How to average color 

Small correction: I wrote and said square root and square in the wrong order when I was showing the conversion of the colors on the board. The values were correct, just wrote it wrong. Also 13/3 is 4.333, not 6.5.... i changed the divisor and didn't update the answer. just horrible. I added a little correction video to the appropriate place in the video.

So it's "Computer Color is Broken" all over again

I am convinced Gneiss could make me watch paint dry.

To be honest, I wasn't expecting the geologist Minecraft RU-vidr to solve one of my biggest problems with doing pixel art out of nowhere, but I'll be danged. I've always had trouble figuring out how to do gradients in my pixel art, especially with the low color palette, and now I've got a pretty quick shorthand for calculating good average colors/have a strong idea where to color pick if I don't want to math it out. So uh... genuinely, thanks a bunch!

"Let's look at this *normal* Minecraft painting" 0:14

Between you and Acerolla, I’m really glad we’re getting quality content on youtube about OKLAB

i really hate when the messy interpolation averaging happens in pixel art stuff, it looks blurrier because it's not taking the most prevalent color and displaying that, it's just mixing them together and assuming that'll look right

Common misconception about sRGB gamma, the gamma curve of the sRGB color space actually comes from the response curve of a CRT display, not the human eye, the two just happen to be similar to each other

One misconception about gamma correction I'd like to address-cameras don't do gamma correction simply because applying a curve to the colors makes them look more accurate to our eyes. We do it because the monitor is applying the opposite curve to the colors being fed into it (approximately but not exactly an x^2.2 curve). The two curves cancel out. The camera stores the colors in a nonlinear space, and the monitor takes those values which are in a nonlinear space and makes them linear again. One benefit of this is that sRGB makes it so that the brightnesses corresponding to the RGB byte values appear to be spaced apart evenly to our eyes (they are distributed more evenly in perceptual brightness), which makes color banding less noticeable than if the relationship was perfectly linear. Another detail is that the sRGB curve was chosen because it closely matched the curve found in CRTs.

That love how when you first learned about color for computers you think oh it's just RGB. Then you get Gama thrown at you and color space .etc

It's a minor tangent to your intro, but maybe a young artist who catches this would be curious: needing to average color values of pixels when transforming an image only happens when the image is a raster or a bitmap. The same need doesn't exist for vector images.

Cool. This is what you were talking about in that discord stream!

1:55 I feel like this applies to alot of things in life, for example if your running away from one lion or two lions is much more important than 102 or 103 lions, same as if you lost 1kg or 2kg of weight is much more important than 52 kilos or 53 kilos.

Man these are always great videos.

The way you visualise in Minecraft is so cool. I don't know how much of it is actually in engine or how much is editing magic, but either way you create a very immersive learning experience

I always love these videos! In undergrad I worked on a project with a species of fish that would change color based on its behavior and social rank. I used an LAB color space to quantify the changes in their color through time!

3:27 The average gamma of sRGB is actually 2.2 instead of 2.4. Although there is 2.4 in its formulae, it averages down to 2.2.

these videos are always so intresting, i love how u can be talking about a topic that has nothing to do with minecraft but still have it perfectly fit with the game

World record for fastest intro ever. Ngl it sounded like I joined part way in the video, then I realized you said "Gneiss here" but fast lol.

super super interesting stuff. this might sound like an insult at first, but the video felt really long. not because it was boring, but because you crammed so much information in the first three minutes i thought the video was gonna end. there aren't many videos that i find have so much helpful info. keep it up!

I had an idea that might make for a good geology video. Given that the overworld is explicitly not made of granite, andesite, diorite, basalt, tuff, or calcite, and that deepslate is some kind of slate or other sedimentary rock under high pressure, and the evidence of stone being some kind of carbonate rock due to the abundance of caves, and volcanic activity only at the deepest points of those caves, I think a plausible explanation for the overworld's strange geology is that the entire world as we know it is made up of what used to be layers of coral-like organisms, hundreds of meters thick, and that the deepslate layer was once the ancient seafloor of a water world.

