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

Visual Computing for Industry, Biomedicine, and Art

Table 1 Characterization of intensity-curvature functional

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

This table can be read by considering: 1. The term in the first column (which is ζ (α_2, α₃) or γ (α_2, α₃) or λ (α_2, 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