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Table 12 RMSD of positional errors of the proposed detector for the noisy ideal slopes, considering noise threshold

From: A one-dimensional slope detection approach

std n

Pre-smooth

Erf

Tanh

Sigmoid

Ramp

Step

Arctan

0.001

1

0.06

0.05

0.15

0.23

0.36

0.08

4

0.06

0.05

0.15

0.21

0.29

0.08

64

0.32

0.29

0.55

0.31

0.35

0.58

0.01

1

2.91

3.15

4.3

4.55

0.35

2.45

4

0.55

0.5

0.68

0.77

0.29

0.48

64

0.44

0.43

0.66

0.41

0.43

0.67

0.1

1

3.16

2.3

3.94

4.86

0.34

2.32

4

1.58

1.46

2.19

2.09

0.35

1.49

64

1.05

1.04

1.28

0.93

0.92

1.32