Image Filtering (Gaussian)

A filter is any kind of processing that has one characteristic: it takes a signal as the input and produces a relevant output signal after processing it in some way. A filter can always be mathematically described.

An example of a 1D filter:

1 2 3 4 3 2 1

An example of a 2D filter:

1 1 1 1 1
1 2 2 2 1
1 2 3 2 1
1 2 2 2 1
1 1 1 1 1

A 2D filter as well as the 1D filter, has to have an odd number of samples in both the vertical as well as the horizontal orientation.

In Matlab:
n represents the number of cells so for a 2D 3x3 filter n=9 for a 1D filter the number of cells in my example above is 7


% 2D Gaussian Filter
x = -1/2:1/(n-1):1/2;
[Y,X] = meshgrid(x,x);
f = exp( -(X.ˆ2+Y.ˆ2)/(2*sˆ2) );
f = f / sum(f(:));



%1D Gaussian Filter
x = -1/2:1/(n-1):1/2;
f = exp( -(x.^2)/(2*sigma^2) );
g = f / sum(sum(f));