Link between blue noise sampling and blue noise textures? You can have blue noise sampling like these poisson disc samples:


And you can have a blue noise texture like this:


I get that in the first image, there is one input (the index of the sample) and two outputs (the x,y coordinate of the point) and that the second image is basically the reverse where there are two inputs (the x,y coordinate of the sample) and one output (the value of the point).

I'm curious though, how are these related?

If you take the DFT of the second image, you can see that it has more high frequency components than low, but I'm not sure how you'd take the DFT of the first set of data points.

I'm wondering if it's possible to take other low discrepancy sequences (say, halton, or jittered grid) and make a texture out of the idea, like the second image?
The missing link between sample locations and the greyscale noise texture is "ordered dithering".

Ordered dithering is a list of pixel locations with a "rank" (order) for each pixel. If you have a white background and want to add two black dots, you add them at the locations for the two pixels rank 0 and rank 1.

Choosing how to rank the order of the pixels to turn on can vary dramatically with different results though. For instance, a bayer matrix is a specific ordering of the points, and blue noise sample points are as well. White noise is just shuffling the points so that they have a random ordering.

How we get from this "ordered dithering" (stippling) to the greyscale color noise images is that we divide each point's rank by the number of points to get a value from 0 to 1, and use that as the points greyscale color.

That gives you the greyscale noise textures.

The greyscale blue noise texture was created with the "void and cluster" algorithm which makes it so that each new dot placed goes in the middle of the largest void.  This has the nice property that you can threshold the blue noise texture at any value, and the result will be blue noise samples of the desired density.

This paper is a great read that talks about these things more deeply:
http://cv.ulichney.com/papers/1993-void-cluster.pdf