"NVIDIA researchers have successfully trained a neural network to find
these jagged edges and perform high-quality anti-aliasing by
determining the best color for each pixel, and then apply proper
colors to create smoother edges and improve image quality. This
technique is known as Deep Learning Super Sample (DLSS). DLSS is like
an “Ultra AA” mode-- it provides the highest quality anti-aliasing
with fewer artifacts than other types of anti-aliasing.
DLSS requires a training set of full resolution frames of the aliased
images that use one sample per pixel to act as a baseline for
training. Another full resolution set of frames with at least 64
samples per pixel acts as the reference that DLSS aims to achieve."
https://developer.nvidia.com/rtx/ngx
At first I thought of sample as it is used in graphics, an intersection of channel and a pixel. But that really doesn't make any sense in this context, going from 1 channel to 64 channels ?
So I am thinking it is sample as in the statistics term but I don't understand how a static image could come up with 64 variations to compare to? Even going from FHD to 4K UHD is only 4 times the amount of pixels. Trying to parse that second paragraph I really can't make any sense of it.
16 bits × RGBA equals 64 samples per pixel maybe? They say at least, so higher accuracy could take as much as 32 bits × RGBA or 128 samples per pixel for doubles.
Books and tutorials on genetic algorithms explain that encoding an integer in a binary genome using Gray code is often better than using standard base 2. The reason given is that a change of +1 or -1 in the encoded integer, requires only one bit flip for any number. In other words, neighboring integers are also neighboring in Gray code, and the optimization problem in Gray encoding has at most as many local optima as the original numeric problem.
Are there other benefits to using Gray code, compared to standard base 2?
Gray Encoding is used to avoid the occurrences of Hamming Walls. As explained in this paper, Section 3.5.
Basically A Hamming wall is a point at which it becomes rare or highly unlikely that the GA will mutate in exactly the right way to produce the next step in fitness.
Due to the properties of Gray Coding, this is much less likely to happen.
Apologies in advance, but this isn't really a photoshop question. Rather, I'm trying to come up with something that is convincing but exploits the compression and features of the gif format as best as possible to produce the smallest possible file for the animation.
Some constraints:
It needs to be at least 20 or 30 frames. I've tried with fewer (and since they're largely uncompressable 15 frames is half the size of 30, generally speaking)
Size needs to be no less than about 256x192
It doesn't need to be color though, nor even full grayscale. I've seen convincing stills with as few as about 16 grays
It can have a pattern, but not one that is instantly obvious to the human eye. If someone takes a single frame and after a minute or two can spot the pattern (which makes it compressable?) that's ok
Frames 2 through n can use quite a bit of alpha, but when I started using big horizontal stripes of alpha, it was instantly noticeable to my eyes. So you don't get to rack up a bunch of RLE with the easy cheat.
All of the above and still needs to look good at 30-33ms frame speed. No variable speed or relying on anything significantly faster than that.
Also acceptable: an apng that complies with the above constraints. Possibly even mpeg, if you can come up with that (I'm ignorant of how the DCT does its magic).
Ideally I could get something down in the 250kbyte range, but I'd settle for anything significantly smaller than the 9 meg monstrosity I cooked up last week.
Oh, and one last thing: obviously I don't expect anyone to supply the graphic for me. I'm just looking for some trick(s) that will let me get there myself eventually.
This is a very interesting question.
Static (random noise) by its nature is actually highly incompressible. Information theory says that true noise is basically incompressible, and the more patterns something contains the more compressible it becomes (to the point of a solid line of 1's or 0's being perfectly compressible.
The ideal would be to create a true noise generator (just random numbers), but that doesn't help within the constraints of your problem.
The best thing I can think of is storing a number of small tiles of static and displaying them in staggered fashion to prevent the eye catching on to any patterns. Aside from that, you won't have much luck compressing this beyond 256 x 192 x 20 / 2 or about 500 kilobytes ( assuming 20 frames with resolution of 256 x 192, using 4 bit color depth ).