I just love, how everything in your videos make perfect sense, and you seem like a very educated person, and then spontaneously 13/3 is 6.5... that makes me laugh so god damn hard

You put a lot of effort into your content. You also have a lot of passion. I think that's awesome!

1:59 reminds me I should listen to Bill Evans again, Thanks! Also, when showing the better average at 2:43, the arch on the graph reminds me of Lambert's Emission Law, even though that has more to do with value rather than color for art related purposes.

Your videos are so interesting, I really enjoy your style of content!

Love this deep dive. I'm always game for more color space talk. Thanks for sharing.

At this rate you're going to do a video on premultiplied alpha.

These videos about color are so fire I can't get enough of them.

Such a banger video. Keep up the good work

i love your freaking good videos about gamma/color

Man, I love this channel +sub

As a programmer and a color science & art nerd, your vids are so nice to see and learn from

The best kind of correct, indeed.

These are so fascinating

Bro, your teaching style × high quality Minecraft visual examples is. Like. Incredible for my soft litl brain.

Your videos about color are great! Any chance you could do one about how colorblind eas changes the perception?

Very neat demonstrations, and here I thought you just did geology stuff

It's been one of the things that has been a pet peeve for me since basically forever. So far that I tend to retouch after averaging just to fix the issue. And yes, our perception is indeed logarithmic. It is important to know if there is 1 lion or if there are 3. But the difference between 10 lions and 13 lions isn't important, it's still a lot of lions coming after you. And the most sensitive area of the human eye is in the green area. Not only is there an overlap of different cone cells, but rods also have their peak there. Oh and many games have separate brightness and gamma sliders. And they do what their name suggests.

I'm excited that we're going down this rabbit hole

for colour spaces, it also depends on what kind of thing you're trying to show as to what colour space is best. for example, to simulate what colour you'll get when you mix 2 different lights together (or really anything to do with lighting or transparency) you'll wanna do this in linear RGB space rather than sRGB or OkLab

I love your videos on colors

Just wait until you discover the joys of a "Scene-referred" color space. Or, in other words, a colorspace with no limit to how bright a color can get. It's the "color space" real life is in, and it's useful in 3D rendering for calculating lighting since there's such a wide range of brightnesses you can have. I've adopted it for my 2D art and it makes it remarkably easy, combined with a linear gamma and a tonemapper, to make great looking lighting with minimal effort.

"But no matter what, there is always averaging" Worth noting that there are ways to get non 90° rotations without any averaging or color changing at all (like doing 3 shears), but outside of authentic low-resolution pixel art, it's fairly limited in actual use

yay new colour video

as a web developer that still doesn’t quite get the CSS color v4 spec, i seriously appreciate these videos

Holy fuck I need this thank you so much. Thank you for your beautiful brain.

This man is a genius with display entities.

I think some gneissname Minecraft calculus explanations would be very interesting to watch. Could be good for trying to learn those concepts too, especially for multivariable calculus with 3 Dimensional concepts! Just a suggestion

It's been fun seeing the arc from geologist to colorist

2:58 OMG, this really looks like a mix of the two colors better than the color on the left side!

“No matter what, there is always averaging” *Skew rotating joined the chat*

"Let's look at this normal Minecraft painting" yeah this painting is so gneiss

Huh neat. I'll take this into account when working with shaders

If this man did math animations or video essays about the math or code it would just become my main resource on learning about computer color

Ohhhh this is definitely a big pet peeve. I think I've seen Captain Disillusion do a video on something very similar to this very topic, iirc "the horrors of the alpha chanel"? If you haven't seen it, I would highly recommend. I think you'd like it and a few of his other videos tbh

