Lossless upscaling and downscaling

[luquinhas0021]

Do you know some upscaling that keeps every detail, even the finest? You know some upscaling that adds true detail in final image (True detail, not noise)?
You know some downscaling that preserves all detail, even the finest?

Thank you.

[feisty2]

pointresize

[nevcairiel]

Its impossible to downscale and preserve "all" detail. The final image is smaller, therefor it won't be "lossless", and detail has to be dropped.
For upscaling, even though pointresize is technically "lossless", the resulting aliasing artifacts will not make for a pleasant image.

Resampling an image, up or down, is always a excercise in compromise. Retention of detail (aka sharpness) vs. reducing aliasing and ringing.

[Ghitulescu]

Downscaling is not possible in a lossless manner.

Upscaling is however possible, if the image is an integer multiple - for instance a pixel in the original image corresponds to 4 (2x2) or 9 (3x3) and so one pixels in the new image. Unless the viewing distance is increased, the visual appearance is bad - interpolation algorithms are way better.

[luquinhas0021]

Ghitulescu, is there loss of details when upscaling is a decimal multiple of source image? If yes, it must be because there is change of proportion of each patch of pixels, right?
Will downscaling to be lossless neither if I put image (Including its textures) on vector plane, to do downscaling and then back it for pixel values?
I didn't know point resize was lossless, but I already saw that alias image, but, anyway, Update: I've tested point resize. In fact, it introduces some aliasing and some blocking, but is neither so much and, taking off all this artifacts, without perceptive sharp loss, the result gets good.
Is Spline 100 lossless? I am asking because I've tested it and the results got better even than NNEDI3 under better parameters. And Spline 100 is the best Spline interpolation method, because makes the most sharpened results, without perceptible artifacts, unless those already was in image, but is well smooth. NNEDI3 is so slow, and a little unstable. Someone here knows if NeuronDoubler is top?
Now, about upscaling with true detail add: is there some? (True detail isn't seem like image noise)
Answer me all question, please!

Thank you

[feisty2]

spline 100? are you talking about 5 taps spline? it can be even sharper, let's say 100 taps (spline40000), it would be slow like hell and produce hell lot of ringings to your upscaled image, so more taps is not always better
resizers other than pointresize = pointresize + convolution, pointresize is lossless, convolution is not, end of the story
"upscaling with true detail add"...? yeah, that, that, that's THE RESIZER everyone wish he has, shame no one ever manages to make one.. maybe we'll have it with AI algorithms in the future

[filler56789]

Originally Posted by feisty2

—

resizers other than pointresize = pointresize + convolution, pointresize is lossless, convolution is not, end of the story
"upscaling with true detail add"...? yeah, that, that, that's THE RESIZER everyone wish he has, shame no one ever manages to make one.. maybe we'll have it with AI algorithms in the future

If you had written «digital sorcery» instead of "A.I.",
then I might agree with you

[Motenai Yoda]

Originally Posted by feisty2

resizers other than pointresize = pointresize + convolution

nope interpolation (bicubic/spline/lanzcos) works with interpolation polynomials.

[feisty2]

Originally Posted by Motenai Yoda

nope interpolation (bicubic/spline/lanzcos) works with interpolation polynomials.

If I'm understanding this correctly, lanczos is a windowed sinc, so clearly not polynomial (it got a "sin(x)" within)
And despite if the kernel (cubic, sinc, spline...) is polynomial or not, the actual process is blow the image up with pointresize first, and smooth the aliasings with a kernel next, and how that kernel works is convolve the image with the kernel function, so, a convolution, that's what i always thought about resizing, but correct me if I got the whole idea wrong

[luquinhas0021]

Feisty2, I talked about Spline 5 taps.
About upscaling with true details add... Wait the scenes of next chapters. No lies.

[colours]

Your posts are moderately incoherent so don't mind me if I'm misinterpreting them.

Ghitulescu, is there loss of details when upscaling is a decimal multiple of source image? If yes, it must be because there is change of proportion of each patch of pixels, right?

No, there will never be a loss of detail with nearest neighbour upsampling. It's just that nearest-neighbour upsampling by a noninteger factor makes things look visually bad.

Will downscaling to be lossless neither if I put image (Including its textures) on vector plane, to do downscaling and then back it for pixel values?

No, for the reason nevcairiel mentioned. It doesn't matter what algorithm is being used; a counting argument shows that this is impossible.

Is Spline 100 lossless? I am asking because I've tested it and the results got better even than NNEDI3 under better parameters. And Spline 100 is the best Spline interpolation method, because makes the most sharpened results, without perceptible artifacts, unless those already was in image, but is well smooth.

