The magic of adding random noise to black and white images.

[00:00] Okay, here we go. How about this one? Any good? This one? I like this

[00:05] one. This one's got something to it. Sorry, I'm dithering.

[00:17] This is a video all about how you take a full color image like this

[00:20] and turn it into a purely black and white image. None of this gray scale

[00:24] ridiculousness. And a while ago, I did a video which was like self-referential where the

[00:30] text would describe how many pixels are in that image of the text. There was

[00:34] a deleted scene about what happens when you go all white or all black using

[00:39] a threshold. So let's go full black and white. What we can do is just

[00:43] pick some threshold and above that level of gray we go white and below it

[00:48] we go black and that's what the slider over here is indicating. I mean that's

[00:52] not part of the The frame, I'm putting that on afterwards. In fact, the count

[00:56] up here for the number of black pixels and white pixels, not part of the

[01:00] image, although spoiler, that's where we're going. The idea with the shot was to demonstrate

[01:04] the difference between black and white, like real black and white, and what people call

[01:08] black and white. It's actually gray scale. And I had a lot of fun, put

[01:12] the code together, we rendered that, and then we cut it. Because do you know,

[01:15] sometimes you put a lot of effort in for the luxury of cutting it out

[01:18] of the edit. And it was already a very full video, a video I love.

[01:21] um underperformed on YouTube what are you gonna do? I liked making it and so

[01:27] we took that scene out but it always kind of stuck with me I was

[01:29] like you know what there is something in that how do you take an image

[01:32] and make it pure black or white and keep as much information as possible we

[01:38] can try it on this shot as well so here it is okay if you

[01:41] did naive 50% threshold it looks like this super dark you can still kind

[01:47] of make me out but uh we've lost basically everything from the background and I

[01:53] mean, classic log perception of darkness, I guess. Cause if we go up to 75%,

[01:57] it looks like this. It's just, it's just, the lamp is the only thing that

[02:02] survives at 75%. And this is 25%. So now the bottom 25% of

[02:08] brightness from zero to 255 goes down to black. Everything else goes to white. You

[02:11] get some detail on my face. There's a little bit up over there, but

[02:17] we're losing a lot there. My head is just vanishing into the wall. I played

[02:21] around for a while, this specific shot I think 35% is the best threshold.

[02:27] That's keeping a decent amount of detail here. You can still kind of see the

[02:32] football's not bad, but like look how severe the shadow is. And this thing, it

[02:36] looks like there's an object there, that's just the shadow of this. The point is,

[02:41] if you're trying to get Detail, and you've only got black or white and a

[02:44] single threshold where you're rounding one way or the other, very hard to keep like

[02:49] fine detail and darker detail, all that kind of jazz. And it gets even worse

[02:54] were we to go somewhere that's much more visually interesting. Such as this! Ah, there's

[02:59] some detail. Now we think the best threshold for this scene is 28.

[03:05] what you're looking at right now. Everything below 28% brightness is going to black and

[03:10] above is going to white. It's the best we could do to kind of keep

[03:12] the detail in the front of the church over there and you can still see

[03:15] some detail in my face but the top of my head is indistinguishable from the

[03:20] sky. The spire is gone on the church. To get that back we tried a

[03:26] threshold of 40 there. That's better but now we've lost so much other detail. So

[03:31] we think 28% is the best. However, what if we weren't applying

[03:37] the same threshold to every pixel, but we mix it up a little? And the

[03:41] result looks like this. Okay, so there's a lot of like static noise going on,

[03:47] but there's definitely more detail. And check it out, you can see me and you

[03:52] can see the spire and you can see basically everything. So somehow by applying

[03:58] randomness, we've put noise into the shot, we've managed to preserve more detail. So

[04:03] compare this to when we had the 28 threshold, the best from before. So over

[04:07] on this side, let's say, random noise. Over here, 28 threshold. Huh?

[04:14] Look at this. Terrible. Different type of terrible. Although actually, if we move the camera

[04:19] around so the spire goes in and out, you can see that it's, you know,

[04:24] we're able to keep that separate from the sky by using randomness and we can't

[04:28] do that with a threshold, at least without losing everything else. So what's the deal

[04:32] with random noise giving us detail back into our black and white image? Well first

[04:36] of all I just want to tell you one thing you don't actually need to

[04:39] know. If we zoom right in on this image down to the pixel level, these

[04:44] individual pixels are actually little groups of 4x4 pixels.

