A Computational Introduction to Digital Image Processing, 2nd Edition

Neighborhood Processing 105

An alternative derivation is to write the equation relating s and k as

s −

s

k

= 1.

If s /k = t, say, then s = t + 1. So if s/k = 2/3, then s = 5/3 and so the filter is

5

3





0 0 0

0 1 0

0 0 0





−

2

3





1

9





1 1 1

1 1 1

1 1 1









=

1

27





−2 −2 −2

−2 43 −2

−2 −2 −2





For example, consider an image of an iconic Australian animal:

MATLAB/Octave

>> k = imread(’koala.png’);

The first filter above can be constructed as

MATLAB/Octave

>> id = [0 0 0;0 1 0;0 0 0];

>> f = fspecial(’average’);

>> u = 3

*

id - 2

*

f

u =

-0.22222 -0.22222 -0.22222

-0.22222 2.77778 -0.22222

-0.22222 -0.22222 -0.22222

and applied to the image in the usual way:

MATLAB/Octave

>> ku = imfilter(k,u); ...