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Archive Notice: This thread is old and no longer active. It is here for reference purposes. This thread was created on an older version of the flipcode forums, before the site closed in 2005. Please keep that in mind as you view this thread, as many of the topics and opinions may be outdated.
 
andrei

April 18, 2005, 03:28 PM

I'm studying ray-tracing, and decided to take a look at non-uniform sampling, especially stochastic sampling. Well, one of the classic methods for stochastic sampling is called Poisson sampling, where the coordinates of the samples are drawn at random from a uniform distribution. I'd like to know what's the connection of this method with the Poisson distribution for random variables and the Poisson stochastic process, because this was not made clear in the books I've read, and I believe it wouldn't make sense using the same name for a different random distribution when there's already one by that name.

Does anyone have any clue ?

 
Reedbeta

April 18, 2005, 08:37 PM

I believe the connection is simply that the cells in the human eye are approximately Poisson distributed over the retina, and Poisson distributing rays in screen space seeks to imitate the ability of the eye to transform high frequencies into noise.

In practice, rather than choosing sample points completely randomly, one usually randomly jitters a regular grid. This is better than a completely random distribution since it avoids the clustering that tends to happen with random numbers, and ensures that every part of the domain gets sampled. It's also fairly easy to extend to importance sampling by replacing the regular grid with one concentrated in important areas and then jittering that.

 
Qndrez

April 18, 2005, 10:47 PM

Another way of avoiding "clusters" is to ensure a minimum distance between two samples. In my ray tracing exploits I've found this solution better samples the space than jittering within a regular grid.

There are many other solutions to this problem out there. Check out PBRT (a book) at www.pbrt.org. It just so happens that their sample chapter discusses this subject in great detail:

http://graphics.stanford.edu/~mmp/chapters/pbrt_chapter7.pdf

You can pick up the whole text for about $80~60.

-Andrew

 
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