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Table 1 Characterization of intensity-curvature functional

From: Intensity-curvature functional based digital high pass filter of the bivariate cubic B-spline model polynomial function

Image intensity gradients f (0, 0) f (0, 0) f (0, 0) f (0, 0)
ζ (α2, α3) << >> << <<
γ (α2, α3) << << >> <<
λ (α2, α3) << << << >>
Behavior of ICF image-like gradient-like gradient-like gradient-like
Image intensity gradients f (0, 0) f (0, 0) f (0, 0) f (0, 0)
ζ (α2, α3) >> << >> >>
γ (α2, α3) >> >> << >>
λ (α2, α3) << >> >> >>
Behavior of ICF image-like gradient-like gradient-like gradient-like
Image intensity gradients f (0, 0) f (0, 0) f (0, 0) f (0, 0)
ζ (α2, α3) ! < < AND ! >> ! > > AND ! < < ! < < AND ! >> ! < < AND ! >>
γ (α2, α3) ! < < AND ! >> ! < < AND ! >> ! > > AND ! < < ! < < AND ! >>
λ (α2, α3) ! < < ! < < AND ! >> ! < < AND ! >> ! >>
Behavior of ICF gradient-like or image-like gradient-like or image-like gradient-like or image-like gradient-like or image-like
  1. This table can be read by considering: 1. The term in the first column (which is ζ (α2, α3) or γ (α2, α3) or λ (α2, α3)); 2. The inequality sign (in the cell of the table); 3. The value of the pixel intensity f(0, 0). For instance: ζ (α2, α3) < < f(0, 0). The symbols: ‘!’, ‘<<’, ‘>>’, ‘AND’; mean different, largely smaller than, largely bigger than, and the logical and, respectively. Thus, the symbol ‘! < < AND ! >>’ reads: not largely less than and at the same time not largely greater than. Moreover, the symbol ‘! > > AND ! < <’ reads: not largely greater than and at the same time not largely smaller than