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Theory and Modern Applications

Table 8 Noise immunity with a \(\pmb{3\times3}\) proposed mask at \(\pmb{\alpha= 0.5}\) and varying standard deviations (Noise SD)

From: A new construction of a fractional derivative mask for image edge analysis based on Riemann-Liouville fractional derivative

Noise type

Noise SD

20

25

30

35

40

45

Motion

Linear image

0.7788

0.7137

0.6056

0.5839

0.5704

0.5569

Non-linear image

0.6364

0.4761

0.4056

0.3939

0.3847

0.3647

Medical image

0.7040

0.5028

0.4251

0.4174

0.4127

0.4025

Gauss

Linear image

0.1249

0.1007

0.0893

0.0785

0.0686

0.0604

Non-linear image

0.1033

0.0793

0.0665

0.0559

0.0480

0.0430

Medical

0.0593

0.0451

0.0336

0.0274

0.0199

0.0178

S & P

Linear image

0.6006

0.5064

0.4258

0.3549

0.3100

0.2409

Non-linear image

0.6909

0.5616

0.4560

0.3974

0.3267

0.2580

Medical image

0.7545

0.6764

0.5963

0.4477

0.3870

0.2940

Speckle

Linear image

0.2526

0.2276

0.2298

0.2117

0.2060

0.1967

Non-linear image

0.2887

0.2305

0.2005

0.1915

0.1629

0.1436

Medical image

0.6337

0.5858

0.5691

0.5267

0.5125

0.4960