2.4.1 Blur Filters
The mean filter is an example of a convolution filter. The mean filter convolution kernel looks like:
original
blur
1/9
1/9
1/9
1/9
1/9
1/9
1/9
1/9
1/9
after blur
Gaussian smoothing as a continuous function would be:
G(x,y)=exp((-x^2+y^2)/2*v^2)/(2*pi*v^2)
the discrete convolution kernel of size 5 with standard deviation v=1.0 is:
original
gaussian
1/273
1
4
7
4
1
4
16
26
16
4
7
26
41
26
7
4
16
26
16
4
1
4
7
4
1
after gaussian
The Gaussian filter is well behaved in the frequency domain, unlike the mean filter which exhibits oscillations in its frequency response.
