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 prr 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]2
Let's say prr=2n1, then the increase in variance scales at a rate of 2n. We can also note if prr=1, then there is no increase in variance.
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 prr 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]2
E[Xrr2]=prrE[prr2X2]
=prr1E[X2]
E[Xrr]2=E[X]2
V[Xrr]=prr1E[X2]−E[X2]
=V[X]+(prr1−1)E[X2]
Let's say prr=2n1, then the increase in variance scales at a rate of 2n. We can also note if prr=1, then there is no increase in variance.