Mathematically, It shouldn't matter at all in which linear color space you calculate the average. That's the whole point of linearity. The results should be the same. Let's take two linear color spaces, let's call them (A B C) and (X Y Z) for example. A,B,C,X,Y, and Z are vectors representing the primary colors of these spaces. Now let's take and arbitrary color D. It has cooordinates (a, b, c) in colorspace (A B C), and (x, y, z) in (X Y Z) D = a*A+b*B+c*C = x*X+y*Y+z*Z |a| |x| D = (A B C). |b | = (X Y Z). |y | |c| |z| Now, E = d*A+e*B+f*C = u*X+v*Y+w*Z (coordinates (d,e,f) in (A B C), and (u, v, w) in (X Y Z) Then, if we take (D+E)/2, we get (a*A+b*B+c*C + d*A+e*B+f*C)/2 = A*(a+d)/2 + B*(b+e)/2 + C*(c+f)/2 |a| |d| |a| |d| |(a+d)/2| (D+E)/2 = 1/2 *( (A B C) .|b| + (A B C).|e| ) =1/2* (A B C). ( |b| + |e|) = (A B C) . |(b+e)/2| |c| |f | |c| |f | |(c+g)/2| so the average has coordinates ((a+d)/2, (b+e)/2, (c+f)/2) in colorspace (A B C) Using the same resoning, it also has coordinates ((x+u)/2, (y+v)/2, (z+w)/2) in colorspace (X Y Z) And assuming matrices (A B C) and (X Y Z) are inversible, you can convert the coordinates of the average from on space to the other and see that you end up with the same result as if you calculated in the other colorspace to begin with. |(a+d)/2| |a| |d| |a| |d| |x | |u| |(x+u)/2| (X Y Z)^-1 . (A B C) . |(b+e)/2| =1/2 * (X Y Z)^-1.( (A B C) .|b| + (A B C).|e| ) =1/2( ( (X Y Z)^-1.(A B C). |b| ) + ( (X Y Z)^-1.(A B C). |e|)) = 1/2(|y | + |v|) = |(y+v)/2| |(c+g)/2| |c| |f | |c| |f | |z | |w| |(z+w)/2| In both spaces, you can just average the coordinates to get the "true" average color. Which makes me wonder why the OKlab average is different than the linear sRGB average. Maybe OKlab isn't linear enough?

Been messing with Doom's color palette for a while now. It taught me a lot...

When you started talking about using the averages of numbers, what I thought was that it would maybe be better to use a logarithmic scale for the average. Like the example you gave with the candles, my guess is that we would perceive proportional increases. Adding adding 4 candles to already existing 4 candles would have about the same effect as adding 1 candle to an existing candle.

Damn those MC visualisation looking sick

I just put down a color and then put the second color over it at half opacity, then color pick the result. That gets what I assume is an average between the colors. It's always lighter than the darker color and darker than the lighter color.

