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  • You can reduce the file size of an image by

  • Removing the number of bits you need to represent

  • Each the colors and if you remove that number of bits

  • You have less colors, you can display so the image looks worse

  • If you've got eight bits, you've got 256 levels of gray or levels of each color if you've got four bits

  • You've only got sixteen if you've got one bit you've either got black or white

  • and so what did ring is it's doing is an attempt to

  • Simulate those extra gray scales. Let's keep it to a gray scales for the purpose of this video

  • Just using black and white pixels or whatever colors you've got on the end for this video

  • We'll just keep it to either having a black or a white pixel

  • So quite often computers certainly early screens or even these days with printing they can either display a

  • Pixel or they can't display it they can either be black or it can be white

  • Let's take this to the extreme because it basically is the same even if you have got more colors

  • Let's assume that we've got a display that can either display a black pixel or a white pixel. It might be a printer

  • It might be a sort of very very simple video display of some sort particularly thought you find on sale

  • an early 80s computer something although might be black and green then but let's go black and white and what we want to do is

  • to be able to display which is that a

  • continuous tone

  • So they they don't just have black or white we go from black through grays to white and again

  • You could extrapolate this out to different colors. And so you need some way of mapping the grays

  • Into black and white a naive way we could do this. We've got an image. Let's say it's a photograph

  • I say it's this video

  • I'm sure I'll apply the special effects to make it look this and we need to convert it to black and white as we can

  • Say anything

  • Below a certain level will make black anything above a certain level will make white so we can do that and if you do that

  • You can pick the level of which you make that switch you get it with an effect like this

  • where you can sort of see it Steve but

  • realistically, you've got lots of white and lots of black that call for a special effect, but not

  • Useful for watching or printing things. So that's a naive approach

  • It's actually a problem that's existed for

  • Years newspapers are printing in general as had this problems pretty much since photography was invented in the 8th

  • Hundreds and the way they get round it is that they convert the image into a series of dots actually this was originally done

  • optically the image that they wanted to print was put in front of a camera and a screen was put in front of it of

  • Lots and lots of small things and it was rephotographed with very high contrast

  • and what happened was whether

  • Holes in the screen were you've got very small pin pricks of light that depending on how bright they were made bigger or smaller

  • discs on the

  • Photographic plate and that's what was printed. So we need to do the same thing

  • On our computer one way to look at it if we wanted to say make this square

  • Gray, if you wanted to make it black, then we could just color in all the pixels

  • So can you have it as white or black but we can also make it

  • Appear grey just like the newspaper did by not coloring all the squares inside we can make it appear

  • gray by coloring in this one and then coloring in

  • This one like this and if you do that and you do that for enough of them next to each other

  • If you zoomed out from that then it would look about 50% gray

  • you could do a lighter gray by just setting one pixel of those four in each one and

  • Just to finish off we could create a darker gray

  • by

  • filling in all

  • But one of the pixels we can create just with a 2x2 grid of pixels a white one a black one

  • 50% gray probably around 25% gray and around 75% greater and get 1 2 3 4 5

  • Different levels of grey just by using a 2x2 grid and selectively coloring in the pixels

  • what's actually happening is that your eye is at acting like a sort of optical low-pass filter and

  • When it's slightly fine of a way you stop seeing the individual pixels and you just see the sort of average gray from the number

  • Of things that are in there you sort of converting the high frequency off the norms of the image into a grayscale

  • Because you're looking at from a distance and so on

  • So that's what did the ring effectively is. It's choosing a pattern of white and black dots to create

  • The image to create the grey or to simulate the gray that was a better way of saying it now

  • How do we do that in a computer now if we think about an image the image if we've sampled it?

