The spatial domain refers to the image plane itself, and approaches in this category are based on direct manipulation of pixels in an image. Frequency domain processing techniques are based on modifying the Fourier transform of an image.
The term spatial domain refers to the aggregate of pixels composing an image and spatial domain methods are procedures that operate directly on these pixels. Image processing function in the spatial domain may he expressed as.
g(x, y) = T[f(x, y)]
f(x, y) is the input image
g(x, y) is the processed image and
T is the operator on f defined over some neighborhood values of
Frequency domain techniques are based on convolution theorem. Let g(x, y) be the image formed by the convolution of an image f(x, y) and linear position invariant operation h(x, y) i.e.,
g(x, y) = h(x, y) * f(x, y)
Applying convolution theorem
G(u, v) = H(u, v) F(u, v)
Where G, H and F are the Fourier transforms of g, h and f respectively. In the terminology of linear system the transform H (u, v) is called the transfer function of the process. The edges in f(x, y) can he boosted by using H (u, v) to emphasize the high frequency components of F (u, v).