Randomly matched up, using the atmosphere-noise based randomizer Madali suggested sometime back (Random.org), here are the match-ups for the next round:
Chan-wook Park vs Darren Aronofsky

vs

Ang Lee vs Christopher Nolan

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Quentin Tarantino vs David Fincher

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Wes Anderson vs Danny Boyle

vs

Post your choice for each of the match-ups, so one from the top 2, then one from the second pairing, then one from the third match-up and one from the last pair.
Once all have voted, we will have the last 4.
For transparency sake, here is how the above was done:
1) Sorted names alphabetically in excel.
2) Used randomizer to assign each director a number.
3) re-sorted the directors based on number against them, smallest to largest.
4) Assigned new numbers to each director from randomizer
5) re-sorted the directors based on the new numbers against them, smallest to largest.
6) Matched up #1 & 2, #3 & 4, #5 & 6, #7 & 8.