  • It's broken up into pixels and then they have a number associated with it to say how bright the artless is. Zero is black

  • 255 is fully white. So what we could do is say well, let's say they're 50% gray. They said they're all 50% gray

  • So let's say this is 128

  • This is 128. That's 128. That's 128 and so on

  • So how do I programmatically convert that grid which is 50% gray

  • Into the grid

  • I've got here

  • Where I say? Okay, I want that one on I want that one off

  • I want that one on I want that one off so we could do it by patter matter

  • We could look at this and say okay these four pixels here or 128 therefore

  • we need to draw that pattern in it and these for

  • 64 every 25% gray so we'll draw that pattern the pixels in it

  • You could do like that, but it's actually a clever way. You can actually do this

  • Let's draw out a grid of the 4 by 4 here

  • so what I'm going to do is I'm going to say if this

  • pixel is greater than 0 I will set it if the value in the pixel is greater than

  • 64 I will set that pixel if it is greater

  • Than 1 to 8

  • I will set that pixel and if it is greater than 1 9 2 I will set that pixel

  • Okay, so these are each of our indifferent your pixels. So go back to my pixels here and I start

  • With this one is 128 greater than 64. Yes, right so we color that in we're at my level again here in math. Yes

  • We now move on to the next pixel is 128 greater than hundred 28

  • No note that we leave that there is 128

  • Greater than that form all there isn't a next one. So we go back to the beginning

  • greater than 64

  • Yes, we set that again. And now we're going across here is 128 greater than hundred twenty-eight. No, so we leave that blank

  • So now we come down onto line two and we do the same thing with the second line here is 128 great at 192

  • No, right. Ok, we leave it is

  • Twenty-eight greater than zero. Yes. Okay, so we get the program to set this pixel here

  • Is it greater than hundred ninety-two? Nope, is it greater than zero? Yes

  • and so we set that one there like that and

  • We're back here. And we do the same thing as a greater than twenty eight and

  • Then no yes

  • No

  • No, yes

  • No, and what happens is that you end up creating the pattern we'd come up here before?

  • Just by applying that

  • Thing there. Okay. Let's try that again and we'll do it a bit quicker this time. Let's say that these are all 24

  • So what happens? Well, we do exactly the same thing. We apply this is 24 great in 64

  • No is 24 greater than hundred twenty-eight. No is 24 great in 64. No, it's 24 greater than hundred twenty-eight

  • No is 24 greater than 192? No is 24 greater than zero. Yes

  • So we fill that in is 24 greater than hundred ninety-two. No zero. Yes, and now I shall go the same faster drew

  • No, no, no. No. Yes. No. No, yes

  • And someone created the pattern that we had

  • For the library a case come up in a different position in that we had it in the top left

  • But let's come in here. That was like any difference to how it would look to art. It's just where the dots are

  • Positioned and you say we've got something that we can now apply

  • Programmatically to create these five different patterns to the image that we can take our image

  • Run that overage and create the same thing we get a nice fine

  • Series of dots for the problem with this is that we've only got five different colors black dark gray mid gray light gray

  • White why don't we wanted more colors?

  • Well the way we could do that is make this matrix bigger and use a number of things

  • But the problem with that is if we do that we have to trade off the resolution of our image

  • Because the dots will become bigger

  • to illustrate that

  • You're going to jump away from the paper to my laptop because why I've done I have created a little video

  • Which takes the image from white to black. So if we play it this is gray scales that goes from white

  • two black over the course of ten seconds

  • 255 or 256 frames are then exported this as a target image sequence relative poem which applies the same algorithm

  • But this time using an 8x8 grid and because I did it at low resolution

  • We can actually see the dots and so on. So if we play the same video this time, it's halftone

  • We can see that the way it's doing it is that the dots they're getting bigger and bigger until eventually

  • you end up with a completely black screen, but

  • whereas before

  • When we got to 50% gray

  • We had relatively small pixels. There was one pixel arm one pixel off

  • We've now got four pixels on four pixels off and bigger squares. So we've got dots that we can see

  • just like the

  • dots in the newspaper, we can actually start to see the individual dots but we still get that effect as if

  • They're getting the images getting darker as we go through it

  • And in fact if Shawn were to sort of point is camera at it that should if you gets it out of focus

  • You know if the camera will act as a low-pass filter and you should see it go from like white to dark gray

  • But it is still a collection of dots next to each other

  • So that's one way that we can dither an image

  • We can sort of apply a regular pattern and ordered patterns as an order. Did they recall this to the image? And

  • Convert the individual pixels

  • Into black and white dots to create the gray scales

  • We can either say it to be white

  • 255 or black zero so we choose the one which is closer

  • So in this case the closest one we could leave it as white

  • 255

You can reduce the file size of an image by

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A2 初級

注文されたディザリング - コンピュータマニア (Ordered Dithering - Computerphile)

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    林宜悉 に公開 2021 年 01 月 14 日
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