Simply encoding your animated gif in 16 color mode should get you to that point.
Well old but still unanswered answer (not checked anyway)
so create the NoSignal image data
If it is not obvious how read this:
NoSignal in asm and C++
encode into gif
Had played with it a bit so I used resolution 320x240, the lowest bit resolution usable is 3 bit per pixel. Lower does not look good. Single global palette only (obvious) here 300KB example
[Notes]
if this is just for some app then generate the image on the run it is really just few lines of code see that linked answer in bullet #1
Yes, you can achieve that with a lossy GIF compression, or rather a specifically rigged compressor that outputs noisy LZW stream.
A best-case scenario for LZW compression is to output X pixels, then X+1 pixels, then X+2 pixels, etc. It's easy to make that noisy.
Try screwing up the gfc_lookup function to (almost) always return longest dictionary item and compress series of noisy frames with it:
https://github.com/pornel/giflossy/blob/master/src/gifwrite.c#L270
Not easily normally. Good randomness (high entropy) by definition does not compress well. Having it greyscale may help, but not much.
If you want to do this on a web page and you have (some) control, you can always write a very small bit of JS to help... if you can do this, then you can do the following:
Create a gif about 1.5x the size you need with high-entropy static.
Set the clipping to the size you want.
Then you randomly move it around by changing the starting offset.
As long as your offsets are a decent distance away from one another (and don't repeat patterns) it is usually difficult to discern it as movement, and it looks truly like static.
I did this trick about 20 years ago on an Amiga to emulate static on a limited-memory demo, and it worked remarkably well... it also does not require fast low-level code as all was done by changing offsets and the co-processor bitblit-ed the rest.
I'm attempting to write a short mini-program in Python that plays around with force-based algorithms for graph drawing.
I'm trying to minimize the number of times lines intersect. Wikipedia suggests giving the lines an electrical charge so that they repel each other. I asked my physics teacher how I might simulate this, and she mentioned using calculus with Coulomb's Law, but I'm uncertain how to start.
Could somebody give me a hint on how I could do this? (Or alternatively, another way to tweak a force-based graph drawing algorithm to minimize the number of times the lines cross?) I'm just looking for a hint; no source code please.
In case anybody's interested, my source code and a youtube vid I made about it.
You need to explicitly include a term in your cost function that minimizes the number of edge crossings. For example, for every pair of edges that cross, you incur a fixed penalty or, if the edges are weighted, you incur a penalty that is the product of the two weights.
Does anyone have any good references for equations which can be implemented relatively easily for how to compute the transfer of angular momentum between two rigid bodies?
I've been searching for this sort of thing for a while, and I haven't found any particularly comprehensible explanations of the problem.
To be precise, the question comes about as this; two rigid bodies are moving on a frictionless (well, nearly) surface; think of it as air hockey. The two rigid bodies come into contact, and then move away. Now, without considering angular momentum, the equations are relatively simple; the problem becomes, what happens with the transfer of angular momentum between the bodies?
As an example, assume the two bodies have no angular momentum whatsoever; they're not rotating. When they interact at an oblique angle (vector of travel does not align with the line of their centers of mass), obviously a certain amount of their momentum gets transferred into angular momentum (i.e. they each get a certain amount of spin), but how much and what are the equations for such?
This can probably be solved by using a many-body rigid system to calculate, but I want to get a much more optimized calculation going, so I can calculate this stuff in real-time. Does anyone have any ideas on the equations, or pointers to open-source implementations of these calculations for inclusion in a project? To be precise, I need this to be a rather well-optimized calculation, because of the number of interactions that need to be simulated within a single "tick" of the simulation.
Edit: Okay, it looks like there's not a lot of precise information about this topic out there. And I find the "Physics for Programmers" type of books to be a bit too... dumbed down to really get; I don't want code implementation of an algorithm; I want to figure out (or at least have sketched out for me) the algorithm. Only in that way can I properly optimize it for my needs. Does anyone have any mathematic references on this sort of topic?
