Mitchell's Best Candidate Algorithm I'm trying to generate an image where black dots are arranged in a blue noise distribution on a white background.

I know that there are other ways to do this, one of the best being "Fast Capacity Constrained Voronoi Tessellation." [Hongwei 09], but I'm using Mitchell's best candidate algorithm.

This algorithm works by generating $N$ random pixel locations as candidates for where the next black pixel should go and chooses the candidate which has the farthest distance to the nearest black pixel.

I've implemented this and have used it to put 455 black pixels on a 64x64 image, using various candidate counts.  Looking at the DFT (frequency magnitude, not phase) of the results, I'm seeing some unexpected frequency data.



Strangely, I never get that "nice concentric rings" DFT frequency amplitude that i'd expect and see in papers regarding blue noise sample patterns.

Are these results expected?

Manually hunting between 100 and 1000 samples, it seems like 400 is pretty near optimal.

 

Is there some "sweet spot" for the number of candidates to use based on image size and desired sample (black pixel) count to get the best result?
Another very simple, easy to implement, algorithm to generate a Poisson-disk/blue noise point distribution is the following one [ 1 ]: 


Decide a radius r, and therefore the expected number N of samples per area (use the formula for maximum packing density of k disks distributed on a toroidal domain see [ 2 ]) 
Generate 10~20 x N samples in your area using a plain unbiased montecarlo sampling
Until all samples respect poisson disk condition:


randomly choose a sample p 
remove all the samples at distance lower than r from p



Eventually step 3 can be furtherly iterated a small number of times choosing the sample with minimal number of surviving samples within distance r.

You can find an implementation of this algorithm in MeshLab.

References

[ 1 ] Efficient and Flexible Sampling with Blue Noise Properties of Triangular Meshes
Massimiliano Corsini, Paolo Cignoni, Roberto Scopigno
IEEE Transaction on Visualization and Computer Graphics, Volume 18, Number 6, page 914--924 - 2012

[ 2 ] A comparison of methods for generating Poisson disk distributions
 Ares Lagae, Philip Dutré,
Computer Graphics Forum vol:27 issue:1 , 2008