I love this guy

You mentioned averaging colors to scale and rotate an image. If you want yet another extremely deep topic filled with subtle misinformation, you can look into filtering, sampling, and antialiasing, which is the math concerning how, exactly, you combine those pixels. Here's some base-level knowledge: - The Sampling Theorem says that for any signal, you can perfectly reconstruct it from a series of samples, as long as the sample rate is greater than twice the highest frequency in the original signal. - For audio, that means using an analog low-pass filter during recording tuned to half the sample rate, and then reconstructing the signal with something like a Sinc filter. Since humans can only hear up to around 20 kHz, you only really need to sample at around 40 kHz (although most audio is sampled slightly higher because low-pass fillters aren't 100% perfect). - For images, it's a bit harder since there is a potentially unlimited frequency (a checkerboard from far away, a hard edge, or a very small object are all examples of high-frequency features). Applying a low-pass filter to an image essentially means blurring. Many cameras actually have an optical low-pass filter, which is just a slightly blurry piece in front of the sensor. For video games, it's a lot harder, since there isn't a real-world analog input to start with. You have to sample at as high a frequency as you can, which means rendering more samples than there are pixels on the screen. Obviously that gets slow quickly, so there are various techniques that try to approximate the result or gather the samples over multiple frames. Sampling is also needed when performing operations on images, such as scaling or rotation. In this case it's typically called resampling. - Image sampling is a bit messier than audio sampling, because if you use a pure-frequency approach such as Sinc, you end up with distracting ringing artifacts. On the other hand, a filter that is too soft will make the image appear too blurry. Typically the Mitchell and Lanczos filters are considered pretty good if you can spare the processing power in your use case, however they are still not perfect, and it depends on use case. - Just averaging the 4 pixels that land in a square is called box filtering, and is one of the lowest-quality filters. It still leads to lots of aliasing in many cases. However, many programs use it because it's simple and it runs fast, leading to many people believing that there's no reason to use anything else. It's what's used in most real-time applications such as vector graphics rendering, web browsers, video games, etc. I would recommend the following articles if you want to know more: - Xiph's article "24/192 music downloads and why they make no sense" - Has some introductory information about audio sampling. - Alvy Ray Smith's Microsoft memo "A Pixel Is Not a Little Square" - A very good (although from 1995) article about many of the misconceptions about sampling and filtering. - The ImageMagick docs page on resampling filters - Provides an overview and comparison of some different resampling filters, as well as a conclusiong on good default choices at the end.

This guy is the solution to when the top result is reddit but the only guy who replies is refusing to acknowledge the question

The same problem happens when you want to create a color gradient. If you simply interpolate linearly between the two colors, then the middle is often kind of greyed and washed out. That's because, if you take any two points in a cube, the average of the two points is often closer to gray than the two points. However, if you interpolate over HSV or HSL instead, you get a much more pleasing result that keeps its luminance and saturation ! The problem is that if the hues are very far away, or on different ends of the spectrum, you might have a gradient that goes red to yellow then green then blue then pink, instead of the red to pink gradient you wanted. It can be solved with a bit of cycle logic, but not from, say, 0° to 180°. I think there's some merit to a nuanced approach between the two, where you interpolate both in RGB space and in HSV space, then convert both colors to RGB and do a weighted average, with the weight being a chosen parameter. 0 gives you full HSV, 1 gives you full RGB, and between the two is a gradient of gradients.

Oh man, I went down this very same rabbit hole recently when investigating why they changed the official color scheme of Neptune, because when I look at Neptune through a physical telescope, I don't see the image that's now being pushed (though I also don't see the dark blue, either, it's more something in between). The new image of Neptune came from a reprocessing of the image's gamma correction, which could be what our eyes see from up close, but from far away where less of its reflected light reaches us & it gets diffused by the atmosphere, it blends more into the darkness of the sky. It does look at least noticeably different from Uranus when looking at both of them from the ground.

There's a way to show that using a simple average doesn't give the right color perceived by our eyes. Make a 2x2 pixel grid, with two different colors in a checkers pattern, and apply this pattern to a bigger image. Make sure the zoom still allows you to see the individual pixels. Then blur the image by squinting your eyes, or removing your glasses. Now find the RGB values of the color you saw, it will be lighter than the simple average.

This was so helpful even tho I only gonna use it for Photoshop

I was curious how Geometric Mean (multiply then take the square root instead of add then half) would apply to colors so I randomized two and calculated the geometric: Color 1: #1a7775 Color 2: #21500a Geo Mean: #1D6222 The Geometric mean will never be brighter than the Arithmetic mean. sqrt(xy)

Gamma is just a compression method, so that dark colors (where you demonstrated the difference matters more) cover more of the 256 possible values. The monitor undoes the gamma function, so it's still outputting linear values (apparently this was just a useful side effect of CRT monitors, and is why gamma exists in the first place). It is objectively incorrect to do any operation to colors before they have been decoded from gamma space, and yet that's exactly what most software does. Example of intended usage of gamma: I'm working on a Minecraft shaderpack. The textures are stored in PNG, which uses sRGB space and is thus gamma encoded. The first thing my code does when it reads a texture value is raise it to the power of 2.2, bringing it back into linear space. No information is lost here, since my shader is working with 16 bit floats. Once all of the calculations are done, such as lighting and post-processing, the very last step in the shader is to encode the result into gamma space by raising it to the power of 1/2.2. When the monitor receives the value, it converts it back into linear space and displays it (from what I know, most software and monitors just use a power of 2.2, rather than the piecewise linear / 2.4 curve specified in the standard).