If you're interested in rotating non-spherical bodies then http://www.myphysicslab.com/collision.html shows how to do it. The asymmetry of the bodies means that the normal contact force during the collision can create a torque about their respective CGs, and thus cause the bodies to start spinning.
In the case of a billiard ball or air hockey puck, things are a bit more subtle. Since the body is spherical/circular, the normal force is always right through the CG, so there's no torque. However, the normal force is not the only force. There's also a friction force that is tangential to the contact normal which will create a torque about the CG. The magnitude of the friction force is proportional to the normal force and the coefficient of friction, and opposite the direction of relative motion. Its direction is opposing the relative motion of the objects at their contact point.
Well, my favorite physics book is Halliday and Resnick. I never ever feel like that book is dumbing down anything for me (the dumb is inside the skull, not on the page...).
If you set up a thought problem, you can start to get a feeling for how this would play out.
Imagine that your two rigid air hockey pucks are frictionless on the bottom but have a maximal coefficient of friction around the edges. Clearly, if the two pucks head towards each other with identical kinetic energy, they will collide perfectly elastically and head back in opposite directions.
However, if their centers are offset by 2*radius - epsilon, they'll just barely touch at one point on the perimeter. If they had an incredibly high coefficient of friction around the edge, you can imagine that all of their energy would be transferred into rotation. There would have to be a separation after the impact, of course, or they'd immediately stop their own rotations as they stuck together.
So, if you're just looking for something plausible and interesting looking (ala game physics), I'd say that you could normalize the coefficient of friction to account for the tiny contact area between the two bodies (pick something that looks interesting) and use the sin of the angle between the path of the bodies and the impact point. Straight on, you'd get a bounce, 45 degrees would give you bounce and spin, 90 degrees offset would give you maximal spin and least bounce.
Obviously, none of the above is an accurate simulation. It should be a simple enough framework to cause interesting behaviors to happen, though.
EDIT: Okay, I came up with another interesting example that is perhaps more telling.
Imagine a single disk (as above) moving towards a motionless, rigid, near one-dimensional pin tip that provides the previous high friction but low stickiness. If the disk passes at a distance that it just kisses the edge, you can imagine that a fraction of its linear energy will be converted to rotational energy.
However, one thing you know for certain is that there is a maximum rotational energy after this touch: the disk cannot end up spinning at such a speed that it's outer edge is moving at a speed higher than the original linear speed. So, if the disk was moving at one meter per second, it can't end up in a situation where its outer edge is moving at more than one meter per second.
So, now that we have a long essay, there are a few straightforward concepts that should aid intuition:
The sine of the angle of the impact will affect the resulting rotation.
The linear energy will determine the maximum possible rotational energy.
A single parameter can simulate the relevant coefficients of friction to the point of being interesting to look at in simulation.
You should have a look at Physics for Game Developers - it's hard to go wrong with an O'Reilly book.
Unless you have an excellent reason for reinventing the wheel,
I'd suggest taking a good look at the source code of some open source physics engines, like Open Dynamics Engine or Bullet. Efficient algorithms in this area are an artform, and the best implementations no doubt are found in the wild, in throroughly peer-reviewed projects like these.
Please have a look at this references!
If you want to go really into Mecanics, this is the way to go, and its the correct and mathematically proper way!
Glocker Ch., Set-Valued Force Laws: Dynamics of Non-Smooth Systems. Lecture Notes in Applied Mechanics 1, Springer Verlag, Berlin, Heidelberg 2001, 222 pages. PDF (Contents, 149 kB)
Pfeiffer F., Glocker Ch., Multibody Dynamics with Unilateral Contacts. JohnWiley & Sons, New York 1996, 317 pages. PDF (Contents, 398 kB)
Glocker Ch., Dynamik von Starrkörpersystemen mit Reibung und Stößen. VDI-Fortschrittberichte Mechanik/Bruchmechanik, Reihe 18, Nr. 182, VDI-Verlag, Düsseldorf, 1995, 220 pages. PDF (4094 kB)