@Vitaliy I think the buckets analogy is flawed. I suppose the topic title does contain the word 'flame' so I should not expect too much. Sorry for wasting everyone's time.

@caveport, I don't have any allegiance to VK or anyone else...but I don't think he is saying that 2k10bit is an accurate representation of the source 4k8bit footage; all I see is simply that mathematically it really is 10bits of data coming from an 8bit down-sample.

That does not mean it solves the limitations of banding, loss of color info, or any of the other side effects of the source 8bit signal.

Correct or no? @Vitaliy_Kiselev

I have tried to show you, repeatedly, even using your own example, that while you can get CLOSE, it isn't (always) EXACT.

Close to what?

Did you spend time and without emotions just read that had been written?

It is also good to understand that it is discussion here no one is forcing someone to share any views.

So, be easy.

Yes you can get 10 bit data, but no, it will not look like 10 bit from a camera. End of speculation for me.... I don't guess, I test!

Cool, happy for you. It is just not test as it does not have properly defined procedure (add here that no one knows how exactly rescaling is being made) and is all but guess.

Re-scaling doesn't remove artifacts. That was always "wishful thinking" and had been proven already in this thread (page 3). The simple procedure that can be analogous to playing with buckets or balls is going to be the single least effective method of trying to get a free lunch with this stuff. There's no magic. It's not a problem that can really be solved with simple or clever spatial filtering alone.

@GlueFactoryBJJ In math, when you make a mistake, you can call it an "analogy," but it is still a mistake. A rounding calculator will correctly reverse an irrational number, and the same is true from digital audio or video, if the code is written properly. Furthermore, an irrational, if algebraic, is easily reversible.

As far as "identical" goes, there are of course different scenarios depending on dither. You can have two images that are absolutely identical, with the same dither, but which are mathematically different because the dither, although unobservable, is produced by a random number generator in some cases. In this case the math is useless as toll to test whether the images are the same, or produced "losslessly".

@GlueFactoryBJJ no one is saying you are lying, I am simply voicing my opinion that your math is not correct as far as digital media goes. We have a difference of opinion. I explained that the way effects are calculated using placeholders, and I explained why these placeholders allow the NLE to reconstruct exactly algebraic processes. The NLE will not calculate the series to infinity, it will use one of several different systems to deal with that last digit. Now, I could be wrong and you could be right, and my calculator could also be wrong, and my DAW as well. I actually never really wondered about that, I just went as far as checking that if I burn a CD or render an MP3 I get the same "number" each time (which is impossible with dither, for obvious reasons).

Windows calculator: how to use.

1. Open calculator. Click view, select "scientific"

2. Type 2, then the square root button, you will see a long number, but you will see a superscript showing that the computer is recognizing an algebraic process.

3. Click the x2 button

4. View the correct answer, which is 2, exactly

As for rounding, all digital media uses rounding and/or dither to shape the last bit. If you have alternative, I don't know what that would be, but you are welcome to develop your own system. It would be difficult to design a system that holds an infinite number of placeholders, but perhaps by using a closed logic system with a non-binary base you could do that. However, such a system would give you the same results as the one currently in use.

There is an alternative to rounding/dither which is truncation. Truncation means simply that you throw the last digits away. Certainly an interesting question as to whether in a high bit space any human could tell whether the last bits were dithered or truncated.

As far as using extra data from downsizing to recreate the extra bits, I would be convinced by a mathematical demonstration of the exact process so if you have one, I would be interested in seeing it.