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Theory and Modern Applications

Table 12 Noise immunity with \(\pmb{9\times9}\) proposed mask at \(\pmb{\alpha= 0.5}\) at 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

0.9818

0.9493

0.9270

0.8973

0.8447

0.8151

Non-linear image

0.9098

0.8058

0.7038

0.6222

0.5671

0.5380

Medical

0.8805

0.7732

0.6670

0.6031

0.5667

0.5427

Gauss

Linear image

0.8422

0.6467

0.6009

0.4269

0.4777

0.3587

Non-linear image

0.6410

0.5999

0.4123

0.3266

0.2665

0.1951

Medical image

0.6285

0.5280

0.4705

0.3381

0.2510

0.2579

S & P

Linear image

0.9254

0.8855

0.8496

0.7843

0.7707

0.7043

Non-linear image

0.8621

0.8072

0.7358

0.6759

0.5891

0.6016

Medical

0.6925

0.5735

0.4810

0.3943

0.4067

0.3767

Speckle

Linear image

0.9186

0.8753

0.8085

0.6825

0.5964

0.6200

Non-linear image

0.8521

0.8050

0.7481

0.6977

0.6382

0.5735

Medical image

0.8218

0.7981

0.7731

0.7530

0.7426

0.7194