Master Thesis - Computer Graphics and Visualization - TU Delft

Unbiased Rendering 2.10 Energy Redistribution Path Tracing
Algorithm 2 : EnergyRedistribution(X0,N,ed)
f (X0) 1
numChains ← U(0,1) + p(X0) N×ed
for i = 1 to numChains do
Y ← X0
for j = 1 to N do
Z ←mutate(Y)
a ← a(Y → Z)
deposit aed energy at Z
deposit (1 − a)ed energy at Y
if a ≥ U(0,1) then
Y ← Z
end if
end for
end for
Finally, a useful property of the ERPT algorithm is that its mutation strategy does not
necessarily need to satisfy ergodicity for the outcome to be unbiased. The reason is that mutation
chains already have their initial samples distributed proportional to f . Note however
that although the outcome will remain unbiased when using only a few ERPT samples, the
error may become unacceptably large. We will discuss this in more detail in section 9.2.2.
Using many ERPT samples with relatively short mutation chains solves this problem.
Although N should not be chosen too large, N should not be chosen too small either. In
ERPT the value of N determines the amount of energy redistribution. For effective energy
redistribution, N should be reasonably large. If N is too small, ERPT effectively deteriorates
into a quantized PT algorithm. To see why, let us look at the extreme case without any
energy redistribution; each mutation chain only contains its initial sample. The number of
chains per initial sample is proportional to f , so each sample will contribute on average
ed U(0,1) + 1
f (X0)
ed p(X0) = f (X0)
p(X0) . All this energy is contributed to a single pixel; the pixel
corresponding to X0. Hence, because each chain contributes a single energy quantum, the
remaining algorithm is a quantized PT algorithm, performing worse than normal PT.
The ERPT algorithm presented in [11] uses only the lens and caustic mutation types
from the MLT algorithm and an N in the order of 100. Note that because lens and caustic
mutations do not change the length or signature of a path, all paths in a mutation chain have
the same length and signature.
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