Future application of fractal maths in computer...imaging (I think) *spawn

[steampoweredgod]

Mod: AlStrong's post was in reply to the idea of supersampling by rendering a game at higher resolution and downsampling to display resolution.

Of course.

Well, you're increasing the texture sampling and shading requirements linearly.

while it was a bit too computationally expensive, years ago on traditional hardware, fractal video compression yields abstract vectorization of arbitrary image detail, yielding perfect resolution independence such that resolution no longer affects quality, akin to vector graphics fractal formula now describe proportions and relations between image components.

One would think algorithm advance and hardware advance would've already made it practical for real time by now, as resolution independence guarantees perfect scaling, but such may still be a few years away(nay maybe even the perpetual 5 years into the future).

Resolution independence is the key here.


note 1 brain is said to've fractal structure
note 2 biologists say form and function are related
note 3 prediction and general intelligence linked by hawkins in book on intelligence
note 4 fractal make perfect receiver, emitter, antenna, and likely compression of message

 

[Shifty Geezer]

while it was a bit too computationally expensive, years ago on traditional hardware, fractal video compression yields abstract vectorization of arbitrary image detail, yielding perfect resolution independence

You're having a giraffe, right? "Perfect resolution independence"?? You cannot describe missing detail with a fractal formula, unless you're original material was created in a way that matches a fractal description. Enlarging with a fractal upscaling algorithm removes the obvious blocks and produces something that has detail, but it's not the same detail that the source had. You cannot take a photograph of a beach scene and use fractals to zoom in on a person and recreate their face, and then zoom in on the reflection in their sunglasses of the paper they were reading to read the text!

One would think algorithm advance and hardware advance would've already made it practical for real time by now, as resolution independence guarantees perfect scaling, but such may still be a few years away(nay maybe even the perpetual 5 years into the future).

Fractal upscaling is always going to be massively more complex than a simple blinear or bicubic upscale. It makes more sense to invest processing time elsewhere (shading, blending multiple textures for variety) than making a few textures look less blurry up close.

 

[steampoweredgod]

You're having a giraffe, right? "Perfect resolution independence"?? You cannot describe missing detail with a fractal formula, unless you're original material was created in a way that matches a fractal description. Enlarging with a fractal upscaling algorithm removes the obvious blocks and produces something that has detail, but it's not the same detail that the source had. You cannot take a photograph of a beach scene and use fractals to zoom in on a person and recreate their face, and then zoom in on the reflection in their sunglasses of the paper they were reading to read the text!

view the VIDEO FOR AN arbitrary photo, an ARBITRARY IMAGE, an arbitrary video A CORRESPONDING FRACTAL FORMULA can be automatically detected. Details that are not present or detectable will simply not appear in the final image it would be as if there were only sand in the area if the captured image did not have detail enough to capture a ball, person, etc lying in the sand, the resolution is infinite(but it won't obviously generate what ain't there, imagine a painter he can obviously scale an image arbitrarily large without pixelation, of course when he does this he won't actually add things that ain't originally implicitly there if he wants to be FAITHFUL to original in scaling).

as for zooming in the other video shows that microscopic biological structure can be deduced through fractal analysis yielding vasculature details, below the level of the instrument used.

In the full documentary, Arthur c. Clarke comments that fractal theory will likely be necessary to understand the workings of the brain and mind if they are ever understood, and it does appear vital in truth towards a new kind of artificial intelligence, a true artificial intelligence or artificial general intelligence.

 

[steampoweredgod]

Fractal upscaling is always going to be massively more complex than a simple blinear or bicubic upscale. It makes more sense to invest processing time elsewhere (shading, blending multiple textures for variety) than making a few textures look less blurry up close.

Except for the fact that it ain't that complex, it is simplicity. let's give the quote one moment please.

And it allows infinite zoom in and zoom out.

edit moment has passed

“Bottomless wonders spring from simple rules repeated without end.”-Mandelbrot

It is the simplicity that it brings towards objects of infinite complexity that makes it special.

 

[Shifty Geezer]

view the VIDEO FOR AN arbitrary photo, an ARBITRARY IMAGE, an arbitrary video A CORRESPONDING FRACTAL FORMULA can be automatically detected.

No, it can't. Are you talking the parrot image, or something else? The zoom of the parrot image hasn't any feather detail - it's just noise in a randomised fashion that adds a sense of detail, but it's not true information and it doesn't match the real world source.

