Mœud deux

August 7, 2018

Pairing functions are fun. Last week, we had a look at the Cantor/Hopcroft and Ullman function, and this week, we’ll have a look at the Rosenberg-Strong function—and we’ll modify it a bit.

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July 31, 2018

Pairing functions are used to reversibly map a pair of number onto a single number—think of a number-theoretical version of std::pair. Cantor was the first (or so I think) to propose one such function. His goal wasn’t data compression but to show that there are as many rationals as natural numbers.

Cantor’s function associates pairs (i,j) with a single number:

…but that’s not the only way of doing this. A much more fun—and spatially coherent—is the boustrophedonic pairing function.

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HSV and HSL (colorpsaces XI)

July 3, 2018

HSV (hue, saturation, value) and HSL (hue, saturation, lightness) are two intuitive, but computationally cumbersome, colorspaces.

The basic idea behind these colorspaces is the good ol’ color wheel, where primary colors are placed on a triangle and secondary colors between; complementary colors are to be found opposite on the circle. That’s intuitive enough, but we still have to make it into a workable colorspace.

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Pantone Colors (Colorspaces X)

June 19, 2018

Let’s have a look at another physical colorspace: Pantone.

The Pantone color system isn’t particularly useful for us as it is mainly concerned with “real world” colors, as in print. It also uses a variety of special dies, for metallic or fluorescent finish. It does, however, allow very accurate and consistent color reproduction for packaging, posters, and comics.

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Munsell Colorspace (Colorspaces IX)

June 12, 2018

While the RGB and its transformed colorspaces are useful for computer graphics and video compression, there are other colorspaces that deal with “real life” materials, like ink and paint. Albert Henry Munsell (1858–1918), a painter, proposed such a system.

Unlike RGB and its friends, the Munsell colorspace isn’t based on mixing three primaries, but rather on hue (tint), value (brightness) and chroma (density of color, or saturation), and colors are arranged on a color wheel, but unlike the usual three/six primary color wheel, Munsell’s has 5 primary colors [1].

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The big picture (Colorspaces VIII)

May 29, 2018

A few posts ago, I said that while the colorspaces looked random, they really weren’t, and that there was underlying order. The structure cannot be easily seen just by looking at the numbers themselves, but at how the numbers are obtained.

The story begins sometimes in the 1950s, were transmitting color TV images started to be the next logical step. Someone (not sure who was first, but it may have been Valensi, in the 1930s) proposed that TV color should be encoded in a perceptually friendly way [1]. It was known for a while that the retina had four types of sensors, rods for brightness with no color information, and three other types corresponding to red, green, and blue, but also that in, and beyond the retina, information travels as brightness, yellow-blue and red-green differences [2,3].

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YCrCb and friends (Colorspaces VII)

May 22, 2018

JPEG, MPEG, and other compression algorithms all use a colorspace other than RGB. The colorspaces they use are such that most of the perceptually useful information is concentrated into one component, essentially brightness, and the color information diffused into the remaining components. Furthermore, we hope that we can heavily quantize the color information. JPEG separates the image into brightness and two other components: brightness is coded full resolution, but the two other components are downsampled 4:1. Yet, it’s not visible in the reconstructed image, because our eyes are good at brightness, but not at chrominance.

But that’s not a surprise. All the colorspaces we’ve seen so far do this, and (are believed to) have the same properties, grosso modo.

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