:

The author of the Luminous Landscape article (if that is the article I'm thinking of) is hung up on fact number one (Changing focal length does not change the relationship of the the sizes of objects in the photo compared to each other.) and fails to resolve it with fact number two (Changing focal lengths does change perspective distortion.) He mistakenly thinks that fact number one contradicts fact number two. He does not have a complete understanding of it.

The mistaken understanding goes like this:

1. First, people discover fact number two, that changing their focal length changes perspective distortion. This is perfectly true.

2. Then people (mistakenly) reason out that if changing focal lengths changes perspective distortion, then it must change the relationship of the sizes of objects compared to each other in the photo. This is completely false.

3. People then learn that (2) is completely false, and using the same mistaken reasoning that made them come up with (2) in the first place, but in reverse, decide that (1) must also be false.

4. Using the same false premise that perspective distortion is caused by changing the relationship of the sizes of objects in the photo (which is what causes normal perspective changes), they conclude that perspective distortion is caused by changing distances to objects.

A big problem with this reasoning is that if perspective distortion were caused by the same changes that normal perspective changes are caused by, then it would not be distortion, but would be normal. Perspective distortion is caused by apparently altering one aspect of perspective, the viewpoint, without making the other corresponding changes in perspective, thereby causing it to become distorted, or give a false perspective. It is akin to an optical illusion.

care to give an example?

Many people share the same opinion on this (math warning):
http://scubageek.com/articles/compression.pdf

example pics:

Looking at the crops, many which include the ground between the objects (so I just can't look at the size), appear to have no distortion, which is why I quoted "perspective distortion"

I'd like to see the real distortion you are talking about.

Marc Sabatella · 10-22-2009, 02:50 PM

Originally posted by Eruditass

Looking at the crops, many which include the ground between the objects (so I just can't look at the size), appear to have no distortion, which is why I quoted "perspective distortion"

That's because you comapring crops, not the originals. Had you compared the originals - by printing them and then viewing them at a "typical" distance - you'd see only the picture taken at 28mm (assuming APS-C) showed the objects in the scene at the same basic sizes they appeared to be in real life. That is, if the sign subtended (there you go, David!) an angle of 10 degrees from where stood when taking the picture, the *image* of the sign on the print would *also* subtend an angle of 10 degrees when viewing the print from a typical distance. The shot taken at 250mm would show the sign (and everything else, of course) looking much larger than it really did when you took the picture. This is "perspective distortion".

audiobomber · 10-22-2009, 02:58 PM

Originally posted by FHPhotographer

Charlie, this is starting to make more sense. Here's a link to what seems to me to be an excellent visual illustration,
Brian

Great link.

Why must these discussions of normal always be so contentious?

Marc Sabatella · 10-22-2009, 03:00 PM

Originally posted by FHPhotographer

Using the power lines in the foreground as a measurement, the red line drawn on the image is (approximately) what my eye saw.

This has been touched on, but I want to be explicit about this: there is no way what you are saying here can be true - at least not as an effect of focal length (see below). If, from where you stood, the mountains came up to the height of the second [edited; I originally said lowest] power line, no lens in the world can possibly change this and make them appear to only come up to the bottom power line. The longer the focal length, the bigger those mountains will appear - but the power lines will get bigger at exactly the same rate, and the mountains will still come up to the second power line.

The only two things that would make a picture come out with the mountains appear smaller relative to the power lines would be if you took the picture from *closer* to the power lines when you made the visual observation that they came up to the second power line, or if you shot it from *lower* than you were standing when you made that visual obseration. both of these could in fact be the case, if only slightly, if you were maybe shooting on a tripod. Maybe *just* enough to explain what you saw, if you were close enough that the couple of feet discrepancy would matter.

If you weren't shooting fro a tripod, then the camera would only be *inches* closer and lwoer than your eyes, and I doubt that would be enough to make as big a differences as you are indicating here - but maybe still, just enough to notice?

Quote:

I'm not saying there's a right perspective or FOV, just that I would like on landscape shots like this that the relationship of the parts to the whole would be close to my vision. In this case, if I had used a 28mm the image would have more closely conformed to the "real" relationship of objects in the image?

As I said above, aside from differences between your position and that of the camera, there is no way any lens will ever change the relationship of the parts. If, from where the camera was position, the mountains only came up to the bottom power line, that would remain true whether shooting a 10mm fisheye, the DA21, a "normal" lens, or the DA*300.

