1. 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.

2. 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.

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

4. 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.

5. 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.

6. 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.

7. 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.

8. 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).

9. Fig. 3.2 (a) Continuous image projected onto a sensor array. (b) Result of image sampling and quantisation

10. 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.

11. Fig. 3.3. Coordinate convention used to represent digital images

12. Fig. 3.4. A digital image of size M x N

13. It is advantageous to use a more traditional matrix notation to denote a digital image and its elements. Fig. 3.5 A digital image

14. The number of bits required to store a digitised image is b = M x N x k 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”

16. 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 are a few pixels, each of which represents of a relatively large part of the scene.

17. Fig. 3.6 Effect of resolution on image interpretation (a) 8x8 image. (b) 32x32 image © 256x256 image

18. Fig.3.7 Effect of quantisation on image interpretation. (a) 4 levels. (b) 16 levels. (c) 256 levels