Posts Tagged ‘threshold’

Color quantization, minimizing variance, and k-d trees

Saturday, May 26th, 2018

A recent question on Stack Overflow really stroke my curiosity. The question was about why MATLAB’s rgb2ind function is so much faster at finding a color table than k-means clustering. It turns out that the algorithm in rgb2ind, which they call “Minimum Variance Quantization”, is not documented anywhere. A different page in the MATLAB documentation does give away a little bit about this algorithm: it shows a partitioning of the RGB cube with what looks like a k-d tree.

So I ended up thinking quite a bit about how a k-d tree, minimizing variance, and color quantization could intersect. I ended up devising an algorithm that works quite well. It is implemented in DIPlib 3.0 as dip::MinimumVariancePartitioning (source code). I’d like to describe the algorithm here in a bit of detail.

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Dithering

Friday, January 7th, 2011

First of all: Happy New Year!

Over the holidays I’ve been learning about dithering, the process of creating the illusion of many grey levels using only black and white dots. This is used when displaying an image on a device with fewer than the 64 or so grey levels that we can distinguish, such as an ink-jet printer (which prints small, solid dots), and also when quantizing an image to use a colour map (remember the EGA and VGA computer displays?). It turns out that this is still an active research field. I ran into the paper Structure-aware error diffusion, ACM Transactions on Graphics 28(5), 2009, which improves upon a method presented a year earlier, which in turn improved on the state of the art by placing dots to optimize the appearance of thin lines. This got me interested in the basic algorithms, which I had never studied before. Hopefully this post will give an understanding of dithering and its history.

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