perspective vs. field of view

[former member]

There are different types of perspective, and once again people are talking past each other. I could not understand Roger's comment regarding mathematical model of perspective as it is easy to code up in FORTRAN. But the definition of "Perspective" as it applies to Computer Generated Images is different from that used by a cognitive psychologist studying how someone looks at an image.

Trying to put this topic into perspective. I can make more bad jokes.

 

[antiquark]

Which is why all the pictures I take with my Horseman SW612 and 55mm lens look exactly like the pictures from my Mamiya 6 with a 75mm lens.

Yes, if you were standing at the same spot when you took the pictures. (According to my personal interpretation of what perspective is.) 🙂

 

[Frankie]

Please excuse me for being dense and for editing my quote of your comment, but I still don't see how this is so.

Being in photogrammetry and specializing in aerial mapping, I can explain things better in viewing a scene from the top down.

Imagine photographing a few square blocks of downtown Manhattan:

• If photographed from space and using a long-long-long focal length lens, the tall building will appear standing straight...because the bundle set of light rays captured are near parallel to the lens principal axis. [Also called orthographic projection and commonly described as orthogonal.]
• If photographed from a helicopter but using a wide angle lens so that the same square blocks are covered, the buildings in the frame centre will still appear standing straight, but surrounding buildings will all appear leaning away as if toppling over...and more pronounced approaching the corners.

A wonderful dynamic illustration of this displacement [lean away] phenomenon is captured in the opening/title sequence of The Fugitive [Harrison Ford]...where leaning buildings in the frame edge become upright as they approach the frame centre.

The space- and air-borne imaging conditions described above illustrate the imaging distance v. lens focal length conditions.

Our way of photography merely rotate the optical principal axis ~90-degrees...we call it terrestrial photogrammetry. All mathematical principals still apply.

 

[Finder]

Yes, if you were standing at the same spot when you took the pictures. (According to my personal interpretation of what perspective is.) 🙂

And that is where thinking about perspective in absolute terms becomes a problem. It really does not describe how we see an image. The definition used in photography tries to address the perception of an image.

Basically my distance to an object is not affected by the equipment--I use both the 6x12 pano camera at the same distances as the 6x6 camera. However, the perception of the images is very different. It would be odd to say to a photographer that if you use a 21mm lens and a 70mm lens your photographs will end up with the same perspective, at least, that is not the common perception. So there are different factors driving this perception of space.

So the three images I posted above are really about that problem. If we take perspective to be the perception of space, then the first and second images have about the same perspective and it is weak. The last has the strongest perspective. If you try to define it through an absolute reference, you are going to have to break out some tools to figure that out. In those images, the first and last would have the same perspective and the middle would have the strongest perspective.

Except for some technical or scientific applications, photography is really about creating an illusion of space rather than making absolute references to it. I don't know too many photographer that go out and make comparison photographs of object distance and focal length as a primary thrust to their work. If I wanted to create stronger perspective in my work, you would not bother recommending a wide-angle lens?

 

[antiquark]

And that is where thinking about perspective in absolute terms becomes a problem. It really does not describe how we see an image. The definition used in photography tries to address the perception of an image.

I was referring to a scientific definition of perspective, in which greater perspective is shown by a greater variation in the size from near to far objects. For example, if someone holds out their hand towards the camera, greater perspective would mean that their hand looks large in relation to the rest of their body.

 

[Finder]

I was referring to a scientific definition of perspective, in which greater perspective is shown by a greater variation in the size from near to far objects. For example, if someone holds out their hand towards the camera, greater perspective would mean that their hand looks large in relation to the rest of their body.

I don't think anyone is arguing this is not true.

 

[Pico]

We have a language problem here.

To some, 'perspective' has a scientific pragamatic definition. To others it means a philosophical stand. To another it is just an issue which they rail against because it is confusing to them.

I believe we have samples of all here; enough for a boring case study.

 

[Frankie]

I was referring to a scientific definition of perspective, in which greater perspective is shown by a greater variation in the size from near to far objects. For example, if someone holds out their hand towards the camera, greater perspective would mean that their hand looks large in relation to the rest of their body.

