Low Discrepancy Sequences

August 1, 2019 · View on GitHub

Source Code: src/families/_2d/samples/lds/

This extends the concept of low discrepancy numbers from 1d to 2d.

Check out the 1d low discrepancy sequence page for an explanation of the basic ideas:

N-Rooks

N-Rooks is a sampling pattern where you treat an NxN image as if it were a chess board. Every sampling position is a rook that could move horizontally or vertically, and should be placed such that none of these rooks could capture / "see" any of the other rooks.

In other words, every column has a single sample point in it, and every row has a single sample point in it.

An easy way to do this is to start by having a diagonal line of the rooks like (0,0) (1,1) (2,2) ... (N-1, N1), and then randomly shuffling the rows.

While this sampling pattern is randomized pretty heavily using white noise, the 1d projections of this pattern on the X and Y axis have no overlap and are a shuffle, making it better than white noise and also pretty easy to generate.

TODO: finish this page!