Take Marilyn Monroe, for example. Consider a photograph taken of her from a distance, so her face fills but a few pixels. How does your algorithm know to recreate her face in the correct proportions as it's blown up? More importantly, how does it know there's a tiny mole to add when that data was not recorded in any measurable way in the source data?

 

[steampoweredgod]

No, it can't. Are you talking the parrot image, or something else? The zoom of the parrot image hasn't any feather detail - it's just noise in a randomised fashion that adds a sense of detail, but it's not true information and it doesn't match the real world source.

Take Marilyn Monroe, for example. Consider a photograph taken of her from a distance, so her face fills but a few pixels. How does your algorithm know to recreate her face in the correct proportions as it's blown up? More importantly, how does it know there's a tiny mole to add when that data was not recorded in any measurable way in the source data?

the guy said it, the guy with the 2+ million grant and probably advanced graduate degree and I've his book right here too... and it has also been done for the mona lisa link

Even arbitrary video compression was in the works but is being hindered by software patents(thank congress for this).

Regards zoom in zoom out, for example if no pore structure in skin was detectable in original image zoom in will just provide smooth color with no structure.

Take Marilyn Monroe, for example. Consider a photograph taken of her from a distance, so her face fills but a few pixels. How does your algorithm know to recreate her face in the correct proportions as it's blown up? More importantly, how does it know there's a tiny mole to add when that data was not recorded in any measurable way in the source data?

An artist can faithfully blow up or scale up the image without adding any new detail nor pixelating the work. IT will only provide the information that was originally implicitly there no more

 

[Shifty Geezer]

(but it won't obviously generate what ain't there, imagine a painter he can obviously scale an image arbitrarily large without pixelation, of course when he does this he won't actually add things that ain't originally implicitly there if he wants to be FAITHFUL to original in scaling).

So it's not perfectly resolution independent, as the information is constrained to a real-world resolution and everything beyond that is interpolation.

as for zooming in the other video shows that microscopic biological structure can be deduced through fractal analysis yielding vasculature details, below the level of the instrument used.

Yeah, great, when your source material is constructed in a fractal way.

In the full documentary, Arthur c. Clarke comments that fractal theory will likely be necessary to understand the workings of the brain and mind if they are ever understood.

So because a fiction writer suggests a scientific theory regards understand the human brain, we should take that as proof positive that fractal compression can solve storage needs next-gen?

Except for the fact that it ain't that complex, it is simplicity. let's give the quote one moment please.

And it allows infinite zoom in and zoom out.

Of limited detail! It's as exciting as an .svg clipart being infinitely zoomable, only beyond certain zoom you'll just see a nice edge. Zoom in on a fractally compressed image 1000x, and you'll just have a screen of coloured noise as four pixels as interpolated, of no practical worth. The real-world benefits of fractal compression are decidedly finite.

And none of this has anything to do with next-gen antialiasing.

 

[steampoweredgod]

So it's not perfectly resolution independent, as the information is constrained to a real-world resolution and everything beyond that is interpolation.

It is perfect, you're asking for it to introduce information that wasn't originally there, and there is an infinity of things that could be put as such... it is impossible to do so in any rational manner, if the info ain't there it ain't there. You can't say it can't produce information that ain't there so it ain't perfectly representing what is there.

So because a fiction writer suggests a scientific theory regards understand the human brain, we should take that as proof positive that fractal compression can solve storage needs next-gen?

Brain information processing and transmiting, fractal structure.
Perfect antenna, fractal antenna.

note 1 brain is said to've fractal structure
note 2 biologists say form and function are related-steampoweredgod

Hmmm, take it as you will.

And if there are patents abound, you ain't got the option but to license or not use at all.

Besides the title is antialiasing or image quality, this ain't the thread on storage.

Next gen tvs are 4k displays, that will hog too much resources unless you do resolution independent representation

Of limited detail! It's as exciting as an .svg clipart being infinitely zoomable, only beyond certain zoom you'll just see a nice edge. Zoom in on a fractally compressed image 1000x, and you'll just have a screen of coloured noise as four pixels as interpolated, of no practical worth. The real-world benefits of fractal compression are decidedly finite.

Resolution independence means it will look the same on a 4k display as on a 2k or 1k display.

Next you'll be telling me vector graphic representation of text is useless as it doesn't add additional nonexistent information.

PS

This is in a way similar to tesselation, what is put there is represented(with tesselation you can also do infinite zoom ins and zoom outs) but you can't expect nonexistent even implicitly info to appear

So in case where one want's to get rid of sampling artifacts and general increase of sampling cost, you want to introduce a shader which adds an extra layer of high frequency noise on top of everything else.

