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
| Variant | Used shortcut |
|---|
| Uniform | U |
| Trained | T |
| NoMax | M |
| Trained + Uniform, balance heuristic | T+U bal |
| Trained + Uniform, power heuristic | T+U pow |
| Trained + Uniform, optimal weights - direct estimator | T+U opt-dir |
| Trained + Uniform, optimal weights - progressive etimator with update step U | T+U opt-prog-U |
| Trained + NoMax, balance heuristic | T+M bal |
| Trained + NoMax, power heuristic | T+M pow |
| Trained + NoMax, optimal weights - direct estimator | T+M opt-dir |
| Trained + NoMax, optimal weights - progressive etimator with update step U | T+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 |
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 |
