RE 17. 2 This image shows the effects of aliasing due to sampling the image at too low a rate. The image should be lines converging at a point. Because of undersampling, it appears as if there are patterns in the lines at various These are known as moire patterns. The quality of representation of the image is determined by how close spatially the pixels are located and how many levels or numbers are used in the quantization, i. e, how coarse or fine is the quantization. The sampling accuracy is usually measured in how many pixels there are in a given area and is cited in pixels/unit length, i. e, pixels/cm. This is known as the spatial sampling rate. One would desire to use the lowest rate possible the number of pixels needed to represent the object. If the sampling rate is too low, then obviously me details of the object to be imaged will not be represented very well. In fact, there is a mathematical theorem which determines the lowest sampling rate possible to preserve details in the object. This rate is known as the Nyquist sampling rate(named after the late Bell Laboratories engineer Harry Nyquist). The theorem states that the sampling rate must be twice the highest possible detail one expects to image in the object. If the object has details closer than, say 1 mm, one must take at least 2 pixels/mm. (The Nyquist theorem actually lys more than this, but a discussion of the entire theorem is beyond the scope of this section. If we sample at a lower rate than the theoretical lowest limit, the resulting digital representation of the object will be distorted. This type of distortion or sampling error is known as aliasing errors. Aliasing errors usually manifest themselves in the image as moire patterns(Fig 17. 2). The important point to remember is that there is a lower limit to the spatial sampling rate such that object detail can be maintained. The sampling rate can also be stated as the total number of pixels needed to represent the digital image, i. e, the matrix size(or grid size). One often sees these sampling rates cited as 256 X 256, 512 X 512, and so on. If the same object is imaged with a large matrix ize, the sampling rate has obviously increased. Typically, images are sampled on 256X 256, 512 X 512, or 1024 X 1024 grids, depending on the application and type of modality. One immediately observes an important sue in digital representation of images: that of the large number of pixels needed to represent the image. A 256 X 256 image has 65, 536 pixels and a 512 X 512 image has 262, 144 pixels! We shall return to this point later when we discuss processing or storage of these images The quality of the representation of the digital image is also determined by the number of levels or shades of gray that are used in the quantization. If one has more levels, then fewer mistakes will be made in assigning values at the output of the transducer. Figure 17.3 demonstrates how the number of gray levels affects the digital representation of an artery. When a small number of levels are used, the quantization is coarse and the quantization error is large. The quantization error usually manifests itself in the digital image by the appearance e 2000 by CRC Press LLC© 2000 by CRC Press LLC The quality of representation of the image is determined by how close spatially the pixels are located and how many levels or numbers are used in the quantization, i.e., how coarse or fine is the quantization. The sampling accuracy is usually measured in how many pixels there are in a given area and is cited in pixels/unit length, i.e., pixels/cm. This is known as the spatial sampling rate. One would desire to use the lowest rate possible to minimize the number of pixels needed to represent the object. If the sampling rate is too low, then obviously some details of the object to be imaged will not be represented very well. In fact, there is a mathematical theorem which determines the lowest sampling rate possible to preserve details in the object. This rate is known as the Nyquist sampling rate (named after the late Bell Laboratories engineer Harry Nyquist). The theorem states that the sampling rate must be twice the highest possible detail one expects to image in the object. If the object has details closer than, say 1 mm, one must take at least 2 pixels/mm. (The Nyquist theorem actually says more than this, but a discussion of the entire theorem is beyond the scope of this section.) If we sample at a lower rate than the theoretical lowest limit, the resulting digital representation of the object will be distorted. This type of distortion or sampling error is known as aliasing errors. Aliasing errors usually manifest themselves in the image as moiré patterns (Fig. 17.2). The important point to remember is that there is a lower limit to the spatial sampling rate such that object detail can be maintained. The sampling rate can also be stated as the total number of pixels needed to represent the digital image, i.e., the matrix size (or grid size). One often sees these sampling rates cited as 256 3 256, 512 3 512, and so on. If the same object is imaged with a large matrix size, the sampling rate has obviously increased. Typically, images are sampled on 256 3 256, 512 3 512, or 1024 3 1024 grids, depending on the application and type of modality. One immediately observes an important issue in digital representation of images: that of the large number of pixels needed to represent the image. A 256 3 256 image has 65,536 pixels and a 512 3 512 image has 262,144 pixels! We shall return to this point later when we discuss processing or storage of these images. The quality of the representation of the digital image is also determined by the number of levels or shades of gray that are used in the quantization. If one has more levels, then fewer mistakes will be made in assigning values at the output of the transducer. Figure 17.3 demonstrates how the number of gray levels affects the digital representation of an artery. When a small number of levels are used, the quantization is coarse and the quantization error is large. The quantization error usually manifests itself in the digital image by the appearance FIGURE 17.2 This image shows the effects of aliasing due to sampling the image at too low a rate. The image should be straight lines converging at a point. Because of undersampling, it appears as if there are patterns in the lines at various angles. These are known as moiré patterns