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

Advances in Continuous and Discrete Models

Theory and Modern Applications

Table 10 Noise immunity with a \(\pmb{7\times7}\) proposed mask at \(\pmb{\alpha= 0.5}\) at varying standard deviations (Noise SD)

Noise type	Noise SD	20	25	30	35	40	45
Motion	Linear image	0.9820	0.9540	0.9259	0.8792	0.8204	0.7992
	Non-linear image	0.8665	0.7562	0.6426	0.5662	0.5219	0.4961
	Medical image	0.8466	0.7085	0.5900	0.5357	0.5082	0.4939
Gauss	Linear image	0.6136	0.3837	0.3749	0.2832	0.2750	0.2799
	Non-linear image	0.5000	0.3616	0.2218	0.1723	0.1367	0.1275
	Medical image	0.5370	0.3380	0.3544	0.1866	0.1445	0.1009
S & P	Linear image	0.8089	0.7549	0.6689	0.6732	0.5958	0.4860
	Non-linear image	0.8150	0.7181	0.6169	0.5534	0.4522	0.4559
	Medical image	0.6529	0.5854	0.4799	0.3947	0.3259	0.2649
Speckle	Linear image	0.7800	0.6257	0.6336	0.4921	0.4228	0.4460
	Non-linear image	0.7456	0.7243	0.6520	0.5742	0.5087	0.4310
	Medical image	0.7720	0.7466	0.7289	0.7109	0.6961	0.6829