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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

\(\delta_{\text{set}} \,\left( {\upmu{\text{m}}/{\text{s}}} \right)\) @ \(N_{\text{set }} = 1000\)
\(v_{\text{ave }} = 60\;\upmu{\text{m}}/{\text{s}}\)
0183654Overall average
\(N_{\text{DFT}} \,\left( \# \right)\)1069.771074.231072.461067.351070.95
 Standard deviation (#)36.4234.8039.9244.2238.84
 Percentage error \(E_{{N\_{\text{DFT}}}} \,\left( {\text{\%}} \right)\)6.987.427.256.747.10
\(v_{{{\text{ave}}\_{\text{DFT}}}} \left( {\upmu{\text{m}}/{\text{s}}} \right)\)61.2660.9360.9761.1561.08
 Standard deviation (µm/s)1.321.261.461.611.41
 Percentage error \(E_{{v\_{\text{DFT}}}} \,\left( {\text{\%}} \right)\)2.091.561.611.911.79