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to produce lower resolution images, or they use artificial data in such a way that the actual land cover proportion within each degraded pixel can therefore be directly calculated. Possible approaches for estimating land cover proportion within mixed pixels include: fuzzy set theory, neural network classification and spectral mixture analysis.

4.6.1 Methods based on fuzzy set theory

Since multiple class membership is fundamental to fuzzy set theory (Hisdal, 1994), fuzzy-set based approaches may be appropriate for defuzzification processes, that is, in resolving the mixture information contained by the mixed pixels. For instance, the supervised fuzzy maximum likelihood classifier proposed by Wang (1990a) is an extension of traditional crisp maximum likelihood. This algorithm was originally intended to resolve the mixed pixel problem. It is based on the fuzzy mean and fuzzy covariance matrix, and outputs fuzzy membership grades for each pixel. The performance of this approach to mixed pixel classification depends on how well these parameters (mean and covariance) are estimated.

The second algorithm for dealing with mixed pixels is the fuzzy c-means (FCM) algorithm (Bezdek et al., 1984). FCM also outputs a membership value for each pixel. Since FCM is an unsupervised clustering algorithm, the resulting clusters must be identified in terms of information classes, which may make the method less attractive than the supervised fuzzy maximum likelihood procedure.

The third possible method uses a fuzzy rule base. As described above, the construction of a fuzzy rule base requires fuzzy partitions on each dimension. The size and the types of fuzzy partitions are controlled by user-defined membership functions. If the spectral relationship between pure pixels and the mixed pixel is known, one can construct suitable fuzzy partitions for each information class, and the resulting overlapped area between different classes will reflect the mixture information. Figure 4.17 illustrates such a process based on a two-class case. For simplicity, presume that the distributions of both classes are sensitive only to dimension DN1 (Figure 4.17). Hence, we only construct the membership functions on axis DN1. Since the distribution of class 1 is more concentrated, we use a narrower trapezoid membership function. As the distribution of class 2 is broader, we use a larger trapezoid membership function (i.e. the basis of the membership function is longer) to model the distribution. The degree of overlapped area of both membership functions is certainly dependent on the spectral behaviour of the mixed pixels. The modelling of the overlapped area determines the performance of fuzzy rule base for solving the mixed pixel problem.

Two issues relating to the use of a fuzzy rule base for solving the mixed pixel problem should be noted here. First, given that the total of the mem

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Classification Methods for Remotely Sensed Data
Classification Methods for Remotely Sensed Data, Second Edition
ISBN: 1420090720
EAN: 2147483647
Year: 2001
Pages: 354

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