Stochastic Sampling

[rcallicotte]

It's beyond me how anyone even understands this.  But, I'm thrilled someone does.

http://graphics.pixar.com/library/StochasticSampling/paper.pdf

[Tangled-Universe]

The technical aspects, the math for example, are complex and not for everyone.

However, the principles often isn't that opaque and if the article is well written it can be understood by everybody with an average interest in the subject. That's always a condition of course for this kind of publication, but there's really a clear distinction in quality of papers in how they are written.
(I work in medical science and funny enough the Science/Nature/Cell papers which are the cream of the crop/groundbreaking are the ones with the clearest introduction, hypothesis, methods and results/discussion.)

Stochastic basically means a process in space and/or time with outcomes depending on stachistic processes.
Stochastic processes are random, like radio-active decay.
Stochastic process are driven by chance and have a certain statistical distribution.
The publically best known distribution is Gaussian distribution, but of course there are other types of distrubtions.

This paper deals with a method of sampling 3D space in a non-uniform way (not evenly spaced sample positions) using a stochastic method.
Ultimately CGI and rendering is about achieving results which appear natural and photoreal using models who mimic these natural phenomena without actually calculating them all brute force.
Stochastic sampling is a random sample method using a statistically random method for spreading sample methods.
So they are basically looking for a statistical method which effectively and efficiently uses samples for rendering.

This paper is from 1986 and is probably a foundation of modern sample methods like Multiple Importance Sampling, which is also non-uniform, but not stochastic since sample positions are chosen on set parameters or conditions, introducing a bias and thus taking away the random nature (stochastic nature) of the sampling method.

Multiple Importance Sampling or other schemes like Monte Carlo are often derived from other fields like economy (importance sampling) or nuclear energy research (Monte Carlo).

Basically these Professors/TD's either discover these themselves or adopt/adapt existing methods from other research fields.
It's the advantage of using math, as it's a universal language.

[rcallicotte]

TU, thanks so much! I didn't get that out of the article quite like that, though understood was almost a science of chaos on sampling points to not overdue aliasing. But, it sounds like this sort of stochastic sampling might be good for shadows, gloss, blur, motion, etc.  Nevertheless, I appreciate your time and this has been helpful.

If anyone is interested, I got this article by doing some research on the Thea Render Engine (http://www.thearender.com/).  That looks like a well driven product.

[pokoy]

But, it sounds like this sort of stochastic sampling might be good for shadows, gloss, blur, motion, etc.

Afaik, this is what Pixar's Renderman is using for motion blur (and probably more). One reason why it's not available everywhere is that it's patented. Every render engine dev must therefore find his own way to utilize a concept and make sure it's solved in a different way.

Another example, there's a technically easy way to implement corner rounding for sharp edges at rendertime. It's a snap to implement in any renderer but mental images have patented the technique and no one else can use it in their engine.

[rcallicotte]

It sounds like this goads others to think about different algorithms to do the same sort of thing then, which probably helps render engines.  This is especially a good idea today with so many render engines.