You are viewing the course site for a past offering of this course. The current offering may be found here.
Lecture 13: Global Illumination & Path Tracing (81)
ABSchloss

Any intuition into common choices for p_rr, or is it extremely variable by scene? If there is a common choice, does it seem to model the real world well? Or is real world modeling inefficient so, if we chose solely for efficiency, we end up with a noticeably different result?

bufudash

How does Russian Roulette, aka reweighing first and terminate if high expense unbiased? Isn't it still true in this case that we cannot account what happens if a light takes n+1 bounces?

visatish

@bufudash I believe it is unbiased by definition because it has the same expected value as the original estimator

visatish

@ABSchloss I looked at some example implementations online, and it seems that prrp_{rr} is not really a constant value but dynamically computed at runtime and changes as the algorithm progresses

ChrisP19

Although the estimator is unbiased, I was curious about its effect on the variance:
V[Xrr]=E[Xrr2]E[Xrr]2V[X_{rr}] = E[X_{rr}^2] - E[X_{rr}]^2

E[Xrr2]=prrE[X2prr2]E[X_{rr}^2] = p_{rr} E[\frac{X^2}{p_{rr}^2}]
=1prrE[X2]= \frac{1}{p_{rr}} E[X^2]

E[Xrr]2=E[X]2E[X_{rr}]^2 = E[X]^2

V[Xrr]=1prrE[X2]E[X2]V[X_{rr}] = \frac{1}{p_{rr}} E[X^2] - E[X^2]
=V[X]+(1prr1)E[X2]= V[X] + (\frac{1}{p_{rr}} - 1)E[X^2]

Let's say prr=12np_{rr} = \frac{1}{2^n}, then the increase in variance scales at a rate of 2n2^n. We can also note if prr=1p_{rr}=1, then there is no increase in variance.

You must be enrolled in the course to comment