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