[04:50] Because what I did, I scaled everything down to 1k, because we film at 4k,

[04:55] I go to a quarter the resolution, Then I do all the processing, the black

[04:59] and whiting, and then we pop it back out again to 4K. And we do

[05:02] that with a kind of hard edge nearest neighbor technique, which means what look like

[05:07] pixels are actually little four by four groups of pixels. But if I did this

[05:11] with true pixels in 4K, by the time we're done, if you're watching it on

[05:16] an HDTV, you're watching it on a phone, it would all just blur together. So

[05:20] that's why the true pixels aren't real pixels, but you should be able to see

[05:24] them. You don't need to know. but I just thought it'd be fun to share.

[05:27] Speaking of things you don't need to know, you don't need to know this video

[05:29] is sponsored by Jane Street because their Academy of Math and Programming is now accepting

[05:33] applications. More about that at the end of the video in the description below. Let's

[05:38] talk about the noise. What the random thresholds are achieving is taking some of the

[05:42] pixels in light regions and pushing them dark when they shouldn't be and taking some

[05:47] pixels in the dark regions and pushing them light. And that's happening random or rather

[05:52] proportional to how far from being light or dark each pixel is. And what that's

[05:58] doing is giving us, well, shades of grey. Because if you had to come up

[06:03] with grayscale colouring from scratch, using only black and white, you'd put together like a

[06:08] palette of greys like this, where you've got more or fewer black pixels in each

[06:13] one, so as you kind of lean back and blur your eyes, they become different

[06:17] amounts of grey. And what the random thresholds are doing is basically this. but in

[06:23] an ad hoc fashion, because the brighter or darker a region is, the more or

[06:28] fewer pixels get pushed in the wrong direction. So we're basically hitting all these in

[06:33] between combinations. The only issue is random noise is of course doing that randomly.

[06:39] If only there was another way, we could do it systematically. New location where we're

[06:45] going to try a new filter, which looks like this. It's not bad. I mean,

[06:51] my head, a little bit disappears into that building, but we're keeping like, look at

[06:55] the detail in the hanging basket and the background is not bad, but it does

[07:00] have that weird kind of old school newspaper feel. And that's because it's based on

[07:06] a repeating pattern. Any dithering scheme that uses repeated pattern, like what we just saw

[07:12] is called ordered dithering. Specifically, I was using a two by two Bayer. ordered

[07:18] dithering which gives you five different shades of grey. Well you get all white and

[07:23] all black and then you get three in the middle where you colour in one,

[07:26] two or three black pixels and that's it. That's your whole spectrum.

[07:32] But it kind of works. You just take that, have it as a repeating tile

[07:36] over the entire size of your image and then use that as your series of

[07:40] filters and the way you can get it to gradually step up is you just

[07:43] set them as different thresholds and it works. But the point is they turn on

[07:48] in that order. But what if we don't want just a two by two repeating

[07:54] pattern? Oh well, you can go so much better. In fact, Bayer dithering works for

[08:00] any two to the n by two to the n grid. Allow me to demonstrate.

[08:04] The secret as such to Bayer dithering is the order in which the pixels flip

[08:08] from black to white or vice versa. And they fire off in a very specific

[08:12] order as an area gets brighter and brighter. The first one to go is the

[08:16] top left, that one there flips first, that's pixel number one. As we get brighter,

[08:20] then number two fires, then number three, and finally we fill it in with number

[08:25] four. You might be thinking for a two by two grid, there's not a lot

[08:28] of ways to do it differently. But if you ever think about it, you could

[08:31] do it wrong if you fired one and then two underneath, The moment you go

[08:36] up into a slightly brighter shade of grey, you get weird vertical lines appearing. And

[08:41] you don't want vertical horizontal lines, which is why we go diagonal and then a

[08:44] corner and then the other diagonal. By staggering the order in which we go from

[08:48] white to black or black to white, you are less likely to get weird patterns.

[08:52] And it's better when you look at it with your human eyeballs and you kind

[08:57] of average it out into a grey. Things get more complicated though, when we go

[09:02] to a bigger grid size. Bayer dithering works for any two to the n grid.

[09:07] So you can basically double it each time to get the next one up. And

[09:10] what you do is you imagine this as being like four lots of the previous

[09:14] ones. There's one there, another one there, another one there. And then you do the

[09:18] same pattern recursively as you scale it up. So of these sub grids,

[09:25] you always do them in that order. This one, then that one, then that one,

[09:27] then that one. And then within each one, you do them in this order. So

[09:31] for example, We're going to do top left for all of them first in this

[09:35] order. So we do top left there, one, top left there, two, and then three,

[09:40] and then four. And now we come down to here and we do them in

[09:44] this order. So there's five, six, seven, eight. Now we're going to do that

[09:49] one in all of them in that order. So that's now

[09:57] nine, 10, 11, 12, and finally 13, 14,

[10:04] 15, 16. And you could repeat this and do an 8x8 or 16x16 and so

[10:08] on. It's a fantastic little recursive algorithm and if you turn the pixels on and

[10:12] off in this order you get a fantastic range of shades of grey.

