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Lecture 13: Global Illumination & Path Tracing (81)

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?


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?


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


@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


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.

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