Eruditass · 10-22-2009, 03:04 PM

Originally posted by Marc Sabatella

That's because you comapring crops, not the originals. Had you compared the originals - by printing them and then viewing them at a "typical" distance - you'd see only the picture taken at 28mm (assuming APS-C) showed the objects in the scene at the same basic sizes they appeared to be in real life. That is, if the sign subtended (there you go, David!) an angle of 10 degrees from where stood when taking the picture, the *image* of the sign on the print would *also* subtend an angle of 10 degrees when viewing the print from a typical distance. The shot taken at 250mm would show the sign (and everything else, of course) looking much larger than it really did when you took the picture. This is "perspective distortion".

Correct me if I'm wrong, but if you print the crop at the same size as the un-cropped longer focal length image and viewed them at the same distance they would appear the same. Certainly, to get a certain complete frame and perspective, you need a certain focal length, but that's not what I'm getting at..

I suppose we have different definitions of "distortion"

newarts · 10-22-2009, 03:09 PM

Of course the absolute sizes of things don't change when you change a lens.

But relative to a subject of a constant size in a frame, A long lens enlarges background items and a short lens enlarges foreground items. This can also be stated in terms of distance to the subject, but it is the same thing as subject distance, magnification, focal length and perspective are related by optics.

Original from luminious-landscape.com

The foreground bunny, midground critter (constant magnification), and background towers were not moved for the two exposures.

Dave in Iowa

Eruditass · 10-22-2009, 03:10 PM

and what causes that is moving your feet. A longer FL magnifies everything the same amount, there is no "distortion"

CFWhitman · 10-22-2009, 03:27 PM

Originally posted by Eruditass

care to give an example?

Many people share the same opinion on this (math warning):
http://scubageek.com/articles/compression.pdf

example pics:

Looking at the crops, many which include the ground between the objects (so I just can't look at the size), appear to have no distortion, which is why I quoted "perspective distortion"

I'd like to see the real distortion you are talking about.

The example that you share here only proves that fact number one is true (Changing focal length does not change the relationship of the the sizes of objects in the photo compared to each other). Remember that cropping a photo changes its angle of view just as switching focal length changes the angle of view (as I said). So if you change to a wider angle of view by using a shorter focal length, and then crop the photo back to the angle of view that you changed from, you haven't affected perspective distortion at all (or, you've changed it and then changed it back). Cropping the photo is the same thing as using a smaller sensor; it changes the relationship between the focal length and the image size. It's this relationship that is important.

Remember too that I said that perspective distortion was akin to an optical illusion, so there may not be "real distortion" in the sense that you mean. What these example pics all do exhibit, since the shorter focal length shots have been cropped to a very narrow angle of view, is compression distortion (sometimes called "telephoto" distortion). Everything in the photos looks like it's right on top of each other because the angle of view makes it appear as if the viewpoint were closer than it really was. From the actual viewpoint, the objects in the picture were all relatively close together. When you make it appear as though the viewpoint were much closer than it really was, then the objects appearing to be relatively close together seems "wrong" because if you were really that close, then the objects would be relatively further apart. It's not how far away the objects are that makes their appearance seem wrong; it's how much closer they appear to be than they really are.

The author of the pdf that you cite goes through a lot of math to prove that perspective exists and that it is relative. I have gone through the math before, but I didn't need to do so to know this. He proves these things, and then he proceeds to draw the wrong conclusions by his proof, because he is clinging to the same false premise that I stated above, that perspective distortion is caused by changing the relationship of the sizes of objects in the photo. In reality perspective distortion is caused by not changing that relationship while seeming to change the viewpoint.

For practical purposes the author may not be likely to encounter a situation where it matters whether his understanding is correct or not, but this is the problem I see with it. By changing focal lengths or otherwise changing the angle of view of a photo, you can make the same two objects photographed from the same place appear to be closer together than they really are, or farther apart than they really are. His understanding of perspective distortion either does not allow for this, or glosses over it without explaining it.

