Big Wet Pixels 3

Still exploring big wet pixels (originally inspired by the #genuary4 prompt) using my watercolor simulation in Unity. Now the pixels are actually pixels: given a random selection of pigments and paper, they try their best to match the color coming in through my webcam. Lovely glitches ensue.

To get this working, I had to go back and solve an old problem that’s bothered me for decades: given an arbitrary set of three pigments and paper, what combination of pigment densities will produce the closest match for any given RGB color? This is non-trivial, because the gamut described by three Kubelka-Munk pigments is non-linear, not necessarily convex, and might even not be an embedding! In our 1997 paper we addressed that problem in a really crude way, which I was never very happy with: quantize the pigment densities into bins, and find the nearest bin in RGB space using a 3d-tree search. So it gave me great satisfaction last weekend when I implemented a continuous solution, using gradient descent.

An animated GIF showing a non-linear 3D color gamut in RGB space. A thin colored line shows the path taken by gradient descent from the middle of the gamut to reach the closest possible point to any given RGB color.

The curved RGB color gamut described by a trio of semi-opaque white, amber and green pigments on purple paper. The white sphere represents the RGB color we’d like to match. A smaller, colored sphere represents the closest approximation that can be produced within the color gamut. A thin, meandering line shows the path taken from the middle of the gamut via gradient descent.

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