Fastest formula to get Hue from RGB

Question 1

Convert the RGB values to the range 0-1, this can be done by dividing the value by 255 for 8-bit color depth (r,g,b - are given values):
```
R = r / 255 = 0.09
G = g / 255 = 0.38
B = b / 255 = 0.46
```
Find the minimum and maximum values of R, G and B.
Depending on what RGB color channel is the max value. The three different formulas are:
- If Red is max, then Hue = (G-B)/(max-min)
- If Green is max, then Hue = 2.0 + (B-R)/(max-min)
- If Blue is max, then Hue = 4.0 + (R-G)/(max-min)

The Hue value you get needs to be multiplied by 60 to convert it to degrees on the color circle. If Hue becomes negative you need to add 360 to, because a circle has 360 degrees.

Here is the full article.

Question 2

In addition to Umriyaev's answer:

If only the hue is needed, it is not required to divide the 0-255 ranged colours with 255.

The result of e.x. (green - blue) / (max - min) will be the same for any range (as long as the colours are in the same range of course).

Here is the java example to get the Hue:

public int getHue(int red, int green, int blue) {

    float min = Math.min(Math.min(red, green), blue);
    float max = Math.max(Math.max(red, green), blue);

    if (min == max) {
        return 0;
    }

    float hue = 0f;
    if (max == red) {
        hue = (green - blue) / (max - min);

    } else if (max == green) {
        hue = 2f + (blue - red) / (max - min);

    } else {
        hue = 4f + (red - green) / (max - min);
    }

    hue = hue * 60;
    if (hue < 0) hue = hue + 360;

    return Math.round(hue);
}

Edit: added check if min and max are the same, since the rest of the calculation is not needed in this case, and to avoid division by 0 (see comments)

Edit: fixed java error

Question 3

Probably not the fastest but this is a JavaScript function that you can try directly in the browser by clicking the "Run code snippet" button below

function rgbToHue(r, g, b) {
    // convert rgb values to the range of 0-1
    var h;
    r /= 255, g /= 255, b /= 255;

    // find min and max values out of r,g,b components
    var max = Math.max(r, g, b), min = Math.min(r, g, b);

    // all greyscale colors have hue of 0deg
    if(max-min == 0){
        return 0;
    }

    if(max == r){
        // if red is the predominent color
        h = (g-b)/(max-min);
    }
    else if(max == g){
        // if green is the predominent color
        h = 2 +(b-r)/(max-min);
    }
    else if(max == b){
        // if blue is the predominent color
        h = 4 + (r-g)/(max-min);
    }

    h = h*60; // find the sector of 60 degrees to which the color belongs
    // https://www.pathofexile.com/forum/view-thread/1246208/page/45 - hsl color wheel

    // make sure h is a positive angle on the color wheel between 0 and 360
    h %= 360;
    if(h < 0){
        h += 360;
    }

    return Math.round(h);
}

let gethue = document.getElementById('gethue');
let r = document.getElementById('r');
let g = document.getElementById('g');
let b = document.getElementById('b');

r.value = Math.floor(Math.random() * 256);
g.value = Math.floor(Math.random() * 256);
b.value = Math.floor(Math.random() * 256);

gethue.addEventListener('click', function(event) {
  let R = parseInt(r.value)
  let G = parseInt(g.value)
  let B = parseInt(b.value)
  let hue = rgbToHue(R, G, B)
  console.log(`Hue(${R}, ${G}, ${B}) = ${hue}`);
});

<table>
  <tr><td>R = </td><td><input id="r"></td></tr>
  <tr><td>G = </td><td><input id="g"></td></tr>
  <tr><td>B = </td><td><input id="b"></td></tr>
  <tr><td colspan="2"><input id="gethue" type="button" value="Get Hue"></td></tr>
</table>

Question 4

The web page Math behind colorspace conversions, RGB-HSL covers this however it contains what I believe is an error. It states for hue calculation to divide by max-min however if you divide by this fractional amount the value increases and easily exceeds the full expected range of -1 to 5. I found multiplying by max-min to work as expected.

Instead of this:

If Red is max, then Hue = (G-B)/(max-min)
If Green is max, then Hue = 2.0 + (B-R)/(max-min)
If Blue is max, then Hue = 4.0 + (R-G)/(max-min)

I suggest this:

If Red is max, then Hue = (G-B)*(max-min)
If Green is max, then Hue = 2.0 + (B-R)*(max-min)
If Blue is max, then Hue = 4.0 + (R-G)*(max-min)

Question 5

You could use one of the mathematical techniques suggested here, but instead of doing it on every pixel, do it on a random sample of ~10% of the pixels. This is still very likely to have high accuracy and will be 10x as fast.

Question 6

You must specify which language and platform you're using because C#, Java and C are very different languages and the performance also varies among them and among the platforms. The question is currently too broad!!!

640×480 is not very large compared to current common resolutions, but "fastest" is subjective and you need to do careful benchmarking to choose which is best for your usecase. An algorithm that looks longer with many more steps isn't necessarily slower than a shorter one because instruction cycles are not fixed and there are many other factors that affect performance such as cache coherency and branch (mis)predictions.

For the algorithm Umriyaev mentioned above, you can replace the division by 255 with a multiplication by 1.0/255, that'll improve performance with a tiny acceptable error.

But the best way will involve vectorization and parallelization in some way because modern CPUs have multiple cores and also SIMD units to accelerate math and multimedia operations like this. For example x86 has SSE/AVX/AVX-512... which can do things on 8/16/32 channels at once. Combining with multithreading, hardware acceleration, GPU compute.... it'll be far better than any answers in this question.

In C# and Java there weren't many vectorization options in the past so with older .NET and JVM versions you need to run unsafe code in C#. In Java you can run native code through JNI. But nowadays all of them also had vectorized math support. Java had a new Vector API in JEP-338. In Mono you can use the vector type in the Mono.Simd namespace. In RyuJIT there's Microsoft.Bcl.Simd. In .NET 1.6+ there's System.Numerics which includes Vector and other

... SIMD-enabled vector types, which include Vector2, Vector3, Vector4, Matrix3x2, Matrix4x4, Plane, and Quaternion.