Matrix Transformations in Color Space

When I started programming in C# five years ago, I quickly latched onto XNA for game programming. I didn't have constant internet access back then, so I bought books to learn from instead. The particular book I learned XNA from had a chapter on shader programming. Back then it seemed like magic to me - my school didn't teach me linear algebra until a year or two ago, I forget - and even today, I grasp the general concept, but have little experience, especially with vertex shaders.
However, one sample shader caught my attention recently: The black-and-white shader. It used a dot product operation to convert a color vector to its monochrome luminance. Other than that, and maybe sepia filters, I never really heard of people using transformation matrices on their color vectors. A quick google search reveals that it's not an entirely new concept - that page predates my birth by over three years. There is quite a bit of cool stuff you can do with this, so let's get crackin!

Prerequisites

Before we can work on the color transformations though, we need to linearize our colors. There's a nice chapter of GPU Gems explaining the concept and general importance of that, and since we use additive and subtractive blending for lighting effects, we should be doing that anyway.
I haven't produced any textures for this project yet, so we can, as advised, assume that all loaded textures are already linearized. However, we still need to perform a gamma correction in the post processing effect, and that has to happen in a pixel shader. Additionally, we should apply the calculated transformation matrix as we render so we'll actually need two different shaders.

I've dabbled in shader programming in HLSL for XNA, but I know that MonoGame uses its own shader system to compile for different platforms. I was pleasantly surprised to find documentation and example code on that at least.
Note that, unless you are using SpriteSortMode.Immediate, applying the Effect manually won't actually work. You need to pass it to SpriteBatch.Begin, but then you'll face a compatibility issue between the sprite batch and you effect: the camera transformation matrix is no longer applied, and neither is the OrthographicOffCenter matrix used internally by every sprite batch. You'll have to apply these manually with a vertex shader. Here is a SpriteBatch compatible pass-through effect that does that:

Color Transformations

Okay, this section is basically about porting Paul Haeberli's color transformations to C#, it's not really my code per se. The first transformation, Changing Brightness/Color Balance is basically provided by XNA, as it only scales the color by the specified parameter; we can use Matrix.CreateScale for that. We can also Apply Offsets to Color Components by using Matrix.CreateTranslation.

Modifying Saturation

This one is pretty simple: the first variant, Converting to Luminance, is a specific case of the saturation problem, and is solved by using a weighted average of all channels for all channels. To arbitrarily Scale Saturation, you need to interpolate between Matrix.Identity and the luminance matrix. I implemented both in one function, since you can just pass 0 to get the monochrome picture:
This is pretty cool, because you can actually pass values outside of (0; 1) to get inverted colors at -1 and boosted saturation for values greater than 1.

Shifting Hue

I'll admit that I don't really understand the math behind this either. I mean, I know how the matrices do their job, but I know too little about color spaces and how they relate to each other to be sure about why you need to do these exact operations. Sorry.
To be honest, it's not even that useful an operation. If we're tinting the map and objects to simulate different lighting situations, hue doesn't usually shift by a fixed offset. Rather, it shifts towards a certain value, generally yellow for increased light and blue for decreased light.

Just combining the other three operations gets us quite far, though; these are the exact same scenes, only rendered with a different color transformation matrix:

The ugliest island map in the world, day and night.