Artificial Intelligence and Soft Computing: Behavioral ... - Arteimi.info

h( x, y) = f(u, v) * g (u, v). (17.5)
Thus one can obtain the noise-free image, when the impulse response
of the filter transfer function is known. A gaussian filter is one of the most
commonly used devices, represented by
g(x, y) = ( 1 / 2 π σ 2 ) exp [ - (x 2 + y 2 ) / 2 σ 2 ] (17.6)
where the standard deviation σ is a parameter of the user’s choice.
The digital filtering by gaussian function attempts to smooth the
frequency response F (u, v) of the image and is thus referred to as smoothing.
We describe different smoothing techniques in the next sub-section.
17.2.1 Smoothing
Smoothing, as evident from its name, is required to reduce the variations in
the amplitude of F(u, v) over a wide range of frequencies u and v. Gaussian
filter undoubtedly is a good scheme for smoothing. Besides gaussian filter,
there exist masking techniques for smoothing. Two such masks, referred to as
the 4-point and the 8-point masks, are presented below.
1 / 8
1 / 8 1 / 2 1 / 8
1 / 8
1 / 32 3 / 32 1 / 32
3 / 32 1 / 2 3 / 32
1 / 32 3 / 32 1 / 32
(a) (b)
Fig. 17.2: (a) 4-point and (b) 8-point masks used for smoothing.
It may be noted from fig. 17.2 that the sum of the weights assigned to
the pixels of a mask must add to unity. A question that naturally arises is how
to employ these masks for smoothing an image. The following steps may be
executed to solve the problem.