Effect of Noise on Accuracy and Speed in rods

The rods used for these tests are generated algorithmically and then have noise added to them algorithmically. They dark-on-gray rods of radius 5 and length 30. The background is at 75% of maximum brighness and the rods are at 25%. The samples are averaged over a uniform grid that has 100 times the resolution in X and Y of the final image. This should make it possible to precisely localize the rods to 1/100th of a pixel. The added noise is Gaussian noise with the mean and variance specified in the table. In the first table, the rod sits still the whole time (the tracker is not initiated at the rod center); this tests how well it can determine that a rod is in fact sitting still in the presence of noise. In the second table, the rod moves in a circle with the noise added; this tests how well a rod can be followed in the presence of noise. In the third table, the rod moves randomly in X and Y and changes its orientations randomly. For all trials, the Video Spot Tracker precision setting is 0.001 and sample_spacing is 0.1. All trials use a dark cone tracking kernel with a radius of 5; the rod3 kernel has a length of 30.

Test 1: Stationary Rod

Noise Level	Motion	Mean Radial Error	Mean X Error	Mean Y Error	Max Radial Error	X Bias	Y Bias	Mean Angle Error	Max Angle Error	Angle Bias	Estimates/Sec	True Log	VST Log	Images
none	Stationary	0.0308849	0.024922	0.018242	0.0308849	-0.024922	0.018242	0	0	0	4.92168	Log	VST Log	Images
Mean=2 Var=1e4	Stationary	0.030405	0.0247431	0.0174607	0.0391631	-0.0247431	0.0174607	0.00596852	0.018646	-0.00253588	3.92564	Log	VST Log	Images
Mean=20 Var=1e5	Stationary	0.0300929	0.0234735	0.0166513	0.0625993	-0.0234735	0.0162888	0.0237994	0.074615	-0.0015711	3.54691	Log	VST Log	Images
Mean=200 Var=1e6	Stationary	0.0452372	0.0261961	0.0298297	0.15623	-0.0194305	0.0100388	0.0935527	0.246193	0.00268504	3.17899	Log	VST Log	Images
Mean=2000 Var=1e7	Stationary	0.131438	0.0659498	0.101702	0.393246	-0.0125751	0.00019502	0.282375	0.675163	0.0270762	2.89941	Log	VST Log	Images
Mean=20000 Var=1e8	Stationary	0.502901	0.237097	0.413041	1.71041	0.00422176	-0.0816018	0.953066	2.78646	0.284471	2.63655	Log	VST Log	Images

Example images follow:

rod_5_30_sym_stat.0_0.0000.bmp	rod_5_30_sym_stat.2_1e4.0000.bmp	rod_5_30_sym_stat.20_1e5.0000.bmp
rod_5_30_sym_stat.200_1e6.0000.bmp	rod_5_30_sym_stat.2000_1e7.0000.bmp	rod_5_30_sym_stat.20000_1e8.0000.bmp

Test 2: Circular Motion

Noise Level	Motion	Mean Radial Error	Mean X Error	Mean Y Error	Max Radial Error	X Bias	Y Bias	Mean Angle Error	Max Angle Error	Angle Bias	Estimates/Sec	True Log	VST Log	Images
none	Circular	0.0163845	0.0105653	0.010212	0.045901	0.00320041	-0.00560312	0.0314952	0.117096	-0.000148258	2.42269	Log	VST Log	Images
Mean=2 Var=1e4	Circular	0.0172567	0.011197	0.0107141	0.0480692	0.0034476	-0.00585893	0.0314064	0.123795	-6.71083e-005	2.41182	Log	VST Log	Images
Mean=20 Var=1e5	Circular	0.0222573	0.0143774	0.0140803	0.0622251	0.00414742	-0.00637166	0.0398578	0.161957	-0.000250617	2.38354	Log	VST Log	Images
Mean=200 Var=1e6	Circular	0.0487747	0.0305726	0.0317839	0.138059	0.00617381	-0.00793413	0.0940205	0.276031	-0.00226763	2.36176	Log	VST Log	Images
Mean=2000 Var=1e7	Circular	0.142142	0.0881446	0.0932669	0.401981	0.00962431	-0.0147294	0.281866	1.1004	-0.018026	2.42519	Log	VST Log	Images
Mean=20000 Var=1e8	Circular	0.489353	0.310573	0.307356	1.75638	0.0156872	-0.0316484	1.01793	3.6611	-0.0952496	2.41472	Log	VST Log	Images

Example images follow:

rod_5_30_sym_circle.0_0.0000.bmp	rod_5_30_sym_circle.2_1e4.0000.bmp	rod_5_30_sym_circle.20_1e5.0000.bmp
rod_5_30_sym_circle.200_1e6.0000.bmp	rod_5_30_sym_circle.2000_1e7.0000.bmp	rod_5_30_sym_circle.20000_1e8.0000.bmp

Test 3: Random Motion

Noise Level	Motion	Mean Radial Error	Mean X Error	Mean Y Error	Max Radial Error	X Bias	Y Bias	Mean Angle Error	Max Angle Error	Angle Bias	Estimates/Sec	True Log	VST Log	Images
none	Random	0.0210238	0.0151785	0.0118897	0.0362043	0.00525892	-0.00632918	0.0338768	0.090191	0.00538893	2.53039	Log	VST Log	Images
Mean=2 Var=1e4	Random	0.0216665	0.0157734	0.0120125	0.038413	0.00551576	-0.00591928	0.0364027	0.089806	0.00673173	2.47986	Log	VST Log	Images
Mean=20 Var=1e5	Random	0.0251692	0.0193236	0.0124603	0.0538664	0.0056134	-0.0050991	0.0461941	0.118241	0.00874627	2.47881	Log	VST Log	Images
Mean=200 Var=1e6	Random	0.0494536	0.0387843	0.0211734	0.123058	0.00532042	-0.00254042	0.0950598	0.216287	0.0163558	2.48852	Log	VST Log	Images
Mean=2000 Var=1e7	Random	0.142333	0.112748	0.0641769	0.350723	0.00350408	0.00577988	0.26414	0.67883	0.0383639	2.5157	Log	VST Log	Images
Mean=20000 Var=1e8	Random	0.547571	0.441106	0.253666	1.23251	-0.0250702	0.0341783	1.01686	2.64395	0.176008	2.3684	Log	VST Log	Images

Example images follow:

rod_5_30_sym_random.0_0.0000.bmp	rod_5_30_sym_random.2_1e4.0000.bmp	rod_5_30_sym_random.20_1e5.0000.bmp
rod_5_30_sym_random.200_1e6.0000.bmp	rod_5_30_sym_random.2000_1e7.0000.bmp	rod_5_30_sym_random.20000_1e8.0000.bmp