Introduction to Digital Image Processing

TRANSFORM DOMAIN SUPERPOSITION 221

3. Perform the scalar multiplication

(9.3-3)

where .

4. Take the inverse Fourier transform

. (9.3-4)

5. Extract the desired output matrix

(9.3-5a)

or

. (9.3-5b)

It is important that the size of the extended arrays in steps 1 and 2 be chosen large

enough to satisfy the inequalities indicated. If the computational steps are performed

with J = N, the resulting output array, shown in Figure 9.3-1, will contain erroneous

terms in a boundary region of width L – 1 elements, on the top and left-hand side of

the output field. This is the wraparound error associated with incorrect use of the

Fourier domain convolution method. In addition, for finite area (D-type) convolu-

tion, the bottom and right-hand-side strip of output elem ...