Effect of Contrast and Noise on Accuracy and Speed

The beads used for these tests are generated algorithmically and then have noise added to them algorithmically. They are bright-on-gray Gaussian spots of standard deviation 10 and maximum value specified. The total image-value maximum is the sum of the background and the maximum value specified. The 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 added noise is Gaussian noise with the mean and variance specified in the table. The fractional intensity of the background is always 0.4 and the amount that the bead is above background is listed in the table (0.5 would mean a total of 0.9 fraction of the total intensity). 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.

Max Bead Value
Noise Level
Mean Radial Error
Mean X Error
Mean Y Error
Max Radial Error
X Bias
Y Bias
Estimates/Sec
True Log
VST Log
Images
0.5
none
0.00238311
0.00159197
0.00146002
0.00968269
0.000287008
0.000150483
2.08038
Log
VST Log
Images
0.5
Mean=2 Var=1e4
0.00468266
0.00291987
0.0030303
0.0129282
0.000713142
4.5e-007
2.01851
Log
VST Log
Images
0.5
Mean=20 Var=1e5
0.0125315
0.00744525
0.00850551
0.0362719
0.00161653
-0.000414608
2.05559
Log
VST Log
Images
0.5
Mean=200 Var=1e6
0.0392239
0.023017
0.0266065
0.115638
0.00447295
-0.00185503
2.04625
Log
VST Log
Images
0.5
Mean=2000 Var=1e7
0.128835
0.0793091
0.0839194
0.373824
0.0134411
-0.00625771
1.9326
Log
VST Log
Images
0.5
Mean=20000 Var=1e8
0.647621
0.396549
0.42019
1.98135
0.0577607
-0.157055
1.89734
Log
VST Log
Images
0.3
none
0.00550601
0.00381107
0.00318363
0.0132924
0.000433517
0.000573667
2.07211
Log
VST Log
Images
0.3
Mean=2 Var=1e4
0.00827249
0.00510363
0.00552047
0.0218352
0.00116078
0.000342183
2.07173
Log
VST Log
Images
0.3
Mean=20 Var=1e5
0.021018
0.0120642
0.01448
0.0619602
0.00270701
-0.000390233
2.13591
Log
VST Log
Images
0.3
Mean=200 Var=1e6
0.065715
0.0386457
0.0443181
0.191028
0.00712592
-0.00267704
2.09833
Log
VST Log
Images
0.3
Mean=2000 Var=1e7
0.234273
0.149288
0.149245
0.6228
0.0228486
-0.014591
2.01162
Log
VST Log
Images
0.3
Mean=20000 Var=1e8
1.01034
0.604975
0.677248
2.84723
0.083363
-0.161279
2.0801
Log
VST Log
Images
0.1
none
0.0164218
0.0102639
0.0104037
0.0335325
0.0007427
0.00131422
2.01443
Log
VST Log
Images
0.1
Mean=2 Var=1e4
0.0240369
0.0151503
0.0151211
0.0667289
0.00292668
0.000399192
2.05823
Log
VST Log
Images
0.1
Mean=20 Var=1e5
0.0634052
0.0383614
0.0415072
0.188709
0.00737821
-0.00176553
1.9791
Log
VST Log
Images
0.1
Mean=200 Var=1e6
0.219654
0.141141
0.13791
0.594428
0.0217988
-0.0093583
2.06332
Log
VST Log
Images
0.1
Mean=2000 Var=1e7
0.888663
0.530669
0.60509
2.42052
0.0706107
-0.10039
2.06716
Log
VST Log
Images
0.1
Mean=20000 Var=1e8
67.9661
30.9322
53.3629
130.156
23.4243
52.5223
2.04291
Log
VST Log
Images


Example images follow:

gaussian_10_sym_circle.0.5.0_0.0000.bmp

gaussian_10_sym_circle.0.5.2_1e4.0000.bmp

gaussian_10_sym_circle.0.5.20_1e5.0000.bmp

gaussian_10_sym_circle.0.5.200_1e6.0000.bmp

gaussian_10_sym_circle.0.5.2000_1e7.0000.bmp

gaussian_10_sym_circle.0.5.20000_1e8.0000.bmp

gaussian_10_sym_circle.0.3.0_0.0000.bmp

gaussian_10_sym_circle.0.3.2_1e4.0000.bmp

gaussian_10_sym_circle.0.3.20_1e5.0000.bmp

gaussian_10_sym_circle.0.3.200_1e6.0000.bmp

gaussian_10_sym_circle.0.3.2000_1e7.0000.bmp

gaussian_10_sym_circle.0.3.20000_1e8.0000.bmp

gaussian_10_sym_circle.0.1.0_0.0000.bmp

gaussian_10_sym_circle.0.1.2_1e4.0000.bmp

gaussian_10_sym_circle.0.1.20_1e5.0000.bmp

gaussian_10_sym_circle.0.1.200_1e6.0000.bmp

gaussian_10_sym_circle.0.1.2000_1e7.0000.bmp

gaussian_10_sym_circle.0.1.20000_1e8.0000.bmp