c Object to be imaged 0001410o o39|9g|97 o59996 The quantization process 0049842I 0069950o o0289400 oo02|300|0 FIGURE 17.1 Digital image formation: sampling and quantization. and converting it to an electrical signal. The quantization process then assigns a number to the electrical signal; the result, which is a matrix of numbers, is the digital representation of the image. Each spatial location in the image (or grid)to which a number is assigned is known as a picture element or pixel (or pel). The size of the sampling grid is usually given by the number of pixels on each side of the grid, e.g., 256 X 256, 512 X 512, 488×380 The quantization process is necessary because all information to be processed using computers must be represented by numbers. The quantization process can be thought of as one where the input energy to the transducer is represented by a finite number of energy values. If the energy at a particular pixel location does not take on one of the finite energy values, it is assigned to the closest value. For instance, suppose that we me a priori that only energy values of 10, 20, 50, and 110 will be represented(the units are of no concern this example). Suppose at one pixel an energy of 23.5 was observed by the transducer. The A/D converter would then assign this pixel the energy value of 20(the closest one). Notice that the quantization process makes mistakes; this error in assignment is known as quantization error or quantization noise In our example, each pixel is represented by one of four possible values. For ease of representation of the data, it would be simpler to assign to each pixel the index value 0, 1, 2, 3, instead of 10, 20, 50, 110. In fact, this is typically done by the quantization process. One needs a simple table to know that a pixel assigned the value 2 corresponds to an energy of 50. Also, the number of possible energy levels is typically some integer power of two to also aid in representation. This power is known as the number of bits needed to represent the energy of each pixel In our example each pixel is represented by two bits. One question that immediately arises is how accurate the digital representation of the image is when one compares the digital image with a corresponding analog image. It should first be pointed out that after the digital image is obtained one requires special hardware to convert the matrix of pixels back to an image that can be viewed on a CRT display. The process of converting the digital image back to an image that can be viewed is known as digital-to-analog conversion, or D/a conversion C 2000 by CRC Press LLC© 2000 by CRC Press LLC and converting it to an electrical signal. The quantization process then assigns a number to the electrical signal; the result, which is a matrix of numbers, is the digital representation of the image. Each spatial location in the image (or grid) to which a number is assigned is known as a picture element or pixel (or pel). The size of the sampling grid is usually given by the number of pixels on each side of the grid, e.g., 256 256, 512 512, 488 380. The quantization process is necessary because all information to be processed using computers must be represented by numbers. The quantization process can be thought of as one where the input energy to the transducer is represented by a finite number of energy values. If the energy at a particular pixel location does not take on one of the finite energy values, it is assigned to the closest value. For instance, suppose that we assume a priori that only energy values of 10, 20, 50, and 110 will be represented (the units are of no concern in this example). Suppose at one pixel an energy of 23.5 was observed by the transducer. The A/D converter would then assign this pixel the energy value of 20 (the closest one). Notice that the quantization process makes mistakes; this error in assignment is known as quantization error or quantization noise. In our example, each pixel is represented by one of four possible values. For ease of representation of the data, it would be simpler to assign to each pixel the index value 0, 1, 2, 3, instead of 10, 20, 50, 110. In fact, this is typically done by the quantization process. One needs a simple table to know that a pixel assigned the value 2 corresponds to an energy of 50. Also, the number of possible energy levels is typically some integer power of two to also aid in representation. This power is known as the number of bits needed to represent the energy of each pixel. In our example each pixel is represented by two bits. One question that immediately arises is how accurate the digital representation of the image is when one compares the digital image with a corresponding analog image. It should first be pointed out that after the digital image is obtained one requires special hardware to convert the matrix of pixels back to an image that can be viewed on a CRT display. The process of converting the digital image back to an image that can be viewed is known as digital-to-analog conversion, or D/A conversion. FIGURE 17.1 Digital image formation: sampling and quantization.