## 1.1.2        Digital Images

Many examples of sequences used in this text are digital images. A digital image, which can be denoted by x(n1, n2), is typically obtained by sampling an analog image, for instance, an image on film. The amplitude of a digital image is often quantized to 256 levels (which can be represented by eight bits). Each level is commonly denoted by an integer, with 0 corresponding to the darkest  level and 255 to the brightest. Each point (n1, n2) is called a pixel or pel (picture element). A digital image x(n1, n2) of 512 x 512 pixels with each pixel represented by eight bits is shown in Figure 1.10. As we reduce the number of amplitude quantization levels, the signal-dependent quantization noise begins to appear as false contours. This is shown in Figure 1.11, where the image in Figure 1.10 is displayed with 64 levels (six bits), 16 levels (four bits), 4 levels (two bits), and 2 levels (one bit) of amplitude quantization. As we reduce the number of pixels in a digital image, the spatial resolution is decreased and the details in the image begin to disappear. This is shown in Figure 1.12, where the image in Figure 1.10 is displayed at a spatial resolution of 256 x 256 pixels, 128 x 128 pixels, 64 x 64 pixels, and 32 x 32 pixels. A digital image of 512 x 512 pixels has a spatial resolution similar to that seen in a television frame. To have a spatial resolution similar to that of an image on 35-mm film, we need a spatial resolution of 1024 x 1024 pixels in the digital image. Figure 1.10 : Digital image of  512x512 pixels quantized at 8 bits/pixel  (a)                                                                           (b)  (c)                                                                           (d)

Figure 1.11:  Image in Figure 1.10 with amplitude quantization     at

(a)    6 bits/pixel  (64 colors)

(b)    4 bits/pixel  (16 colors)

(c)    2 bits/pixel  (4 colors)

(d)    1 bit/pixel   (2 colors)  (a)                                                                           (b)  (c)                                                                           (d)

Figure 1.12:   Image in Figure 1.10 with spatial resolution of

(a)        256x256 pixels

(b)        128x128 pixels

(c)        64x64 pixels

(d)        32x32 pixels