Comparison of light selection techniques and their combinations in the Staircase II scene

Comparison of different combination strategies for a trained light selection technique (Trained) and a defensive technique (Uniform, NoMax). In contrast to the balance/power heuristic, the optimal MIS weights are never worse than any of the two techniques alone. See Section 8.2 in the main paper for discussion.

Compared variants

VariantUsed shortcut
UniformU
TrainedT
NoMaxM
Trained + Uniform, balance heuristicT+U bal
Trained + Uniform, power heuristicT+U pow
Trained + Uniform, optimal weights - direct estimatorT+U opt-dir
Trained + Uniform, optimal weights - progressive etimator with update step UT+U opt-prog-U
Trained + NoMax, balance heuristicT+M bal
Trained + NoMax, power heuristicT+M pow
Trained + NoMax, optimal weights - direct estimatorT+M opt-dir
Trained + NoMax, optimal weights - progressive etimator with update step UT+M opt-prog-U

Equal-time comparison

Number of iterations is set so each variant takes approximately 20 s to render.

Variant Time [s] Iterations MSE Speedup (to T+U pow) Speedup (to T+M pow)
U 19.07 49 3.05E-002 0.02 0.02
T 19.13 41 4.67E-004 1.35 1.15
M 19.76 44 1.46E-001 0.00 0.00
T+U bal 19.19 32 7.43E-004 0.85 0.72
T+U pow 19.32 32 6.33E-004 1.00 0.85
T+U opt-dir 19.11 31 2.43E-004 2.61 2.22
T+M bal 19.53 30 5.02E-004 1.26 1.07
T+M pow 19.54 30 5.38E-004 1.18 1.00
T+M opt-dir 19.23 29 7.14E-005 8.86 7.53
T+U opt-prog-1 19.79 25 3.47E-004 1.82 1.55
T+U opt-prog-2 19.91 28 3.23E-004 1.96 1.66
T+U opt-prog-3 19.35 28 3.47E-004 1.82 1.55
T+U opt-prog-4 19.59 29 3.55E-004 1.78 1.52
T+U opt-prog-5 19.89 30 3.60E-004 1.75 1.49
T+U opt-prog-6 19.68 30 3.80E-004 1.67 1.42
T+U opt-prog-7 19.78 30 3.97E-004 1.59 1.35
T+U opt-prog-8 19.79 30 4.16E-004 1.52 1.29
T+U opt-prog-9 19.50 30 4.37E-004 1.45 1.23
T+U opt-prog-10 20.21 31 4.35E-004 1.45 1.24
T+M opt-prog-1 19.84 24 1.21E-004 5.25 4.46
T+M opt-prog-2 19.59 26 1.32E-004 4.81 4.09
T+M opt-prog-3 19.64 27 1.44E-004 4.38 3.72
T+M opt-prog-4 19.44 27 1.65E-004 3.82 3.25
T+M opt-prog-5 19.87 28 1.75E-004 3.61 3.07
T+M opt-prog-6 19.81 28 1.95E-004 3.24 2.75
T+M opt-prog-7 19.61 28 2.15E-004 2.95 2.51
T+M opt-prog-8 19.58 28 2.32E-004 2.73 2.32
T+M opt-prog-9 19.91 28 2.50E-004 2.53 2.15
T+M opt-prog-10 20.08 29 2.50E-004 2.53 2.15
Ref U T M T+U bal T+U pow T+U opt-dir T+M bal T+M pow T+M opt-dir T+U opt-prog-1 T+U opt-prog-2 T+U opt-prog-3 T+U opt-prog-4 T+U opt-prog-5 T+U opt-prog-6 T+U opt-prog-7 T+U opt-prog-8 T+U opt-prog-9 T+U opt-prog-10 T+M opt-prog-1 T+M opt-prog-2 T+M opt-prog-3 T+M opt-prog-4 T+M opt-prog-5 T+M opt-prog-6 T+M opt-prog-7 T+M opt-prog-8 T+M opt-prog-9 T+M opt-prog-10

Equal-sample comparison

Each variant renders 20 iterations, i.e. draws 20 samples per technique per pixel. For the single-technique variants results with the same total number of samples per pixel (i.e. 40) are also included.

