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Table 2 M -estimators used in the proposed method

From: Robust c-prototypes algorithms for color image segmentation

 

Loss function ρ( x)

Influence function ψ( x)

Simple-Cut

x 2 2 , x r r , otherwise

x , x r 0 , otherwise

Hampel

x 2 2 , 0 x < α α x , α x < β α r β , β x < r r , x < r

x , 0 x < α α sgn x , α x < β α r x r β sgn x , β x < r 0 , x < r

German-McClure

x 2 / 2 1 + x 2

x 1 + x 2 2

Asad

x 2 45 r 8 3 x 8 10 r 4 x 4 + 15 r 8 , x r 8 r 2 45 , otherwise

2 x 3 1 x r 4 2 , x r 0 , otherwise

Insha

r 2 4 tan 1 x r 2 + r 2 x 2 r 4 + x 4 , x 0

x 1 + x r 4 2 , x 0