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I was looking for someone commenting this. There's no mystery, it's really just geometry. Imagine casting a ray from your eyeball to a pixel on the monitor. Then imagine the same ray at the same angle on the actual scene. If the pixel matches the correct part of the scene, then the image appears natural.

But that's really a tiny field of view. Perhaps the easiest way to see this is that it's the same geometry as having a monitor-sized window in a wall at the same distance, and looking outside. That would be really tiny window, and you wouldn't expect to see much of the outside without getting a lot closer.

As a result, most pictures are taken at a wider field of view than what would be natural for typical viewing distances, to show more of the scene. Which explains the distortions that make everything at a distance appear tiny.

You fundamentally can't "solve" this without dramatically increasing the FOV that you're viewing things with -- VR being the obvious idea.

The mystery is "why can I view the world with my eyes and see a wide angle, straight lines, and "natural" perspective, but when I take pictures with a wide angle, everything looks "weird."

You can throw away the straight lines and shoot with a fisheye lens (no straight lines, wide angle, fairly natural depth), you can crop in (depth fine, but now I'm missing stuff around the edges), and you can shoot with a wide rectilinear lens (wide angle, straight lines, "exaggerated" perspective).

As far as I know, the answer is simply that your eyes aren't rectilinear but your brain fudges it to make straight lines seem straight when the image on our retina actually curves.

The effect is most prominent when standing in a small room. It's impossible to take a single picture of it that conveys what you want: a wide rectilinear lens will exaggerate how big the room is (and look weird around the edges), a "normal" rectilinear lens will be so cropped in that you can't see most of the room, and a fisheye lens will make all straight lines curve, especially around the edges. None of them really represent the visual experience of being in the room. Just look at how weird real-estate listings can get when they try to show you a picture of a small bathroom.

Probably a big part of it is that the high-resolution area of the retina is quite small. So in that small area, the perspective is close to perfect, and then we mentally stitch together a larger image by moving our eyes around. But the larger image that's stitched together is in the shape of a sphere rather than a flat surface, with each point on the sphere corresponding to a direction the eyes could be pointing.

Yes. Also image aspect ratio and the relationship between horizontal and vertical is complex. Our eyes themselves move reasonably comfortably 15 degrees in all directions (maybe a little less up), but peripheral vision is greater in width than height and we are used to turning our heads to see objects in horizontal field of view more than vertical.

The problem isn't taking the photo, but that the size you are viewing the photo at is simply too small and flat. Human field of view is somewhere around 200x130°, you are not going to capture that on a tiny flat bit of paper which might just be 40x30°. Reaching the 200° isn't even possible with a flat photo. You can try to make it aesthetically pleasing, but you can't make it accurate without making it bigger and curved.

When you enlarge the photo and display it at the field of view it was captured at, as you can do in VR, the whole problem disappears and the photo just looks like the real world. Use two cameras and it'll even be in 3D.

If you drop the requirement that you have a reasonably-sized flat image, you can get a perfect representation... as long as you stand in exactly one spot to view it (or throw it into VR).

If you intentionally use a nonlinear perspective like the Turner painting in the article, you can get an image that looks great flat, and still produces a wide angle of view and "natural" dense of depth with low perceived distortion, and will look fine from across the room or up close. It probably does a better job of recreating what it is like to be there than a mechanical linear perspective photograph. The only problem is you can't get images like that out of a camera.

> As far as I know, the answer is simply that your eyes aren't rectilinear

That's true, but not the problem. Think about this logically. The goal is to show the exact same color at the same angle. If you achieve that (possible with VR, also possible with a normal photo but for a tiny angle only), it doesn't matter how the eye or processing in the brain warps the image afterwards.

Though you can't solve it to be geometrically correct, that doesn't mean you can't find a projection that is perceptually better than all the simple ones. That seems to be what artists are doing with their ad-hoc tweaks. TFA mentions a computerized one near the end that seems to be aiming for that too. Or you could imagine some clever ML algorithm that might treat different objects differently, not just remapping pixels blindly.

An easy way to make your point is to do what "artistic types" in e.g. cartoons do to make a viewfinder to estimate a shot: use your thumbs and forefingers in front of your face to make a rectangular "window." Now recognize how much smaller this window is than your field of view.

That's exactly how I came to understand the effect. I was looking at a picture of a sunset I had taken and wondering why the sun looked so much smaller than when I was there. I remembered that the sun, like the moon, is roughly the size of the thumbnail when the arm is completely stretched out, so I zoomed in the image until the sun was the right angular size, and the sizes of all the objects then appeared as in real life, only observed through tunnel vision.

While I was reading this article I actually pulled out my phone and moved it around near my eye until I could get the camera picture to 'line up' with its surroundings. It was indeed possible (and somewhat trippy), but the phone was about 2.5" from my eye. So yeah, assuming you're not holding your phone that close (as no one is, since few people can even focus that close, myself included,) it's going to be smaller than reality.

They mention this under the "What if there is no true perspective?" section:

Second, they point out that viewers almost always view pictures from the “wrong” location. A cornerstone of linear perspective is the idea that the viewer must be at the focal center of the image to view it correctly. If you view a linear perspective image from the focal center, it should be like looking through a window—indeed, Leonardo da Vinci wrote that linear perspective images only work from the focal center. Yet, in reality we don’t do this. Most of the photos we look at would have to be viewed with one’s eye a few inches from the page. People in art galleries walk all around and view paintings from all sorts of angles. Hence, the whole idea of linear perspective falls apart.

I think that's why you see people taking photos with their iPads, in many cases, it feels more real because it's a larger representation of the photo.

Photography + VR headsets will be interesting.

I'm wondering for years already, why there's no head mounted display for mirrorless

I love photospheres for this reason.

Damn, I haven't been outside properly and taken a nice photosphere in a long time.