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Estimation of forest parameters through Fuzzy classification of TM Data
B-Fuzzy Estimation: The supervised classification method for estimating environmental parameters from spectral images is based on a fuzzy strategy already applied to marine investigations. A fuzzy set is characterized by a membership function that associates with each element areas number between 0 and 1 which represents the “fuzzy membership grade”. In this way, each element of the set may have partial and multiple membership and mixed, uncertain situations can be properly handled. When applied to the supervised classifications of remotely sensed data, the fuzzy membership grades can be seen as a measure of the extent to which a pixel belongs to all the cover categories. The membership grades have been also demonstrated to be related to the cover proportions of the categories within the pixels. These grades can there fore be used to weight the measured parameters of the known classes by a strategy similar to that adopted for the statistical estimation of Geological parameters. Once the spectral signatures for each reference class have been defined, the membership grade of each pixel with respect to class i (Fi) can be found as: 
With: Pi: maximum likelihood probability of attribution to the class considered. n: Number of measurement variables Ci: Variance – Covariance matrix of the class considered. Mi: Mean vector of the class considered Xi: Pixel vector Pri: Prior probability of the class considered defined from the frequency histograms of the training sets. In practice, all the reference categories (plots) can be considered as individuals having representative environmental and spectral features. In this way the spectral signatures are found assigning full membership functions to all the reference pixel of the categories, which corresponds to computing the fuzzy mean vectors and the fuzzy variance – covariance matrices as “hard” ones. Since known environmental parameters are associated to all the reference categories, the same parameters can be estimated for unknown pixels by using the membership grades as weighting factors. Thus: 
Where: Ve: Estimated value for the pixel. Vmi: Measured value of class i. Clearly, the method is only valid if the entire range of variability of the study parameters is covered by a sufficient number of representative known categories. As was seen above, such an assumption can be considered realistic in the current case.  Figure 3: Fuzzy Analysis 4: Results: The results of fuzzy classification and PCI classification show that the algorithm can extremely enhance the classification. With comparison among RMSE of PCI and fuzzy classification, we can be seen that RMSE decreases from 3.84 m2/ha in PCI classification to 1.69 m2/ha in fuzzy classification, this show a promote in classification using fuzzy estimation. 5: Conclusion: The proposed fuzzy methodology showed great promise for the estimation of forest parameters. However the procedure was only tested on a single data set. Further testing in different areas and with other imagery data would be useful to validate the results obtained. In general, the method should benefit from a higher density of references plots, even if this could involve an increasing burden of computational complexity. From a methodological viewpoint, this approach should be most effective in reducing biases in the estimated parameters. Also, the use of fuzzy classification permits considerable flexibility in the estimation procedures. For probabilistically inserted into the process. Theoretically, the fuzzy approach to estimation could be applied to an enormous series of problems of environmental monitoring, such as agricultural, oceanographic and geological investigations. In all these cases, the method can be expected to produce optimum performance thanks to its probabilistic, flexible nature. Research is currently directed towards the exploration of these possibilities. 6: Refrences:
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