Fundamentals of Digital Image Processing - Control of Color Imaging Systems: Analysis and Design - page 28

2.4 IMAGE SAMPLING AND QUANTIZATION
To process an image digitally (using a computer), it must be available in digital form.
The digitized image is obtained by sampling the continuous tone image on a discrete
grid and quantizing the sample values using a

finite number of bits. To understand
the process of image sampling, we need to revisit the 2-D sampling theorem [3,5].
Assume that we have a band-limited 2-D signal (such as an image). Real-world
images are not truly band limited; however, they can be approximated by band-
limited functions. A 2-D function f ( x, y )

is said to be band limited if its Fourier

transform F (v x , v y ) is zero outside a bounded region in the frequency plane (v x , v y ) ,

as shown in Figure 2.6.
The ideal rectangular image sampler is a 2-D array of discrete delta functions
placed on a rectangular grid (Figure 2.7) with spacing of

D x and D y, that is,

ω y

ω y 0

ω x

ω x 0

FIGURE 2.6 Region de ning a band-limited signal.

s ( x , y )

Δ x

x

Δ y

….

….

….

y

FIGURE 2.7 Sampling function s ( x, y ) .