Brain algorithmics add immense amounts of noise at every level and quite frankly trounces all other algorithmic procedures.

 

[Shifty Geezer]

the guy said it, the guy with the 2+ million grant and probably advanced graduate degree and I've his book right here too... and it has also been done for the mona lisa link.

That is lossy compression, like JPEG or Wavelet, only with a different mathematical breakdown. Zoom in on that fractal image on the Mona Lisa 1000 times and will you recreate the original? No. The resolution is accurate to the original sampling resolution. Upscaling beyond that creates an approximation of decreasing accuracy, until you end up with a subtly varying screen of colour where you've stretched 4 pixels to 1920x1080 to fill the screen.

So what are the benefits to implementing fractal textures in games? You could walk up to a wall and have detail interpolated from a small source file which would look better than a lowish resolution texture with a simple upscale. That'd be good. But it'd also come at considerable cost in performance - it's got to be at least one order of magnitude slower than a LERP between a few samples. and now with the prospect of megatexturing, developers could create incredibly detailed scenes, using offline fractal formula to help should they choose, while having a low processing-performance requirement to implement and render trading that for storage, meaning more processing for other things.

 

[steampoweredgod]

That is lossy compression, like JPEG or Wavelet, only with a different mathematical breakdown. Zoom in on that fractal image on the Mona Lisa 1000 times and will you recreate the original? No. The resolution is accurate to the original sampling resolution. Upscaling beyond that creates an approximation of decreasing accuracy, until you end up with a subtly varying screen of colour where you've stretched 4 pixels to 1920x1080 to fill the screen.

So what are the benefits to implementing fractal textures in games? You could walk up to a wall and have detail interpolated from a small source file which would look better than a lowish resolution texture with a simple upscale. That'd be good. But it'd also come at considerable cost in performance - it's got to be at least one order of magnitude slower than a LERP between a few samples. and now with the prospect of megatexturing, developers could create incredibly detailed scenes, using offline fractal formula to help should they choose, while having a low processing-performance requirement to implement and render trading that for storage, meaning more processing for other things.

In a sense the benefits are the same as using tessellation, that's about as simply as I can put it. You may say it adds nothing but hogs resources but others may disagree.

Besides who the hell is going to play by infinitely zoomin in the camera? That feature need not be of use or practicality for the benefits of resolution independence to emerge and aid.

 

[Shifty Geezer]

It is perfect, you're asking for it to introduce information that wasn't originally there, and there is an infinity of things that could be put as such... it is impossible to do so in any rational manner, if the info ain't there it ain't there. You can't say it can't produce information that ain't there so it ain't perfectly representing what is there.

Maybe that's not what you meant (it's very hard to understand you as you throw in unrelated pointers to a general theory instead of talking through the actual subject,hence this wild topic derailment), but then that makes your point moot anyway.

If the fractal image cannot be upscaled with infinite detail, then for full accuracy you need an image of the original size, right? So for a perfect 4k image, you'd need a 4k texture. That same 4k texture will look the same on 2k and 1k sets as it's downscaled, because averaging information to lower densities preserves the information. The only advantage of a fractal image is it'll compress small (like JPEG2000) and then upscale with an inherent interpolation that makes moderate upscaling, like 2x-4x, more pleasing to the eye than a straight bilinear interpolation. Which is nice, but it's also costly, and not the only way of doing things. One could also encode with wavelet, say, and then add some algorithmic processing to make the upscale better. And in that regard, procedural, analytical upscaling is likely to be better than fractal upscaling, because you can derive more detail approximations from neightbouring pixels and past/future pixels and generate inbetween pixels in a less-generalised manner.

So what's the benefit of fractal textures/images that you're proposing in contrast to AlStrong's point about supersampling an image being costly? You're suggesting that a game is rendered at 720p, fractally encoded, and then upscaled to 4k? That's just proposing a fancy upscaler.

 

[steampoweredgod]

Maybe that's not what you meant (it's very hard to understand you as you throw in unrelated pointers to a general theory instead of talking through the actual subject,hence this wild topic derailment), but then that makes your point moot anyway.