10-22-2009, 03:00 PM	#26
Marc Sabatella Veteran Member Join Date: Sep 2006 Location: Denver, CO Photos: Gallery Posts: 10,685	Originally posted by FHPhotographer Using the power lines in the foreground as a measurement, the red line drawn on the image is (approximately) what my eye saw. This has been touched on, but I want to be explicit about this: there is no way what you are saying here can be true - at least not as an effect of focal length (see below). If, from where you stood, the mountains came up to the height of the second [edited; I originally said lowest] power line, no lens in the world can possibly change this and make them appear to only come up to the bottom power line. The longer the focal length, the bigger those mountains will appear - but the power lines will get bigger at exactly the same rate, and the mountains will still come up to the second power line. The only two things that would make a picture come out with the mountains appear smaller relative to the power lines would be if you took the picture from closer to the power lines when you made the visual observation that they came up to the second power line, or if you shot it from lower than you were standing when you made that visual obseration. both of these could in fact be the case, if only slightly, if you were maybe shooting on a tripod. Maybe just enough to explain what you saw, if you were close enough that the couple of feet discrepancy would matter. If you weren't shooting fro a tripod, then the camera would only be inches closer and lwoer than your eyes, and I doubt that would be enough to make as big a differences as you are indicating here - but maybe still, just enough to notice? Quote: I'm not saying there's a right perspective or FOV, just that I would like on landscape shots like this that the relationship of the parts to the whole would be close to my vision. In this case, if I had used a 28mm the image would have more closely conformed to the "real" relationship of objects in the image? As I said above, aside from differences between your position and that of the camera, there is no way any lens will ever change the relationship of the parts. If, from where the camera was position, the mountains only came up to the bottom power line, that would remain true whether shooting a 10mm fisheye, the DA21, a "normal" lens, or the DA300. Last edited by Marc Sabatella; 10-22-2009 at 03:35 PM.*

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10-22-2009, 11:00 AM	#16
FHPhotographer Veteran Member Join Date: Jul 2008 Location: Fountain Hills, AZ Photos: Gallery \| Albums Posts: 1,297 Original Poster	Charlie, I think I followed that, on the other, hand I might not have. But I'm working on the core idea you suggested "Whichever length lens is used to capture a photo, the sizes (and therefore apparent distances) of objects in the picture relative to each other will remain the same. However, their apparent sizes (and therefore distances) relative to the viewpoint will change" and it might come clear, eventually. Thanks, Brian Last edited by FHPhotographer; 10-22-2009 at 11:01 AM. Reason: typo

10-22-2009, 11:04 AM	#17
FHPhotographer Veteran Member Join Date: Jul 2008 Location: Fountain Hills, AZ Photos: Gallery \| Albums Posts: 1,297 Original Poster	After reading the posts, I think it's time for a suitably ambiguous quote from Garry Winogrand, "Photography is not about the thing photographed. It is about how that thing looks photographed." Brian

10-22-2009, 11:21 AM	#18
CFWhitman Senior Member Join Date: Jan 2007 Location: Upstate New York, US Photos: Albums Posts: 225	Originally posted by audiobomber Dammit Charlie, you're making me dizzy. Sorry. This subject has one hurdle for people to get over. They seem to have trouble resolving these two facts with each other. 1. Changing focal length does not change the relationship of the the sizes of objects in the photo compared to each other. 2. Changing focal lengths does change perspective distortion. If you can resolve these two facts with each other, and understand that number one not only does not contradict number two, but is actually the cause of it, then you've got it made.

10-22-2009, 11:34 AM	#19
FHPhotographer Veteran Member Join Date: Jul 2008 Location: Fountain Hills, AZ Photos: Gallery \| Albums Posts: 1,297 Original Poster	Dave, interesting stuff and you hit it spot on with "To me, like you I suspect, almost all landscapes are "too small" and almost all wide angles are "too wide". Following the "foveal-field rule" the most precisely focused part of the image is that central 1%, and using my messed-up math tells me that for a 13 x 8.5" print (always my abiding interest) a K20 image at 360 ppi reduced to the finest focus point would be .13 " x.08 " print, glad I got a 14.2MP camera to crop to that detail Brian Last edited by FHPhotographer; 10-22-2009 at 05:07 PM. Reason: clarity, I hope

10-22-2009, 11:39 AM	#20
Eruditass Veteran Member Join Date: Jul 2009 Photos: Gallery Posts: 2,207	"Perspective distortion" is not created by focal length, but by your feet, which you often use to create identical framing. Two images with radically different focal lengths taken from the same physical spot have the exact same perspective relationship between objects. Crop a wide angle and compare it to a telephoto. There is a luminous landscape article on it.

