Effect of Precision and Sample Spacing on Accuracy and Speed

The beads used for these tests are generated algorithmically. They are dark-on-gray discs of radius 10 and Gaussian spots of radius 10. There is no noise in these images. The background is at 75% of maximum brightness, and the darkest spot on the disc or Gaussian is 25%. The disc samples are averaged over a uniform grid that has 100 times the resolution in X and Y of the final image. The Gaussian samples are averaged over a uniform grid that has 10 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 Video Spot Tracker is run with different settings for precision and sample_spacing to see the effect on speed and accuracy of tracking. Blank entries for the speed column indicate that the tracking completed too rapidly to get a good estimate of timing, which means that they are faster than any of the columns that do include timing. The tracking kernel was a symmetric kernel with a radius 15 in all of the runs.

Test 1: Disc spots

Precision	Sample Spacing	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
0.001	0.1	Disc	Circular	0.00743436	0.00468908	0.00451773	0.0148228	0.0044655	-0.0043383	1.99448	Log	VST Log	Images
0.001	0.2	Disc	Circular	0.00739587	0.00459836	0.0044849	0.0155594	0.00433522	-0.00427318	8.44615	Log	VST Log	Images
0.001	0.5	Disc	Circular	0.00810546	0.00543041	0.00488998	0.015716	0.00524672	-0.00455797	45.3363	Log	VST Log	Images
0.001	1.0	Disc	Circular	0.00953301	0.00587397	0.00591962	0.0198051	0.00418872	-0.00409412	76.237	Log	VST Log	Images
0.001	2.0	Disc	Circular	0.0197425	0.0107352	0.0142437	0.0357732	0.00263438	-0.00426504	79.3517	Log	VST Log	Images
0.05	0.1	Disc	Circular	0.0129057	0.00816208	0.00807875	0.0282234	0.00602792	-0.00188875	3.65353	Log	VST Log	Images
0.05	0.2	Disc	Circular	0.0127145	0.00816208	0.00782458	0.0240442	0.00602792	-0.00136792	13.7667	Log	VST Log	Images
0.05	0.5	Disc	Circular	0.0130212	0.00814958	0.0082825	0.0303151	0.00602792	-0.00214917	62.1252	Log	VST Log	Images
0.05	1.0	Disc	Circular	0.0135332	0.0087075	0.0084425	0.0360147	0.0057675	-0.00214917	69.0476	Log	VST Log	Images
0.05	2.0	Disc	Circular	0.0221798	0.012385	0.0147508	0.0511646	0.00160083	-0.00267	84.8024	Log	VST Log	Images
0.1	0.1	Disc	Circular	0.0237945	0.0152475	0.0154417	0.0429671	-0.0004825	-0.00683667	3.99762	Log	VST Log	Images
0.1	0.2	Disc	Circular	0.0237804	0.015235	0.0154375	0.0429671	3.83333e-005	-0.0073575	15.7221	Log	VST Log	Images
0.1	0.5	Disc	Circular	0.0240692	0.0159367	0.015105	0.0509166	0.00316333	-0.00371167	61.9726	Log	VST Log	Images
0.1	1.0	Disc	Circular	0.0245487	0.015765	0.0157825	0.0514596	-0.00100333	-0.00631583	73.7723	Log	VST Log	Images
0.1	2.0	Disc	Circular	0.0307436	0.0186508	0.01987	0.0625799	0.00472583	-0.00371167	73.0661	Log	VST Log	Images

Example images follow:

disc_10_sym_circle.0000.bmp

Test 2: Gaussian spots

Precision	Sample Spacing	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
0.001	0.1	Gaussian	Circular	0.00297098	0.00176737	0.00198623	0.0067591	-0.000222033	0.000137683	2.07679	Log	VST Log	Images
0.001	0.2	Gaussian	Circular	0.00299796	0.00178228	0.0020025	0.0067591	-0.000238317	0.000121417	8.59592	Log	VST Log	Images
0.001	0.5	Gaussian	Circular	0.00300051	0.00182863	0.00196703	0.00655224	-0.0002383	0.000113275	43.5747	Log	VST Log	Images
0.001	1.0	Gaussian	Circular	0.0030555	0.00182948	0.00204448	0.00713394	-0.00026275	0.000210958	79.2214	Log	VST Log	Images
0.001	2.0	Gaussian	Circular	0.00440043	0.00269138	0.00295858	0.0104137	0.000111617	0.000194617	87.1841	Log	VST Log	Images
0.05	0.1	Gaussian	Circular	0.0111159	0.00693375	0.00728917	0.0205127	0.00029875	0.00149667	3.42039	Log	VST Log	Images
0.05	0.2	Gaussian	Circular	0.0111159	0.00693375	0.00728917	0.0205127	0.00029875	0.00149667	13.5428	Log	VST Log	Images
0.05	0.5	Gaussian	Circular	0.0111159	0.00693375	0.00728917	0.0205127	0.00029875	0.00149667	60.951	Log	VST Log	Images
0.05	1.0	Gaussian	Circular	0.011122	0.00694	0.00728917	0.0205127	0.000559167	0.00149667	64.7466	Log	VST Log	Images
0.05	2.0	Gaussian	Circular	0.0115707	0.00727917	0.0075375	0.028302	0.000559167	0.000455	100.062	Log	VST Log	Images
0.1	0.1	Gaussian	Circular	0.0233884	0.01523	0.0150192	0.0446534	-0.00308667	-0.0011075	4.10906	Log	VST Log	Images
0.1	0.2	Gaussian	Circular	0.0233884	0.01523	0.0150192	0.0446534	-0.00308667	-0.0011075	15.6017	Log	VST Log	Images
0.1	0.5	Gaussian	Circular	0.0233884	0.01523	0.0150192	0.0446534	-0.00308667	-0.0011075	57.6301	Log	VST Log	Images
0.1	1.0	Gaussian	Circular	0.0233986	0.0152425	0.0150192	0.0446534	-0.0036075	-0.0011075	65.7864	Log	VST Log	Images
0.1	2.0	Gaussian	Circular	0.0236494	0.0153125	0.0152133	0.0459639	-0.00256583	-0.000586667	91.3415	Log	VST Log	Images

Example images follow:

gaussian_10_sym_circle.0_0.0000.bmp