3 Image Sampling Quantisation 3 1 Basic Concepts

3. Image Sampling & Quantisation 3. 1 Basic Concepts • To create a digital image, we need to convert continuous sensed data into digital form. • This involves two processes: sampling and quantisation • The basic idea behind sampling and quantization is illustrated in Fig. 3. 1.

• Figure 3. 1(a) shows a continuous image, f (x, y), that we want to convert to digital form. • To convert it to digital form, we have to sample the function in both coordinates and in amplitude. • An image may be continuous with respect to the x‑ and y‑coordinates and also in amplitude.

• Digitizing the coordinate values is called sampling. • Digitizing the amplitude values is called quantization.

Fig 3. 1 Generating a digital image (a) Continuous image. (b) A scan line from A to B in the continuous image. (c) Sampling & quantisation. (d) Digital scan line.

• The one‑dimensional function shown in Fig. 3. 1(b) is a plot of amplitute (gray level) values of the continuous image along the line segment AB in Fig. 3. 1(a). • To sample this function, we take equally spaced samples along line AB, as shown in Fig. 3. 1(c). • Location of each sample is given by a vertical tick mark in the bottom part of the figure.

• The samples are shown as small white squares superimposed on the function. The set of these discrete locations gives the sampled function. • However, the values of the samples still span (vertically) a continuous range of gray‑level values. • In order to form a digital function, the gray‑level values also must be converted (quantized) into discrete quantities.

• The right side of Fig. 3. 1(c) shows the gray‑level scale divided into eight discrete levels, ranging from black to white. • The vertical tick marks indicate the specific value assigned to each of eight gray levels. • The continuous gray levels are quantized simply by assigning one of the eight discrete gray levels to each sample.

• The assignment is made depending on the vertical proximity of a sample to a vertical tick mark. • The digital samples resulting from both sampling and quantization are shown in Fig. 3. 1(d) and Fig 3. 2 (b).

Fig. 3. 2 (a) Continuous image projected onto a sensor array. (b) Result of image sampling and quantisation

3. 2 Representing Digital Images • The result of sampling and quantisation is a matrix of real numbers as shown in Fig. 3. 3, Fig. 3. 4. and Fig 3. 5. • The values of the coordinates at the origin are (x, y) = (0, 0). • The next coordinate values along the first row are (x, y) = (0, 1). • The notation (0, 1) is used to signify the 2 nd sample along the 1 st row.

Fig. 3. 3. Coordinate convention used to represent digital images

Fig. 3. 4. A digital image of size M x N

• It is advantageous to use a more traditional matrix notation to denote a digital image and its elements. Fig. 3. 5 A digital image

• The number of bits required to store a digitised image is • b=Mx. Nxk Where M & N are the number of rows and columns, respectively. • The number of gray levels is an integer power of 2: • L = 2 k where k =1, 2, … 24 • It is common practice to refer to the image as a “k-bit image”

• The spatial resolution of an image is the physical size of a pixel in that image; i. e. , the area in the scene that is represented by a single pixel in that image. • Dense sampling will produce a high resolution image in which there are many pixels, each of which represents of a small part of the scene. • Coarse sampling, will produce a low resolution image in which there a few pixels, each of which represents of a relatively large part of the scene.

Fig. 3. 6 Effect of resolution on image interpretation (a) 8 x 8 image.

Fig. 3. 7 Effect of quantisation on image interpretation. (a) 4 levels. (b) 16 levels. (c) 256 levels