A photogrammetric expression of your statement is best in terms of image scale where f = focal length, and D = imaging distance [or for us, the flying height]:

Scale = f/D​

If one uses a 50mm lens to photograph two objects contained in a scene: Object A at 10m and Object B at 11m from the perspective centre, then:

Scale at Object A = 50mm/10m or 1:200; and​

Scale at Object B = 50mm/11m or 1:220; resulting in a 10% difference.​

Object B will look 10% smaller than object A.​

If a 25mm lens is chosen instead, in order to maintain the same scale [thus coverage] at object A, the imaging distance must now be 5m:

Scale at Object A = 25mm/5m or 1:200; but​

Scale at Object B = 25mm/6m or 1:240; resulting in a 20% difference.​

Object B will now look 20% smaller....quite a bigger difference.​

The rate in variation of imaging scale is the reason for the imaged perspective differences...or perception differences in others' usage of language.

Now play with the space- v. air-borne imaging example...use 100km flying height for space and 1km for aerial, and the Manhattan building at 100m tall, and you will see the dramatic scale difference between building top/bottom that causes apparent building leans.

 

[antiquark]

Scale = f/D​

Interesting, if you wanted to, you could concoct a "perspective" equation. It would be the scale of an object divided by the scale of an object one meter behind it. (To pick a number).

So, you would get:

Perspective = (f/D) / (f/(D + 1))
​

And if you simplified it, the f's would cancel out, giving

Perspective = (D + 1)/D
​

Which shows that this "Perspective formula" actually depends only on the distance to the subject, and not the focal length.

However that would only be somewhat correlated with a person's psychological interpretation of the perspective in an image.

 

[Frankie]

Interesting, if you wanted to, you could concoct a "perspective" equation. It would be the scale of an object divided by the scale of an object one meter behind it. (To pick a number).


So, you would get:

Perspective = (f/D) / (f/(D + 1))​

And if you simplified it, the f's would cancel out, giving

Perspective = (D + 1)/D​

Which shows that this "Perspective formula" actually depends only on the distance to the subject, and not the focal length.

However that would only be somewhat correlated with a person's psychological interpretation of the perspective in an image.

You would be correct if one does not have to maintain the same FoV in both cases...the OP.

 

[antiquark]

You would be correct if one does not have to maintain the same FoV in both cases...the OP.

Wouldn't the same FoV basically mean identical images? (And thus identical perspective?)

 

[Frankie]

Wouldn't the same FoV basically mean identical images? (And thus identical perspective?)

No.

Same FoV can be achieved by different focal length lenses but at different imaging distance.

 

[antiquark]

I understand, in contrast to AoV, angle of view.

 

[Jeicob]

Jeicob: How did you do that fill-in?

Mirrored (flipped) down right corner to the left side, a little patchwork and a splash in the sky to break up any hard lines created by the patches.
I'm not used to do this kind of work and I only used a couple of minutes using M$ Paint.

I like some space in the direction of peoples eyes - and I actually think it made the photograph look less strange?
But again; the right print size would have made wonders I guess

Being in photogrammetry and specializing in aerial mapping, I can explain things better in viewing a scene from the top down.

Imagine photographing a few square blocks of downtown Manhattan:

• If photographed from space and using a long-long-long focal length lens, the tall building will appear standing straight...because the bundle set of light rays captured are near parallel to the lens principal axis. [Also called orthographic projection and commonly described as orthogonal.]
• If photographed from a helicopter but using a wide angle lens so that the same square blocks are covered, the buildings in the frame centre will still appear standing straight, but surrounding buildings will all appear leaning away as if toppling over...and more pronounced approaching the corners.

A wonderful dynamic illustration of this displacement [lean away] phenomenon is captured in the opening/title sequence of The Fugitive [Harrison Ford]...where leaning buildings in the frame edge become upright as they approach the frame centre.

As a hang glider pilot I have to say that the perspective of a bird puts ones visual brain on a lot of work - nice kind of work though 😎

Not the best example on this subject but a nice film: http://www.youtube.com/watch?v=hCPitOaTUpU