What is Digital Data?
Digital Data
Images with a
continuous gray tone or color, like a photograph are called analog images. On
the other hand, a group of divided small cells, with integer values of average
intensity, the center representing the cell's value, is called a digital
image. The spatial division into a group of cells is called sampling as
illustrated in Figure 1,
while conversion of analog images into integer image data is called quantization as
illustrated in Figure 2 and
3.
Figure 1: Concept of sampling
Figure 2: Concept of quantization
Figure 3: Quantization in the case of a signal
containing a noise
A digital image has coordinates of pixel number, normally counted from left to right, and line number, normally counted from top to bottom.
The most important factor in sampling is pixel size or sampling frequency. If the pixel size is large or the sampling frequency is long, the appearance of the image becomes worse, while in the reverse case the data volume becomes very large. Therefore the optimum sampling should be carefully considered.
Shannon's sampling theorem, for specifying the optimum sampling, is given as follows.
"There will be no loss of information if sampling is taken with a half frequency of the maximum frequency involved in the original analog frequency wave."
Let the analog intensity be f and the unit intensity v (>0) as divider in quantization. Let the quantized intensity be fd, fd is given by n as illustrated Figure 2. The difference between f and fd is called quantization error.
The question is how to determine the number of quantization levels or the unit intensity as divider. If the number of levels is too small, the quantization error will increase. In the reverse, the data volume increases with information less data because of the noise level, as shown in Figure 3.
For example in Figure 3, the quantization should be divided by a level larger than that of the noise. In this example, four levels would be an appropriate quantization.
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