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Table 1 Results of the first kind of simulation conducted using the first 400 synthetic bead samples: the percentage errors \(E_{{N\_{\text{DFT}}}}\) and \(E_{{v\_{\text{DFT}}}}\) of the total number \(N_{\text{DFT}}\) and the average speed \(v_{{\text{ave}}\_{\text{DFT}}}\) of a group of synthetic beads due to their Gaussian speed distributions set at four different standard deviations \(\delta_{\text{set}}\)

From: A collective tracking method for preliminary sperm analysis

\(\delta_{\text{set}} \,\left( {\upmu{\text{m}}/{\text{s}}} \right)\) @ \(N_{\text{set }} = 1000\)

\(v_{\text{ave }} = 60\;\upmu{\text{m}}/{\text{s}}\)

0

18

36

54

Overall average

\(N_{\text{DFT}} \,\left( \# \right)\)

1069.77

1074.23

1072.46

1067.35

1070.95

 Standard deviation (#)

36.42

34.80

39.92

44.22

38.84

 Percentage error \(E_{{N\_{\text{DFT}}}} \,\left( {\text{\%}} \right)\)

6.98

7.42

7.25

6.74

7.10

\(v_{{{\text{ave}}\_{\text{DFT}}}} \left( {\upmu{\text{m}}/{\text{s}}} \right)\)

61.26

60.93

60.97

61.15

61.08

 Standard deviation (µm/s)

1.32

1.26

1.46

1.61

1.41

 Percentage error \(E_{{v\_{\text{DFT}}}} \,\left( {\text{\%}} \right)\)

2.09

1.56

1.61

1.91

1.79