Color, math and Minecraft. 3 of my favorites :)

I think the music in combination with the moving video and talking is a bit much when you're explaining things gneiss! 🤔

I never thought i could learn so much from minecraft

=D he's back with more

The candle example is kind of weird to me. Going from 1 to 2 is an increase of 100%, but going from 99 to 100 is just a 1.01% so it's not the same in both cases. Stand-up Maths did a video called "Rotation without rotating." that shows how to rotate pixel art (and images in general) without averaging or losing any information.

cool video, i love colors

You can rotate images by skewing them only, you don't lose pixels and don't have to average

“Geology of Vintage story” when?

It might be because I'm tired but I have no idea what this video is about. I understood the color averaging thing due to srgb no problem, but I have literally zero idea what the 3D graphs were supposed to show and what was plotted on them.

If you are shrinking pixel art do you really want to be averaging or is there a better way, like some kind of median filter? that way it will be picking one of the colours present in the original image rather than mixing them

reminds me of ‘computer color is broken’ from minutephysics

Hey gneiss I’m asking to see what rock type you think netherrack is Context is that this total overhaul mod called terrafirmacraft adds 20 rock types to the game based on real rocks, and these can be used to knap tool heads with stats based on the type of rock they’re made from, being sedimentary, metamorphic, igneous extrusive and intrusive. The dev has been making an addon to implement the nether in the same theme and while playtesting I realized that netherrack and black stone don’t have rock types assigned because of course they don’t they’re fictional stones, but this also means we can’t knap tool heads from them. Someone theorized that they’re either igneous intrusive or metamorphic in the context of the nether being deep in the crust and very hot making it either or depending on how long the stone has been formed

7:15 i understood all the arguments in the video but ngl to me the blending without gamma still looks better to me

I really hate the term "gamma correction". There is nothing correct about it and the term itself doesn't tell you weather or not it means applying or removing the gamma curve. IMO we should just say linear or gamma space, which is much clearer.

can you make a video of the blocks in grayscale?

Thought this was gonna be advice on how to avg color.

0:01 looks like Minecraft terracotta

you lost me but the visuals go crazy

Is there any research in conceptual colour spaces for people with CVD? I have deuteranomaly and I'm really interested in knowing how my colour space is different to others.

I feel like Ive beem dueped into learning

I could swear I have seen this same topic being covered in a completely different method, by a completely different channel, many, many moons ago.

Nothing worse when the mipmaps optimize 0rgb and 255r0gb to brown. It just merged them, point UV assignment just need 8x8 pixels necessary which looks so wrong on the map.

this is useful

On top of that color interpolation is going to be different if you are doing print (substractive color) or screen (aditive color). I always thought the correct srgb gama was power 2.2 not power 2. And isn't it supposed to be linear in the bottom 0.1% of the luminosity curve to avoid infinit tangent at zero? Maybe it's not an issue anymore. It used to be one though.

Probably a weird question but what is the best way to create a gradient between two colors that look "visually" good using programming.

You said that photoshop by default uses the darker colors, is there a way to make photoshop use a different method?

Solution : store pixel arrays in hsl and have the monitor convert it in real time (or specialised gpu task right before outputting) that way gamma correction wouldn't matter right ?

have you made your own minecraft world/server/mod?

The new sethbling

I am not sure if using HSV colors is easier for averaging, since the hue is by definition separated from all sorts of saturation and brightness.

Could you explain a little the differences between OkLab and CIELAB? I get the impression OkLab is basically a better CIELAB?