If the fractal image cannot be upscaled with infinite detail, then for full accuracy you need an image of the original size, right? So for a perfect 4k image, you'd need a 4k texture. That same 4k texture will look the same on 2k and 1k sets as it's downscaled, because averaging information to lower densities preserves the information. The only advantage of a fractal image is it'll compress small (like JPEG2000) and then upscale with an inherent interpolation that makes moderate upscaling, like 2x-4x, more pleasing to the eye than a straight bilinear interpolation. Which is nice, but it's also costly, and not the only way of doing things. One could also encode with wavelet, say, and then add some algorithmic processing to make the upscale better. And in that regard, procedural, analytical upscaling is likely to be better than fractal upscaling, because you can derive more detail approximations from neightbouring pixels and past/future pixels and generate inbetween pixels in a less-generalised manner.

So what's the benefit of fractal textures/images that you're proposing in contrast to AlStrong's point about supersampling an image being costly? You're suggesting that a game is rendered at 720p, fractally encoded, and then upscaled to 4k? That's just proposing a fancy upscaler.

Fractals have infinite complexity, infinite detail and infinite resolution and can be infinitely upscaled according to those involved in fractal mathematics. The fractal image is an image of infinite detail that is downscaled to a finite representation, no matter how high your resolution a wall covered with ipad retina display, is still a lower resolution than infinity.

Now that you believe that infinite resolution is meaningless and unrelated in a thread about resolution and image quality, then I stand i sheer awe, amazement, and bewilderment.

 

[Shifty Geezer]

Besides who the hell is going to play by infinitely zoomin in the camera? That feature need not be of use or practicality for the benefits of resolution independence to emerge and aid.

You never actually expressed what your application of fractals was going to be in the context of rendering a game, so the only point of discussion I had was your claim to infinite resolution being practically useful.

(And you can you please start using real English? "That feature need not be of use or practicality for the benefits of resolution independence to emerge and aid," is grammatical gibberish, and unnecessarily verbose like legalese.)

 

[steampoweredgod]

You never actually expressed what your application of fractals was going to be in the context of rendering a game, so the only point of discussion I had was your claim to infinite resolution being practically useful.

(And you can you please start using real English? "That feature need not be of use or practicality for the benefits of resolution independence to emerge and aid," is grammatical gibberish, and unnecessarily verbose like legalese.)

That is english as it is becoming. In any case the point stands that feeding 4k displays or retina(ipad) walls would require insane resources, fractal representations and algorithms(which again can be further progressed and developed, don't say what the early versions could or could not do, but what the future more evolved algorithms will do.) would aid via resolution independence(infinite resolution mathematical representation) in the way that vector representation would aid in text presentation..

 

[Shifty Geezer]

Fractals have infinite complexity, infinite detail and infinite resolution and can be infinitely upscaled according to those involved in fractal mathematics. The fractal image is an image of infinite detail that is downscaled to a finite representation.

I know that. We all know that. You can 'zoom' into a fractal indefinitely. But if your fractal is expressing something that's not relevant to the image, then it's no use. Imagine if each pixel of an FPS game was somehow encoded with a Mandlebrot Set, so as you zoom in 1000x you start to see the familar Mandelbrot shapes. You could zoom in forever to infinite detail, but it'd all be pointless as it has nothing to do with the FPS game or detail. We'd only be interested in the ability of the fractal to describe the pixels of the game. If they could be enlarged preserving the detail, that'd be great, but they can't. And a fractal's ability to downscaled is immaterial as we can downscale a bitmap just fine. What actual relevance has this infinie detail got to the task at hand then? Rather than point to fractal antennae and fractal fractal biological structures, give a real-world application of fractal-encoding in the game situation where it'll be useful. This is, after all, a 3D graphics forum.

 

[steampoweredgod]

I know that. We all know that. You can 'zoom' into a fractal indefinitely. But if your fractal is expressing something that's not relevant to the image, then it's no use. Imagine if each pixel of an FPS game was somehow encoded with a Mandlebrot Set, so as you zoom in 1000x you start to see the familar Mandelbrot shapes. You could zoom in forever to infinite detail, but it'd all be pointless as it has nothing to do with the FPS game or detail. We'd only be interested in the ability of the fractal to describe the pixels of the game. If they could be enlarged preserving the detail, that'd be great, but they can't. And a fractal's ability to downscaled is immaterial as we can downscale a bitmap just fine. What actual relevance has this infinie detail got to the task at hand then? Rather than point to fractal antennae and fractal fractal biological structures, give a real-world application of fractal-encoding in the game situation where it'll be useful. This is, after all, a 3D graphics forum.

Look dude you see the image of the eye by the eye in the pic of the eye of the youtube vid. You say it is lossy, but see it clearly, the original pixelated one is the one that looks lossy in comparison.