Variant Time [s] Iterations MSE Overhead (to T+U pow) Overhead (to T+M pow) Improvement (to T+U pow) Improvement (to T+M pow)
U 8.00 20 7.48E-002 -34.52% -38.93% 0.01 0.01
U 40 15.71 40 3.77E-002 28.54% 19.90% 0.03 0.02
T 9.39 20 8.99E-004 -23.15% -28.32% 1.13 0.89
T 40 18.61 40 4.71E-004 52.30% 42.05% 2.15 1.70
M 8.97 20 1.46E-001 -26.60% -31.54% 0.01 0.01
M 40 17.83 40 1.46E-001 45.90% 36.09% 0.01 0.01
T+U bal 12.19 20 1.19E-003 -0.26% -6.97% 0.85 0.67
T+U pow 12.22 20 1.01E-003 0.00% -6.72% 1.00 0.79
T+U opt-dir 12.52 20 3.76E-004 2.44% -4.45% 2.69 2.13
T+M bal 13.08 20 7.46E-004 7.00% -0.19% 1.36 1.07
T+M pow 13.10 20 8.02E-004 7.21% 0.00% 1.26 1.00
T+M opt-dir 13.44 20 1.02E-004 9.93% 2.54% 9.90 7.83
T+U opt-prog-1 15.70 20 4.46E-004 28.48% 19.84% 2.27 1.80
T+U opt-prog-2 14.25 20 4.80E-004 16.64% 8.79% 2.11 1.67
T+U opt-prog-3 13.83 20 5.25E-004 13.13% 5.53% 1.93 1.53
T+U opt-prog-4 13.62 20 5.69E-004 11.44% 3.95% 1.78 1.41
T+U opt-prog-5 13.32 20 6.10E-004 8.95% 1.63% 1.66 1.31
T+U opt-prog-6 13.31 20 6.51E-004 8.93% 1.60% 1.56 1.23
T+U opt-prog-7 13.11 20 6.97E-004 7.31% 0.09% 1.45 1.15
T+U opt-prog-8 13.21 20 7.37E-004 8.08% 0.82% 1.37 1.09
T+U opt-prog-9 13.14 20 7.77E-004 7.51% 0.28% 1.30 1.03
T+U opt-prog-10 12.96 20 8.16E-004 6.05% -1.08% 1.24 0.98
T+M opt-prog-1 16.54 20 1.52E-004 35.32% 26.23% 6.68 5.29
T+M opt-prog-2 15.16 20 1.90E-004 24.07% 15.73% 5.35 4.23
T+M opt-prog-3 14.73 20 2.24E-004 20.53% 12.43% 4.52 3.58
T+M opt-prog-4 14.38 20 2.59E-004 17.64% 9.73% 3.90 3.09
T+M opt-prog-5 14.25 20 2.95E-004 16.57% 8.73% 3.43 2.72
T+M opt-prog-6 14.19 20 3.32E-004 16.14% 8.33% 3.05 2.42
T+M opt-prog-7 14.11 20 3.68E-004 15.45% 7.69% 2.75 2.18
T+M opt-prog-8 14.03 20 4.03E-004 14.76% 7.04% 2.51 1.99
T+M opt-prog-9 14.10 20 4.34E-004 15.40% 7.64% 2.33 1.85
T+M opt-prog-10 13.87 20 4.62E-004 13.47% 5.84% 2.19 1.74
Ref U U 40 T T 40 M M 40 T+U bal T+U pow T+U opt-dir T+M bal T+M pow T+M opt-dir T+U opt-prog-1 T+U opt-prog-2 T+U opt-prog-3 T+U opt-prog-4 T+U opt-prog-5 T+U opt-prog-6 T+U opt-prog-7 T+U opt-prog-8 T+U opt-prog-9 T+U opt-prog-10 T+M opt-prog-1 T+M opt-prog-2 T+M opt-prog-3 T+M opt-prog-4 T+M opt-prog-5 T+M opt-prog-6 T+M opt-prog-7 T+M opt-prog-8 T+M opt-prog-9 T+M opt-prog-10