This point is getting a little trivial and don't want to start a huge discussion but if you take 1080p video and display it on a UHD monitor it only occupies 1/4 of the screen which means it's only 25% of the resolution of UHD. You would have to increase it's area by 4X to cover the entire UHD screen. It's really not that complicated in my mind. Doubling the sides of a rectangle increases it's area by 4X. UHD has 4X as many pixels as 1080p and therefore has 4X the resolution.
On the differences between standards, the standards I'm referring to is the one sold with most 4K HDTV's these days which translates to 2160p (twice 1080p).
On the difference in human perception between 4K and 2K, that doesn't really affect the 4X difference in resolution either. An increase of resolution of video does not necessarily have a proportional increase in human perception, but that does not affect the true resolution. And imaging tools can take full advantage of the true resolution.
The point IS trivial but you still have to keep saying its 4x Resolution.
Ive just had a look whats about on this. Look up books like "
Don't confuse pixel numbers with resolution! "
There are many text books and papers on this, im sure that they can put it across to you much better than I can.
Your thinking it terms of AREA each time, I agree with you that there is 4x the information(pixels) HD to 4K, BUT,
this is not the resolution ratio.
A
flat object of course always has 2 dimensions.
BOTH these dimensions
gobble up information and I think that's where you are going wrong.
Try this, imagine you have a 1.77
test card set up on a wall.
You point your 4K camera at it, you set your zoom to
2x.
You have the camera connected to a 4K TV.
You look at the TV and move the camera tripod to a position where the test card fills the screen.
The test card will now occupy a pixel area of 3840 by 2160 on the TV screen and the zoom is set to 2x.
You now zoom out back to unity 1x.
What area (pixel by pixel) do you think the test card NOW occupies within the 4K TV
Its 1920 by 1080, i.e. a 4x reduction in pixels but a 2x actual reduction.
You have now reduced the info (pixels) for each object seen by 4, i.e. you have reduced the
Resolution by 2
Now reverse it and zoom from 1x to 2x, the test card will go from 1920 by 1080 to 3840 by 2160, a 4x increase in Pixels but only a 2x increase.
And most important of all, QED for this is that a 4K camera can resolve an object ONLY half the size of the smallest object the HD Camera can resolve.
ONLY, i.e. no smaller. i.e. has twice the resolution.
If as you think, the resolution is 4x then this would NOT be the case.