That's as perfect as it gets and it can be modified such that infinite zoom in produces continuous lines and change and not randomness, fractals have intrinsic underlying order or simplicity.


If instead of using it to try and compress but instead to try and represent faithfully the algorithms would likely be subject to modification. Any apparent short comings at present may merely be due to the idea of trying to do aggressive compression.

 

[Shifty Geezer]

That is english as it is becoming. In any case the point stands that feeding 4k displays or retina(ipad) walls would require insane resources, fractal representations and algorithms(which again can be further progressed and developed, don't say what the early versions could or could not do, but what the future more evolved algorithms will do.) would aid via resolution independence(infinite resolution mathematical representation) in the way that vector representation would aid in text presentation..

Right! You've finally expressed a problem and how fractals can help with it. And you are right. Except, as I say, we can use alternative upscaling algorithms. Fractal encodes don't necessarily have the advantage. The current, principle implementation of the early fractal research that I know of is the GenuineFractals upscaling PhotoShop plugin, that does a good job, but can still be rivalled by other methods. When tackling higher-resolutions (no different to this gen rendering sub-HD and upscaling), there are penty of possible approaches, especially for a simple quadrupling of pixel resolution.

 

[steampoweredgod]

Right! You've finally expressed a problem and how fractals can help with it. And you are right. Except, as I say, we can use alternative upscaling algorithms. Fractal encodes don't necessarily have the advantage. The current, principle implementation of the early fractal research that I know of is the GenuineFractals upscaling PhotoShop plugin, that does a good job, but can still be rivalled by other methods. When tackling higher-resolutions (no different to this gen rendering sub-HD and upscaling), there are penty of possible approaches, especially for a simple quadrupling of pixel resolution.

Try and handle a a retina(ipad) wall if you can.

In information transmission, reception and emission, fractal is perfect exact mathematical solution.

All in the computer is information, it is very possible that fractal encoding is also perfect method, though this has yet to be seen.

Remember that the brain is nothing more than a network, which seems to use fractal structure in its design.

Infinite resolution will always surpass any finite resolution however big.

 

[Shifty Geezer]

Look dude you see the image of the eye by the eye in the pic of the eye of the youtube vid. You say it is lossy, but see it clearly, the original pixelated one is the one that looks lossy in comparison.

Lossy means information is removed. Fractal encoding removes original information, just like JPEG. It replaces it with other information that approximates the source, which in this case intrinsically interpolates 'detail'. I look at the results of that upscale and I see blocks of colour with a bit of blur and edge disruption. It's nothing like that eye would look if taken at the high detail. It's just a fancy upscale.

If instead of using it to try and compress but instead to try and represent faithfully the algorithms would likely be subject to modification.

Okay, if not compressing it could be used to ecnode an original at full quality and then upscale it by interpolating information. That's still just a fancy upscaler though, and a cmoputational expensive one. GenuineFractals has been around since 1997, and its results are still obviously upscaled. The original pixels can still be seen in the results, only splodged around a bit to break up their edges, as it were. There is no regeneration of crisp detail. The only way you get that is to capture more information, or to render more information. That's why current graphics are representations of vectors, and not bitmaps. We already have perfect zoom and such, of finite datasets limiting what we can do and the qualities we can achieve. Fractals aren't going to solve that because they are limited in the types of information they can express.

 

[steampoweredgod]

Lossy means information is removed. Fractal encoding removes original information, just like JPEG. It replaces it with other information that approximates the source, which in this case intrinsically interpolates 'detail'. I look at the results of that upscale and I see blocks of colour with a bit of blur and edge disruption. It's nothing like that eye would look if taken at the high detail. It's just a fancy upscale.

Okay, if not compressing it could be used to ecnode an original at full quality and then upscale it by interpolating information. That's still just a fancy upscaler though, and a cmoputational expensive one. GenuineFractals has been around since 1997, and its results are still obviously upscaled. The original pixels can still be seen in the results, only splodged around a bit to break up their edges, as it were. There is no regeneration of crisp detail. The only way you get that is to capture more information, or to render more information. That's why current graphics are representations of vectors, and not bitmaps. We already have perfect zoom and such, of finite datasets limiting what we can do and the qualities we can achieve. Fractals aren't going to solve that because they are limited in the types of information they can express.

It is believed by many, even some of the greatest of minds of the past and present, that the universe itself may be a mathematical structure.

If reality itself turns out to be fractal in nature. you will find that an exact representation will also be fractal in nature.