Depth of field (DOF) does NOT change with sensor size

I made no such suggestion -- just that Leslie's observation gives us a hard number. Further below you agree the use of the format diagonal isn't especially meaningful. So otherwise we have nothing but repeated empirical observation. We know as you pointed out that perspective is also dependent on print viewing distance. What is or should that distance be -- a normal distance? If we have an average distance that applies to most viewers we can back calculate the lens focal length required to match the FOV to the print. It is then fair to say that if you view a 16 x 20 inch print from 40 inches you will be in the correct position to experience perspective as it appeared from the camera position using a 70mm lens on a 35mm camera. It's also fair to say that if you stay at that 40 inch distance and are presented a 16 x 20 image taken with a 20mm lens on a 35mm camera you're likely to experience the image as distorted, but not necessarily as it's actually pretty easy to fool your brain about what it's seeing.

The numbers along with understanding are useful tools.

Joe

We've gone well off topic here, but it's interesting so I'll throw one more thought into the mix:

What if perspective only exists in a 2D representation of an object?

It's not as weird as it at first sounds. It's just as photographers we automatically assume that what we capture is a representation of a 3D object and therefore how we interpret a picture on a 2D plane is the same as how we see and interpret the actual object in 3D.

What if that wasn't true?

It is very difficult to demonstrate on a computer screen because everything I show you will be a 2D representation and will therefore be seen as a 2D representation. Here's a little experiment you can do with your hands, with palm facing you hold them in front of your eyes with one at arms length and the other about half way but do it so they don't overlap. They look of a very similar size.

Now move them together so they overlap. It's called consistency scaling, you understand that both your hands are the same size and so your interpretation of them will try to be of the same size until they overlap. At which point the illusion is destroyed and you see them in relation to each other and the difference in size becomes apparent.

The camera though will always present a literal recording free of human perceptive effects on a 2D surface through monocular vision. You may at first glance try to see them the same size, but in a static flat 2D rendition of monocular vision you allow yourself to compare actual scaling because you allow the introduction of imaginary *vanishing points* that are just converging lines on a 2D surface.

Here is another:

ex-1.jpg


On the left is either an oval or a circle, it's ambiguous in a 2D representation. On the right you clearly see it as a circle within a rectangle. Think about this for a second, if you understand it as a rectangle then you understand and see it to have parallel sides so your human perception in the real 3D world has no vanishing point. It's only when I represent it in 2D that the vanishing point becomes clear, that you see clearly how a 3D object is represented in 2D space. I've added something in a 2D space that clearly influences your interpretation of what you see and makes you equate it to a 3D object. The reality is that it is an oval in a rhomboid on a 2D surface yet you don't interpret the reality, you see the illusion.

Artists used to do it by either tracing lines on a sheet of glass or through use of a camera obscura. Vanishing points and perspective only become visible in 2D representations, in the 3D representation you eye/brain is doing as much as it can to subtract or cancel perspective in order to allow you a consistent view as you walk through the landscape. One where objects maintain a consistent size and distance relative to each other, one where they don't change relative to your position.

I can distort our rectangle and circle in many ways by moving the imaginary vanishing point around, from the Degas style of *off the page* to one with a virtual horizon on the page:

ex-2.jpg


It still looks like a circle in a rectangle. But ask yourself if it were a real 3D object do vanishing points move as you walk around the object? How dizzy would you get if they did?

Here's another. Imagine yourself walking past a 2D image, is the perspective or vanishing point actually fixed or is it entirely dependant on the position of the observer?

img082_sRGB_ss2.jpg


In this 2D representation there is a clear indication of a vanishing point towards the middle of the frame. But if we move to the right then the implied vanishing point moves off the left of the frame:

ex-3.jpg


And yet your impression is that you are still standing directly in front of the chair. If you walked past the subject then your impression would be entirely different, that the objects are static and their edges parallel.

2D representations clearly do not behave in the same way as real 3D objects. This begs the question of whether trying to understand the 3D world in terms of how perspective works in a 2D image is preventing you from understanding how we actually see the real 3D world? Perhaps there is no real correlation between how we create the illusion of depth in a 2D image and we interpret the 3D world. Perhaps 2D images will always be a distortion and never a representation, that we only see them as representative because the *hypothesis generator* in our brains equates them to the view we are most familiar with - reality. In images we create an illusion of reality, not reality itself. Illusions work because we do not see them properly not because they are an accurate representation of reality. Even tilting the camera and displaying the image vertically distorts your perception...

Renaissance perspective actually has five elements, linear perspective is but one. Trying to understand 2D images by only linear perspective is also trying to limit understanding into a rationalisation that is already understood and fails to recognise anything outside what is understood.
 
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Speaking of 3D perception of a 2D object:

(Scroll to 7:23.)

 
Speaking of 3D perception of a 2D object:

The illusion actually works in 3D as well. It's because you make the assumption that best fits your experience, that the head is a positive fold rather than negative. It highlights that a lot of what we see isn't so much real but the interpretation that makes to most realistic sense to us, the one that's most consistent to our experience and learning.
 
Well, this has been a blast to read. Sure have missed this site. Thanks for the entertainment, all. :trink39:
 

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