[10:19] But what would that look like back out in the real world? Welcome back to

[10:23] the scene from before. We're still in the 2x2 Bayer filter and just

[10:29] Take a little note of what you can and can't see. And ready? Here's the

[10:33] 4x4! Ah, isn't that special? You can see these bricks! Ready? Okay, back to 2x2.

[10:39] They're gone. 4x4, they're back. You can see all the brickwork over here. Look at

[10:44] the background and my face. In fact, if we do, we'll do a split screen

[10:48] as soon as this car comes through. You know what? Do it now! I'm over

[10:51] here. This is the 2x2 side where that car is just driven through. Ah! Look

[10:57] at the emotion you can see now. And if you're thinking, well, hang on, if

[11:01] the 4x4 is this good, imagine the 8x8. Well, here's the 8x8. It's the same.

[11:07] Here's 16. Up off a point, doesn't make a big difference. So for this scene

[11:12] at the resolution we're using, the 4x4, what a winner. So there's your two options.

[11:17] Use completely random thresholds and get a nice organic look, but maybe not... as many

[11:22] nice separations of grays as we would like or you use something ordered like Bayer

[11:27] dithering you get loads of nice distinct grays but you get a weird repeating newspaper-esque

[11:33] look. There are only two options I'm afraid it's not like there's some fantastic third

[11:39] option in the middle with the best of both of course there is it's called

[11:43] blue noise instead of using pure random noise you can use blue noise and you

[11:49] get much better grays And here is blue noise out in the wild. You don't

[11:53] even know what this scene looks like. All you can see is this dithered version,

[11:57] but it's not bad. Look how the posts, the posts like you can see they

[12:00] get darker as you go back. You can almost make out there's like brickwork and

[12:05] tiles. Just have a look at what detail you can get. We can also compare

[12:09] this to pure random. Actually, we can do our split screen again. So I'm blue,

[12:14] blue noise on this side. Random noise on this side, or come with me, round

[12:19] over here, past producer Nicole with the bounce, because it makes so much difference once

[12:23] we've given the shot. There's a tree, there you go. Blue noise and random noise.

[12:30] You be the judge. Right, we all love blue noise, but what actually is it,

[12:33] and how does it differ from true random noise? If we were to extract our

[12:38] random thresholds for every pixel and just visualize them going from white to black, it

[12:42] would look like this. There you go, it's just standard random noise. Blue noise

[12:48] looks like this, subtly different. So in the true random, your brain is doing

[12:54] human brain things. It's looking for patterns. You might be spotting some like threads or

[12:59] filaments in there because real random noise clumps. Like you're gonna have hot spots and

[13:03] cold spots at every different scale. Whereas blue random noise, that's a lot more like

[13:10] It was like remember when, well some of you might remember when the iPod Shuffle

[13:13] came out and it was true random and everyone got upset because they'd occasionally hear

[13:17] the same song twice in a row? Yes, because that's randomness. You get every possible

[13:22] string and arrangement in there somewhere including things repeating which is why you get like

[13:26] bright spots and dark spots. All people wanted was a shuffle and blue noise is

[13:32] much closer to being a shuffle. You don't just things in randomly you make sure

[13:37] on average they're all roughly evenly spaced. It's nicely distributed noise and

[13:43] you can see that if we blur them both because if we blur blue noise

[13:47] on a small like let's say five pixel radius it goes totally gray whereas true

[13:52] noise you can still see hot spots and cold spots. There's still some structure in

[13:57] there because white noise has structure at every frequency is why it's called white noise.

[14:02] Whereas blue noise only has variation on very small distances, high frequency like blue.

[14:09] You also get different color audio noise, not going near that. I'm pretty sure it's

[14:15] the same thing. But the point is, this is not pseudo random, but it's not

[14:20] true random. It's blue random and it looks a lot better. Isn't blue noise amazing?

[14:27] It's just incredible detail, but you don't get a repeating pattern. And the reason you

[14:31] get the best of both worlds is it is still pretty random, but also it

[14:36] has that same property of bare dithering, whereas the pixels turn on, the

[14:41] order in which they turn on is very evenly distributed. So if I take this

[14:45] blue noise and I cycle it all the way from completely black to completely white

[14:49] and see when the different parts of the filter turn on and, I guess, turn

[14:52] off, you'll see at the extremes, it's just a bunch of points fairly

[14:58] evenly distributed, but yet randomish. In fact, if we pause it there, if you told

[15:02] a bunch of humans arrange themselves in a room randomly, they'd end up standing a

[15:06] bit like this. Because humans would think random means evenly distributed, but a bit offset.