Depends on (a) your definition of "lossless" and (b) how exactly you're resampling. (Mathematically, it's an overdetermined linear system and hence reversible; practically, the limited numerical precision makes this not quite correct.) Though the more important question here really should be: why do you care about losslessness when it seems that your main priority is a nice-looking result?

Now, about upscaling with true detail add: is there some? (True detail isn't seem like image noise)

For every possible detail that can be added to an image on upscaling, there are infinitely many other possible details that can be added. Since there's no unique way of adding detail, we shouldn't expect any upscaling algorithm to be able to make this arbitrary decision.

[colours]

Originally Posted by feisty2

And despite if the kernel (cubic, sinc, spline...) is polynomial or not, the actual process is blow the image up with pointresize first, and smooth the aliasings with a kernel next, and how that kernel works is convolve the image with the kernel function, so, a convolution, that's what i always thought about resizing, but correct me if I got the whole idea wrong

Terminology weirdness aside, this is half correct. The image isn't blown up with a box filter; it's filtered directly.

[feisty2]

Originally Posted by colours

Terminology weirdness aside, this is half correct. The image isn't blown up with a box filter; it's filtered directly.

you are right, did some more search on Wikipedia and found new pixels are the weighted averaged results of the pixels around them, never again will I just take words from others only because they seem somehow reasonable, yeah, screwed up by rumor yet again.

[luquinhas0021]

Colours, I don'r express myself good when I said loss of details when I do a upscaling of decimal factor (Like 1.5 x 1.5 times). Really, the proportions of "lines" of every patch of pixels changes (Example: 1920 x 1080 (1:1.7778)) to 2048 x 1080 (1:1.896)), but, in fact, the details are stretched.
I'm not totally convinced that there's no way of exist some lossless downscaling, neither by to vector space conversion of image.
About true detail add upscaling... There's way of, at least, suppose the new details: if you consider every pixel just like a color, and this color is the mix of n other details (Other colors) and consider that the frame, whatever, is a image in real world and it is being seen by a human. As you might know, the human eye (Specifically the fovea centrallis) has a angular resolution that depends of wavelength and contrast, but, anyway, when I come n times closer, I will see n times more details, taking those initial dot. I considered just one eye because the image in computer is 2D (The 2 eyes, together, see 3D images). And I'm considering that all image is seen in fovea centrallis. This is impossible in practice, but is ideal, ideal for my idea and doesn't introduces artifacts (lol).
I can restrict the uncountable possibilities for the n other details that comes from one color when i do the neighborhood analysis. But, pay attention, for this method works well, is necessary a so fine Edge detector algorithm or a sum of information (True edges) of various edge detectors (And delete the artifacts that one Edge detector detects, but other doesn't, knowing that one type of edge detector detects some type (s) of artifact (s). The neighborhood analysis will be done in pixel that compose the edge, each one. Another neighborhood analysis will be done in pixel that are included in the edge . It's like a internal area of a circle. The question is if is necessary create new edges, and, if yes, where: included in pre-existent edge or in internal area of it, if exist it, course. Other question is what format of new edges will have.
Ben, I am still working on principle of my method, so i wish you help me with it, especially you, Colours, because you seem to be so wise.
Which the best edge detector? If not exist the best in every cases, which is the best in detect one and other type of edge?
Is there some edge detector that doesn't detect artifacts (Noise, aliasing, ringing, halo, jaggies,...)?

[colours]

Originally Posted by luquinhas0021

I'm not totally convinced that there's no way of exist some lossless downscaling, neither by to vector space conversion of image.

Okay, here's the counting argument. Say you have a picture with N samples (e.g. N = 3110400 for 1920×1080p YV12), and you want to reduce it to any fewer number of samples, M < N. There are 256^N possible input pictures, and there are 256^M output pictures, and since the latter is a smaller number, there can be no injective (or invertible) function from the set of N-sample pictures to any subset of the set of M-sample pictures.

It doesn't matter what kind of function you come up with. The pigeonhole principle denies you.

Now, it does turn out that if you try to vectorise a picture with a sufficiently sophisticated algorithm, you can indeed (sometimes) store the original picture with fewer bits than storing individual pixels. But this is just the concept of lossless compression. It doesn't mean that you can rasterise the vectors at a lower resolution, re-vectorise this, and then re-rasterise at a higher resolution to get back the original. The first rasterisation step is already lossy, thanks to the pigeonhole principle.

Originally Posted by luquinhas0021

About true detail add upscaling... There's way of, at least, suppose the new details: if you consider every pixel just like a color, and this color is the mix of n other details (Other colors) and consider that the frame, whatever, is a image in real world and it is being seen by a human.

