Remote Sensing - a tool for environmental observation

Figure 517 minimum distance to mean classifier

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Figure 5.17 Minimum distance to mean classifier (Campbell, 1987). Several methods exist to compute distances in multi-dimensional spaces such as the spectral 6- dimensional space of the Landsat TM. One of the simplest methods is the Euclidean distance. n D ab = [ Σ (a i - b i )² ] ½ i=1 where i is one of n spectral bands, a and b are pixel values in the different spectral bands and D ab is the Euclidean distance between the two pixels. This measure can be applied to many dimensions (or spectral channels). Figure 5.18 illustrates the Euclidean distance measure. The parallelepiped classifier or box classifier is also very popular as it is fast and efficient. It is based on the ranges of values within the training data to define regions within the multi- dimensional space. Hence, it creates imaginary boxes in the spectral space. Figure 5.19 shows an example of the parallelepiped classification procedure with only two spectral bands for simplicity. The spectral values of unclassified pixels are projected into the data space and those
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81 that fall within the regions defined by the training data are assigned to the corresponding categories. Although this procedure is accurate, direct and simple, one disadvantage is obvious. Spectral regions for training categories may intersect or overlap (in such a case classes are assigned in sequence of classification). A second disadvantage is that other parts of the image may remain unclassified because they do not ‘fall’ into a box. The maximum likelihood classifier is the most advanced classifier but it requires a considerable amount of computation time. As computers have become very fast and powerful, the latter is no longer a problem and the maximum likelihood classifier is widely used nowadays. The maximum likelihood approach does not only take into account the average DN- values of the training areas, it also accounts for the variance of pixel values of the training areas. The variances are used to estimate the probability of membership for a certain land cover class. Figure 5.21 shows a three-dimensional plot with the probability density functions of several land cover classes in spectral band 3 (visible red) and 4 (near infrared). The variance of the pixel values of the class ‘sand’ is very small (a distinct peak), the variance for urban is large. (Compare this with the Veluwe TM image exercise). Notice that the variance for the class ‘water’ is larger in band 3 than in band 4. Figure 5.18 Illustration of the Euclidean distance measure (Campbell, 1987).
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82 Figure 5.19 Parallelepiped classifier (Campbell, 1987). The equiprobability contours shown in figure 5.20 serve as a decision rule to assign pixels to certain land cover classes. The equiprobability contours are drawn using information from the training areas. The probability differs from one spectral band to another. The maximum like- lihood classifier is a very powerful classifier but it is sensitive for the quality of the training data: the likelihoods (or probabilities) are computed based on the assumption that the training data have a multi-variate, normal (Gaussian) frequency distribution. Remote sensing data do not
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