This blog post by Aaron Hertzmann is the first online tutorial I have found that gives a well-informed discussion of perspective distortion in photographs.
As I have said many times before, there is a lot of nonsense talked about perspective distortion. It is nice to see something available online that gets it right.
Absolutely, 100%, and I would encourage that we read it without trying to fit it withi our own per-concieved ideas/frameworks or perceptions. and he leaves the door open at the end. But I must make a couple of points relevant to our previous discussions.
Please note that the author makes no attempt to link human vision to the maths of linear perspective, or any attempt to describe what we see in terms of the maths of linear perspective. He doesn't say "exactly the same", quite the opposite:
In principle, linear perspective requires you to have only one eye open, and to have it located right at the COP, in order for the picture to “look right.”
With "telephoto compression", (we use the common label for continuity) and wide angle distortion he also indicates that the former is when you look at a photo of a distant object and the latter a photo of a close object. It is not the singular effect of the COP, the case of a single photo viewed from in front of, then behind the COP causing the distortion. It is the effect of the correct mapping of the linear perspective locked into the photo then mis-interpreted by the human eye as a result of looking from the comfortable viewing distance that is either in front of or behind the COP respectively.
The last paragraph on the subject is revealing:
Throughout art history and perception research, there is a long history of assuming that linear perspective is the “right” way to make pictures, and any distortions or misperceptions must be “user error,” i.e., mistakes made by the artist or the brain. To me, this seems backwards. If human vision doesn’t perceive pictures according to the “rules” of linear perspective, then the “rules” aren’t quite right.
Or to put it another way, in mathematical terms when using the human eye it is the photo that shows telephoto compression that's closer to correct linear perspective and the one that "looks right' that's the distortion of linear perspective. If we keep trying to link linear perspective to the "correct" answer and use that as the basis of "what we see" then we quite literally get it back to front, you treat what is in fact the variable as the constant and vice-versa.
Sorrry, but in all our conversations we always fail at one simple point, one simple mathematical truth. It is your desire to rationalise and understand perspective, and you choose to do it in the language you are both familiar with and understand, but read the quote above. We do not see the world as a series of still images where we can ray trace, it is quite impossible for the human brain to do this, as well as counterproductive as it wouldn't present a workable or understandable solution. So quite simply:
Linear perspective is never equal to what you see.
Any attempt to equate one with the other without also allowing for the nature of human vision will be wrong. It's a blanket truth.