[15:12] It's not a grid. And that's exactly what we get here. Blue noise is what

[15:16] humans think true noise is. But it's not. Blue

[15:22] noise. If you're thinking, come on, Matt, what about the dithering system you came up

[15:28] with? Well, who's to think I'm gonna come up with a course I did. And

[15:32] we'll talk about that in a moment. But first I wanna thank the sponsor of

[15:35] this video, Jane Street, because their AMP course is accepting applications now.

[15:41] AMP is Jane Street's Academy of Math and Programming. It's for recent high school graduates

[15:47] who had some kind of barrier to their education, but they want to pursue an

[15:51] education in math or computer science. AMP runs from the very end of June right

[15:57] through to the very end of July, 2026. And over that month, the curriculum will

[16:00] focus on solving problems involving things like mathematics, computer programming, game theory, and

[16:06] much more. Not only will Jane Street cover your travel to New York City, your

[16:10] accommodation, your food and all fees associated with the course, but if you make it

[16:14] onto AMP, they will also give you a $5,000 scholarship to help you further your

[16:18] education. To apply for AMP, you don't need any particular background in finance or coding.

[16:24] You just need to be intellectually curious and have a love of mathematics and computer

[16:28] science. The deadline for applying for AMP, if you are a high school student or

[16:33] you know a high school student and you can pass this on to them, is

[16:35] the 11th of March. So get onto it. It's a huge amount of fun. I

[16:39] go every year, so you get to see me. I mean, there's a perk. I

[16:43] just love solving the sorts of puzzles that they have at AMP. In fact, they

[16:46] gave me one recently that I could have a go at. Imagine you're in a

[16:50] three-game tennis competition where to be the champion, you have to win two consecutive games.

[16:56] Your opponents are Jenny, the best tennis player in the club, and Carla, who is

[17:01] less good. You either have to play Jenny, Carla, Jenny, or Carla, Jenny, Carla. Your

[17:07] non-tennis challenge is which way around would give you the greatest probability of winning two

[17:13] consecutive games. I like this puzzle because there is kind of an intuitive way to

[17:17] look at it, but also you can just work it out. which I did. Here's

[17:20] all my working. I had a lot of fun doing it. I hope seeing this

[17:24] really clears things up. All the puzzle details will also be in the description if

[17:28] you want to try, as will the details for applying to AMP. Thank you so

[17:32] much. I mean, I know this is not for everyone, but if you are that

[17:34] high school student or you know someone who is, this could be a life-changing opportunity.

[17:38] So please do spread the word. Huge thanks to Jane Street for not only running

[17:42] AMP, but also sponsoring this video. And now for my dithering technique, because I first

[17:48] came across all of this and got obsessed by it when I watched a bunch

[17:51] of YouTube videos about the mass behind the video game Return of the Obra

[17:57] Dinn. And in that game, everything is black and white dithered. Although within each shot,

[18:02] there's different types of dithering and you move around in 3D, but the dithering works.

[18:07] It's just incredible. I will link to the videos I watched below if you want

[18:11] to check them out, but it just got me thinking, oh, you can come up

[18:14] with different types of dithering. In fact they used new types of dithering for that

[18:18] video game. So I was like well I'm going to do my own. But what

[18:21] could I possibly base Parker dithering on? Well I thought what about the

[18:26] original Parker thing? I used the Parker square. I used a three by three

[18:32] grid where that's 29%, 1%, 47% etc thresholds. Now

[18:38] is that a good way to do it? No! In fact I'm now Parker dithered.

[18:43] And you'll see. So the issue is, because we got some one percenters here,

[18:49] they're like always white. Because what's going to get below one percent? So you always

[18:54] get this, if you zoom in, these little pair of diagonal pixels are just always

[18:58] on. But I think that adds a certain amount of fun texture to a scene.

[19:03] And it works outside as well. Check it out. There's the tree from before. That's

[19:07] not a bad amount of detail. If you come over here, other side of producer

[19:10] Nicole again, you can feel of this. There's your tiles up there. We've got the

[19:14] posts from before. That guy walking through, it's not bad. Even this shot isn't bad

[19:20] with the Parker filter, huh? We've got the spire and I think that weird texture,

[19:25] nice moody element on the graveyard. And while we're here, thank you for visiting my

[19:31] MySpace page. So that's it. Thanks for watching. Don't forget to like,

[19:37] subscribe and dither that bell, whatever it is they say. Oh, and I'm still on

[19:42] tour. Come and see me on tour. That's the highest resolution you will ever see

[19:48] me in. Full color too.