As a model of line spread of slanted edge consider the function
|Fig 1b||Fig 1c|
Fig 1a - LSF with sigma = 1 and k = 0.09; Fig 1b - xz section at y = 0; Fig 1c - yz section at x = 0;Consider applying 2d Gaussian blur with sigma = to . Regarding the Gaussian blur's separability we can represent it as two sequenced convolutions in x and y directions:
Gaussian blur has two more properties:
Tilde means equality up to an intensity scaling constant. The constant doesn't matter in our case because we always scale the LSF to fit in range [0..1].
Using the mentioned properties we can rewrite Eq. 1:
Thus, applying 2d Gaussian blur with sigma = to 'ideal' slanted edge is similar to applying 1d Gaussian blur with sigma = to every scan line, where k is the edge slope.
Oleg Kurtsev (firstname.lastname@example.org)