Effect of Noise on Accuracy and Speed

The beads used for these tests are generated algorithmically and then have noise added to them algorithmically. They dark-on-gray discs of radius 10. The background value is 75% of maximum brightness and the disc is at 25%. The disc 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 spots 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 disc sits still the whole time (the tracker is not initiated at the bead center); this tests how well it can determine that a bead is in fact sitting still. In the second table, the bead moves in a circle with the noise added; this tests how well a bead can be followed in the presence of noise. For all trials, the Video Spot Tracker precision setting is 0.001 and sample_spacing is 0.1. All trials use a symmetric tracking kernel with a radius of 15.

Test 1: Stationary Bead

Noise Level	Bead Type	Motion	Mean Radial Error	Mean X Error	Mean Y Error	Max Radial Error	X Bias	Y Bias	Estimates/Sec	True Log	VST Log	Images
none	Disc	Stationary	0.0150648	0.010234	0.011055	0.0150648	0.010234	-0.011055	3.59545	Log	VST Log	Images
Mean=2 Var=1e4	Disc	Stationary	0.0144168	0.0098859	0.0104689	0.0161624	0.0098859	-0.0104689	3.46502	Log	VST Log	Images
Mean=20 Var=1e5	Disc	Stationary	0.014173	0.00976864	0.0100588	0.0196649	0.00976864	-0.0100588	3.06358	Log	VST Log	Images
Mean=200 Var=1e6	Disc	Stationary	0.0146407	0.00984484	0.009451	0.0304166	0.00953428	-0.00884788	2.87702	Log	VST Log	Images
Mean=2000 Var=1e7	Disc	Stationary	0.0256116	0.0170566	0.0156188	0.066041	0.00849914	-0.0043753	2.65527	Log	VST Log	Images
Mean=20000 Var=1e8	Disc	Stationary	0.0911199	0.060483	0.0556007	0.207681	0.0069561	0.0131833	2.46691	Log	VST Log	Images

Example images follow:

disc_10_sym_stat.0_0.0000.bmp	disc_10_sym_stat.2_1e4.0000.bmp	disc_10_sym_stat.20_1e5.0000.bmp
disc_10_sym_stat.200_1e6.0000.bmp	disc_10_sym_stat.2000_1e7.0000.bmp	disc_10_sym_stat.20000_1e8.0000.bmp

Test 2: Circular Motion

Noise Level	Bead Type	Motion	Mean Radial Error	Mean X Error	Mean Y Error	Max Radial Error	X Bias	Y Bias	Estimates/Sec	True Log	VST Log	Images
none	Disc	Circular	0.00806795	0.00483482	0.00543805	0.0147858	0.00456758	-0.00525318	2.11427	Log	VST Log	Images
Mean=2 Var=1e4	Disc	Circular	0.00804868	0.00485778	0.00538497	0.0156302	0.00459498	-0.00515909	2.03392	Log	VST Log	Images
Mean=20 Var=1e5	Disc	Circular	0.00822389	0.00500767	0.00548386	0.0170433	0.00451365	-0.00503703	2.02709	Log	VST Log	Images
Mean=200 Var=1e6	Disc	Circular	0.0107793	0.00702044	0.00690986	0.0270938	0.00452174	-0.00454056	2.03444	Log	VST Log	Images
Mean=2000 Var=1e7	Disc	Circular	0.0255572	0.0169086	0.0160437	0.0685741	0.00426953	-0.00308391	2.09108	Log	VST Log	Images
Mean=20000 Var=1e8	Disc	Circular	0.0850371	0.0529734	0.0555646	0.203978	-5.17917e-005	0.00335335	1.97878	Log	VST Log	Images

Example images follow:

disc_10_sym_circle.0_0.0000.bmp	disc_10_sym_circle.2_1e4.0000.bmp	disc_10_sym_circle.20_1e5.0000.bmp
disc_10_sym_circle.200_1e6.0000.bmp	disc_10_sym_circle.2000_1e7.0000.bmp	disc_10_sym_circle.20000_1e8.0000.bmp

Test 3: Random Motion

Noise Level	Bead Type	Motion	Mean Radial Error	Mean X Error	Mean Y Error	Max Radial Error	X Bias	Y Bias	Estimates/Sec	True Log	VST Log	Images
none	Disc	Random	0.00844141	0.00535416	0.00518495	0.0148395	0.00513604	-0.00498903	2.05384	Log	VST Log	Images
Mean=2 Var=1e4	Disc	Random	0.00844246	0.00527162	0.00523082	0.0150425	0.00507905	-0.00498898	2.08843	Log	VST Log	Images
Mean=20 Var=1e5	Disc	Random	0.00871978	0.00552038	0.00549998	0.0194282	0.00507911	-0.00487504	2.08548	Log	VST Log	Images
Mean=200 Var=1e6	Disc	Random	0.0114386	0.00734114	0.0071401	0.0326477	0.00501396	-0.0046797	2.12901	Log	VST Log	Images
Mean=2000 Var=1e7	Disc	Random	0.0272841	0.0185386	0.0164134	0.0798651	0.00455825	-0.00418331	2.09561	Log	VST Log	Images
Mean=20000 Var=1e8	Disc	Random	0.0855137	0.056087	0.0516094	0.227354	0.00397233	-0.00327187	2.07582	Log	VST Log	Images

Example images follow:

disc_10_sym_random.0_0.0000.bmp	disc_10_sym_random.2_1e4.0000.bmp	disc_10_sym_random.20_1e5.0000.bmp
disc_10_sym_random.200_1e6.0000.bmp	disc_10_sym_random.2000_1e7.0000.bmp	disc_10_sym_random.20000_1e8.0000.bmp