
174 A Computational Introduction to Digital Image Processing, Second Edition
Ideal Filtering
Low Pass Filtering
Suppose we have a Fourier Transform matrix F , shifted so that the DC coefficient is
in the center. Recall from Figure 7.6 that the low frequency components are toward the
center. This means we can perform low pass filtering by multiplying the transform by a
matrix in such a way that center values are maintained, and values away from the center
are either removed or minimized. One way to do this is to multiply by an ideal low pass
matrix, which is a binary matrix m defined by:
m(x, y) =
1 if (x, y) is closer to the center than some value D,
0