Let's be clear here. Do you mean a convex combination, or just a "mix" in general? In the latter case, you could mix 0 and 1 to get any real number at all, and perhaps you don't already know this, but pretty much every decent rescaling/resampling algorithm uses nonconvex combinations.

Originally Posted by luquinhas0021

The 2 eyes, together, see 3D images

No. Two eyes see two 2D images.

Originally Posted by luquinhas0021

I can restrict the uncountable possibilities for the n other details that comes from one color when i do the neighborhood analysis.

You "can", but only in the sense that you have a non-uniform probability distribution for each sample based on some model you have of images. Which is not saying a lot, and brings me back to the exact same point I mentioned before: how can an algorithm magically know, given your model, which of these possibilities for each sample is the correct one? You could add detail, sure, but this detail would be meaningless unless it actually corresponds to, you know, real detail. And not something your algorithm pulled out of its arse.

Originally Posted by luquinhas0021

But, pay attention, for this method works well, is necessary a so fine Edge detector algorithm or a sum of information (True edges) of various edge detectors (And delete the artifacts that one Edge detector detects, but other doesn't, knowing that one type of edge detector detects some type (s) of artifact (s). The neighborhood analysis will be done in pixel that compose the edge, each one. Another neighborhood analysis will be done in pixel that are included in the edge . It's like a internal area of a circle. The question is if is necessary create new edges, and, if yes, where: included in pre-existent edge or in internal area of it, if exist it, course. Other question is what format of new edges will have.

I'm not sure what you're getting at here, but there's already a wealth of literature regarding edge-directed interpolation and the like.

Originally Posted by luquinhas0021

Which the best edge detector? If not exist the best in every cases, which is the best in detect one and other type of edge?
Is there some edge detector that doesn't detect artifacts (Noise, aliasing, ringing, halo, jaggies,...)?

Rule 12. Also, I don't recall if I bothered elaborating on this in the other thread, but a perfect edge detector basically cannot exist. Don't ask for the impossible.

[luquinhas0021]

No, Colours, the vision proportioned by two eyes together, and interpreted by the visual cortex, in brain, gives a 3D vision of the world. It's the stereoscopic vision.

The concept of mixing colors isn't mathematical itself, it's fisical.
Look at the color in extreme left (1 x 1) and compare it with 2 x 2 image. Looks like colors were demixed from 1 x 1 to 2 x 2, isn't? When we compare 2 x 2 and 5 x 5 image, we see white pixels. But white isn't seemed with blue. This makes me believe that when i have a upscaling of non-integer factor (Like 2 x 2 to 5 x 5; 5/2 = 2.5. So the upscaling is 2.5 times on line and 2.5 times on column), when we demixe the colors, the result is of image same colors pixels, but different intensities, and of image different colors pixels. If we don't want make mistake (Or intolerable mistake!), we talk the different colors are, usually, white or grey. It's clear it's just a example, but gives an idea of general. This images show us the bigger upscaling factor is, minor is the chance of suppose correctly the details.
Ben, i understood that doesn't exist a perfect edge detector.

My English still isn't very good. And i will continue improving my idea.

[feisty2]

and how are you planning to "demix" a color?
it's like a single equation (the color you wanna demix) with a lot of unknowns (the target image you'd like to get)
the equation you get is actually a curve running through a high dimensional space (the space would have dimensions the same amount of the unknowns in the equation)
you'll never get a constant solution from it

[luquinhas0021]

If I consider the color like being a sinusoidal wave, I can decompose that in it components using Fourier Transform. So the result won't be contant, but any result (Any demix) will be in result of Fourier Transform. Like I say, this project is still in beginner stage. I subscribe me in this forum for get help.
So i wish you, Colours and whoever that know about help me.

[feisty2]

A real and mathematically possible "color demixer" is a deconvolution algorithm, it's been used to "refocus" blurry photos. But still you can't use it to upscale images, it's like a sharp and detailed photo got blurred by some filter, now pixels in this blurred photo got smaller differences than the original one cause pixels were "mixed" with each other (but still they got different values, just the difference got smaller), and a deconvolution algorithm can "demix" these pixels and restore them to their original status. But it won't work on upscaling cause you don't have that many pixels to do it.

[luquinhas0021]

Ben, I'm not talking you are stupid, but, how says, one image worth it more than one thousand of words. In that case, more than one image! It's clear, especially in n x y to kn x ky upscaling (K is natural number), that the k x k resultant colors of one color included in n x y colors, are a demix of one that color (Or some so close to demix), and, somehow, the demix has some relationship with neighborhood. So I (Or we) have to know what is this relation and how colors are demixed.
I won't give up on my idea.