10-22-2009, 12:43 PM	#21
CFWhitman Senior Member Join Date: Jan 2007 Location: Upstate New York, US Photos: Albums Posts: 225	Originally posted by Eruditass "Perspective distortion" is not created by focal length, but by your feet, which you often use to create identical framing. Two images with radically different focal lengths taken from the same physical spot have the exact same perspective relationship between objects. Crop a wide angle and compare it to a telephoto. There is a luminous landscape article on it. Perspective distortion is created by altering the angle of view, which is directly influenced by focal length as well as by cropping the photo, but not at all by distance (Changing distance alters the perspective, but not the distortion). The author of the Luminous Landscape article (if that is the article I'm thinking of) is hung up on fact number one (Changing focal length does not change the relationship of the the sizes of objects in the photo compared to each other.) and fails to resolve it with fact number two (Changing focal lengths does change perspective distortion.) He mistakenly thinks that fact number one contradicts fact number two. He does not have a complete understanding of it. The mistaken understanding goes like this: 1. First, people discover fact number two, that changing their focal length changes perspective distortion. This is perfectly true. 2. Then people (mistakenly) reason out that if changing focal lengths changes perspective distortion, then it must change the relationship of the sizes of objects compared to each other in the photo. This is completely false. 3. People then learn that (2) is completely false, and using the same mistaken reasoning that made them come up with (2) in the first place, but in reverse, decide that (1) must also be false. 4. Using the same false premise that perspective distortion is caused by changing the relationship of the sizes of objects in the photo (which is what causes normal perspective changes), they conclude that perspective distortion is caused by changing distances to objects. A big problem with this reasoning is that if perspective distortion were caused by the same changes that normal perspective changes are caused by, then it would not be distortion, but would be normal. Perspective distortion is caused by apparently altering one aspect of perspective, the viewpoint, without making the other corresponding changes in perspective, thereby causing it to become distorted, or give a false perspective. It is akin to an optical illusion.

10-22-2009, 01:40 PM	#22
FHPhotographer Veteran Member Join Date: Jul 2008 Location: Fountain Hills, AZ Photos: Gallery \| Albums Posts: 1,297 Original Poster	Charlie, this is starting to make more sense. Here's a link to what seems to me to be an excellent visual illustration, Brian

10-22-2009, 01:56 PM	#23
Eruditass Veteran Member Join Date: Jul 2009 Photos: Gallery Posts: 2,207	Originally posted by CFWhitman Perspective distortion is created by altering the angle of view, which is directly influenced by focal length as well as by cropping the photo, but not at all by distance (Changing distance alters the perspective, but not the distortion). Quote: The author of the Luminous Landscape article (if that is the article I'm thinking of) is hung up on fact number one (Changing focal length does not change the relationship of the the sizes of objects in the photo compared to each other.) and fails to resolve it with fact number two (Changing focal lengths does change perspective distortion.) He mistakenly thinks that fact number one contradicts fact number two. He does not have a complete understanding of it. The mistaken understanding goes like this: 1. First, people discover fact number two, that changing their focal length changes perspective distortion. This is perfectly true. 2. Then people (mistakenly) reason out that if changing focal lengths changes perspective distortion, then it must change the relationship of the sizes of objects compared to each other in the photo. This is completely false. 3. People then learn that (2) is completely false, and using the same mistaken reasoning that made them come up with (2) in the first place, but in reverse, decide that (1) must also be false. 4. Using the same false premise that perspective distortion is caused by changing the relationship of the sizes of objects in the photo (which is what causes normal perspective changes), they conclude that perspective distortion is caused by changing distances to objects. A big problem with this reasoning is that if perspective distortion were caused by the same changes that normal perspective changes are caused by, then it would not be distortion, but would be normal. Perspective distortion is caused by apparently altering one aspect of perspective, the viewpoint, without making the other corresponding changes in perspective, thereby causing it to become distorted, or give a false perspective. It is akin to an optical illusion. care to give an example? Many people share the same opinion on this (math warning): http://scubageek.com/articles/compression.pdf example pics: Looking at the crops, many which include the ground between the objects (so I just can't look at the size), appear to have no distortion, which is why I quoted "perspective distortion" I'd like to see the real distortion you are talking about.

10-22-2009, 02:50 PM	#24
Marc Sabatella Veteran Member Join Date: Sep 2006 Location: Denver, CO Photos: Gallery Posts: 10,685	Originally posted by Eruditass Looking at the crops, many which include the ground between the objects (so I just can't look at the size), appear to have no distortion, which is why I quoted "perspective distortion" That's because you comapring crops, not the originals. Had you compared the originals - by printing them and then viewing them at a "typical" distance - you'd see only the picture taken at 28mm (assuming APS-C) showed the objects in the scene at the same basic sizes they appeared to be in real life. That is, if the sign subtended (there you go, David!) an angle of 10 degrees from where stood when taking the picture, the image of the sign on the print would also subtend an angle of 10 degrees when viewing the print from a typical distance. The shot taken at 250mm would show the sign (and everything else, of course) looking much larger than it really did when you took the picture. This is "perspective distortion".

