Images

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Majorant scale = 0.1

Majorant scale = 0.3

Majorant scale = 0.6

Majorant scale = 1.0

Majorant scale = 1.5

Majorant scale = 2.5

Majorant scale = 5.0

1: Track-length

2: Next-flight

3: Ratio tracking

4: Unidir-MIS

5: Bidir-MIS

6: P-Cumulative

7: P-CMF

8: Ground Truth

Track-length

Next-flight

Ratio tracking

Unidir-MIS

Bidir-MIS

P-Cumulative

P-CMF

Ground Truth

Charts

Relative performance obtained by dividing the error of each estimator by the error from ratio tracking. For each estimator we compare the performance while scaling the global majorant by 1, 1.5, 2, 5, and 10 respectfully. All estimators are ran for approximately the same number of extinction calls for every majorant scale, however, the number of extinction calls varies across the different majorant scales. The number of extinction calls was chosen based on the average number of extinction calls necessary for the bidirectional estimator to complete two pixel samples. Lower values mean better performance. A value of 1 means the estimator performs equivalently to ratio tracking. For majorant scales where a path returns numerical infinity for an estimate, all error values are reported as zero, so the first few bars may be nonexistant.

RMSE

MSE

MAD

MARD

EFF

Error Metrics

Relative performance per scene configuration is displayed by varying the background color between red and green. Red meaning an estimator performs poorly in comparison to the others, while green means it performs comparatively well. Note: Track Length is biased for all non-bounding majorants, and all estimators whose error metrics are infinite have blacked out boxes.

RMSE
Majorant scale	Track-length	Next-flight	Ratio tracking	Unidir-MIS	Bidir-MIS	P-Cumulative	P-CMF
0.1	Infinity	84.97	86.15	83.55	59.74	9.065	20.00
0.3	Infinity	0.8110	0.6170	0.7310	0.5186	0.3076	0.3078
0.6	Infinity	0.2457	0.09758	0.2000	0.2474	0.1285	0.1104
1.0	0.1078	0.2219	0.05848	0.1767	0.2104	0.07778	0.07222
1.5	0.1050	0.2142	0.04648	0.1692	0.1913	0.06982	0.05184
2.5	0.1028	0.2090	0.03434	0.1640	0.1725	0.05327	0.03782
5.0	0.1020	0.2050	0.02360	0.1601	0.1521	0.03727	0.02564

MSE
Majorant scale	Track-length	Next-flight	Ratio tracking	Unidir-MIS	Bidir-MIS	P-Cumulative	P-CMF
0.1	Infinity	7219	7422	6981	3569	82.18	400.1
0.3	Infinity	0.6577	0.3807	0.5343	0.2689	0.09463	0.09472
0.6	Infinity	0.06037	0.009521	0.04001	0.06118	0.01652	0.01219
1.0	0.01162	0.04924	0.003420	0.03123	0.04428	0.006050	0.005216
1.5	0.01103	0.04587	0.002160	0.02863	0.03659	0.004874	0.002687
2.5	0.01056	0.04370	0.001179	0.02688	0.02975	0.002838	0.001431
5.0	0.01041	0.04201	0.0005567	0.02564	0.02314	0.001389	0.0006575

MAD
Majorant scale	Track-length	Next-flight	Ratio tracking	Unidir-MIS	Bidir-MIS	P-Cumulative	P-CMF
0.1	Infinity	1.174	1.264	1.191	0.9023	0.5758	0.6800
0.3	Infinity	0.2551	0.1551	0.2259	0.2469	0.1416	0.1367
0.6	Infinity	0.1879	0.05697	0.1552	0.1841	0.07687	0.06436
1.0	0.06157	0.1639	0.03325	0.1328	0.1516	0.04485	0.04129
1.5	0.06023	0.1556	0.02595	0.1248	0.1362	0.03912	0.02945
2.5	0.05915	0.1502	0.01901	0.1194	0.1221	0.02947	0.02156
5.0	0.05870	0.1460	0.01299	0.1152	0.1074	0.02040	0.01481

MARD
Majorant scale	Track-length	Next-flight	Ratio tracking	Unidir-MIS	Bidir-MIS	P-Cumulative	P-CMF
0.1	Infinity	40.46	45.43	41.74	32.64	22.74	26.04
0.3	Infinity	4.111	3.927	3.972	3.281	2.560	2.548
0.6	Infinity	0.7926	0.5465	0.7168	0.6517	0.6030	0.5436
1.0	0.3032	0.4223	0.2107	0.3702	0.3366	0.2530	0.2321
1.5	0.3001	0.3488	0.1419	0.2962	0.2791	0.1907	0.1520
2.5	0.2972	0.3115	0.09724	0.2578	0.2409	0.1378	0.1033
5.0	0.2947	0.2843	0.06336	0.2298	0.2054	0.09344	0.06722

EFF
Majorant scale	Track-length	Next-flight	Ratio tracking	Unidir-MIS	Bidir-MIS	P-Cumulative	P-CMF
0.1	Infinity	5.834e+5	5.998e+5	5.641e+5	2.884e+5	6641	3.233e+4
0.3	Infinity	53.14	30.77	43.18	21.73	7.647	7.654
0.6	Infinity	5.874	0.9265	3.893	5.953	1.608	1.186
1.0	1.939	8.214	0.5706	5.209	7.386	1.009	0.8702
1.5	2.803	11.66	0.5490	7.276	9.300	1.239	0.6829
2.5	4.535	18.76	0.5063	11.54	12.77	1.219	0.6144
5.0	9.046	36.50	0.4837	22.28	20.10	1.207	0.5712