With Russian Roulette, the value computed for the estimate given a sample is $\frac{X}{p_{rr}}$ with probability $p_{rr}$ and 0 with probability $(1-p_{rr})$. In other words, with probability $(1-p_{rr})$ sometimes we "kill the sample", but weight the result when we don't kill the sample to keep the estimate unbiased.
Therefore, the expected value of the new estimate ${RR}(X)$ is: $E[{RR}(X)] = p_{rr}\frac{E[X]}{p_{rr}} + (1-p_{rr})0 = E[X]$
pavelkang
From the previous slide, it seems that we kill the sample if: the value in brackets is small. From this slide, we kill the sample with (1 - prr) probability. How are they the same principle?
kayvonf
The are the same concept because the probability is derived from how small we jump ahead and look at the pseudocode on slide 46. There, we're trying to estimate the amount of light reflected from the surface in the direction -ray. Therefore, E[X/p_rr] on this slide corresponds to the value computed in the last line of pathtrace(Ray r) on slide 46.
The probability of termination, which on this slide corresponds to (1-p_rr), takes on a value proportional to the absorption of the surface (1-rho). When absorption is high (the surface is almost black), then the amount of light reflected from the surface will be low, and so with high probability we kill the path. Note that, E[X/p_rr] is proportional to reflectance (1-absorption).
With Russian Roulette, the value computed for the estimate given a sample is $\frac{X}{p_{rr}}$ with probability $p_{rr}$ and 0 with probability $(1-p_{rr})$. In other words, with probability $(1-p_{rr})$ sometimes we "kill the sample", but weight the result when we don't kill the sample to keep the estimate unbiased.
Therefore, the expected value of the new estimate ${RR}(X)$ is: $E[{RR}(X)] = p_{rr}\frac{E[X]}{p_{rr}} + (1-p_{rr})0 = E[X]$
From the previous slide, it seems that we kill the sample if: the value in brackets is small. From this slide, we kill the sample with (1 - prr) probability. How are they the same principle?
The are the same concept because the probability is derived from how small we jump ahead and look at the pseudocode on slide 46. There, we're trying to estimate the amount of light reflected from the surface in the direction
-ray. Therefore, E[X/p_rr] on this slide corresponds to the value computed in the last line ofpathtrace(Ray r)on slide 46.The probability of termination, which on this slide corresponds to (1-p_rr), takes on a value proportional to the absorption of the surface (
1-rho). When absorption is high (the surface is almost black), then the amount of light reflected from the surface will be low, and so with high probability we kill the path. Note that, E[X/p_rr] is proportional to reflectance (1-absorption).