10-22-2009, 02:58 PM	#25
audiobomber Veteran Member Join Date: May 2008 Location: Sudbury, Ontario Photos: Albums Posts: 6,806	Originally posted by FHPhotographer Charlie, this is starting to make more sense. Here's a link to what seems to me to be an excellent visual illustration, Brian Great link. Why must these discussions of normal always be so contentious?

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10-22-2009, 03:04 PM	#27
Eruditass Veteran Member Join Date: Jul 2009 Photos: Gallery Posts: 2,207	Originally posted by Marc Sabatella That's because you comapring crops, not the originals. Had you compared the originals - by printing them and then viewing them at a "typical" distance - you'd see only the picture taken at 28mm (assuming APS-C) showed the objects in the scene at the same basic sizes they appeared to be in real life. That is, if the sign subtended (there you go, David!) an angle of 10 degrees from where stood when taking the picture, the image of the sign on the print would also subtend an angle of 10 degrees when viewing the print from a typical distance. The shot taken at 250mm would show the sign (and everything else, of course) looking much larger than it really did when you took the picture. This is "perspective distortion". Correct me if I'm wrong, but if you print the crop at the same size as the un-cropped longer focal length image and viewed them at the same distance they would appear the same. Certainly, to get a certain complete frame and perspective, you need a certain focal length, but that's not what I'm getting at.. I suppose we have different definitions of "distortion"

10-22-2009, 03:09 PM	#28
newarts Inactive Account Join Date: Dec 2008 Location: Ames, Iowa, USA Photos: Albums Posts: 2,965	Of course the absolute sizes of things don't change when you change a lens. But relative to a subject of a constant size in a frame, A long lens enlarges background items and a short lens enlarges foreground items. This can also be stated in terms of distance to the subject, but it is the same thing as subject distance, magnification, focal length and perspective are related by optics. Original from luminious-landscape.com The foreground bunny, midground critter (constant magnification), and background towers were not moved for the two exposures. Dave in Iowa

10-22-2009, 03:10 PM	#29
Eruditass Veteran Member Join Date: Jul 2009 Photos: Gallery Posts: 2,207	and what causes that is moving your feet. A longer FL magnifies everything the same amount, there is no "distortion"

10-22-2009, 03:27 PM	#30
CFWhitman Senior Member Join Date: Jan 2007 Location: Upstate New York, US Photos: Albums Posts: 225	Originally posted by Eruditass care to give an example? Many people share the same opinion on this (math warning): http://scubageek.com/articles/compression.pdf example pics: Looking at the crops, many which include the ground between the objects (so I just can't look at the size), appear to have no distortion, which is why I quoted "perspective distortion" I'd like to see the real distortion you are talking about. The example that you share here only proves that fact number one is true (Changing focal length does not change the relationship of the the sizes of objects in the photo compared to each other). Remember that cropping a photo changes its angle of view just as switching focal length changes the angle of view (as I said). So if you change to a wider angle of view by using a shorter focal length, and then crop the photo back to the angle of view that you changed from, you haven't affected perspective distortion at all (or, you've changed it and then changed it back). Cropping the photo is the same thing as using a smaller sensor; it changes the relationship between the focal length and the image size. It's this relationship that is important. Remember too that I said that perspective distortion was akin to an optical illusion, so there may not be "real distortion" in the sense that you mean. What these example pics all do exhibit, since the shorter focal length shots have been cropped to a very narrow angle of view, is compression distortion (sometimes called "telephoto" distortion). Everything in the photos looks like it's right on top of each other because the angle of view makes it appear as if the viewpoint were closer than it really was. From the actual viewpoint, the objects in the picture were all relatively close together. When you make it appear as though the viewpoint were much closer than it really was, then the objects appearing to be relatively close together seems "wrong" because if you were really that close, then the objects would be relatively further apart. It's not how far away the objects are that makes their appearance seem wrong; it's how much closer they appear to be than they really are. The author of the pdf that you cite goes through a lot of math to prove that perspective exists and that it is relative. I have gone through the math before, but I didn't need to do so to know this. He proves these things, and then he proceeds to draw the wrong conclusions by his proof, because he is clinging to the same false premise that I stated above, that perspective distortion is caused by changing the relationship of the sizes of objects in the photo. In reality perspective distortion is caused by not changing that relationship while seeming to change the viewpoint. For practical purposes the author may not be likely to encounter a situation where it matters whether his understanding is correct or not, but this is the problem I see with it. By changing focal lengths or otherwise changing the angle of view of a photo, you can make the same two objects photographed from the same place appear to be closer together than they really are, or farther apart than they really are. His understanding of perspective distortion either does not allow for this, or glosses over it without explaining it.