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Assessing Uncertainty in Fuzzy Land Cover Maps Obtained by Remote Sensing
ATKINSON, P.M. (firstname.lastname@example.org), University of Southampton, Department of Geography, Highfield, Southampton SO17 1BJ, U.K.
Key Words: error, fuzzy classification, remote sensing, uncertainty
A common objective of remote sensing is the mapping of land cover. Traditionally, this has been achieved using hard classifiers such as the maximum likelihood classifier. In these circumstances, accuracy is readily assessed using the confusion matrix or contingency table. Based on this matrix the overall userís and producerís accuracies can be estimated as can the same accuracies per class. Further, Kappa statistics can be estimated that allow for randomness in the matrix. During the last 10 years or so, researchers have increasingly applied fuzzy classifiers, such as the fuzzy c-means classifier and the mixture model that estimates the membership of a pixel, to each class. Clearly, where a pixel represents a mixture of land cover classes (for example, 20 percent cereals, 50 percent heathland, and 30 percent forest) fuzzy classifiers provide the opportunity for greater accuracy, and for this reason, fuzzy classification has become a fundamentally important approach in remote sensing. There is no accepted standard method for assessing the accuracy of a fuzzy classification. A scatterplot between the observed values and the estimated values provides a useful graphical representation of the accuracy of the estimates; however, quantitative summary of the information in the scatterplot has proved elusive and researchers have often used ad-hoc combinations of statistics, such as the mean error, root mean square (RMS) error, and correlation coefficient.
The RMS error is insufficient because it is insensitive to the variance per class and the overall number of classes. For example, a class that has small membership x in all pixels (say 0%stlgxstlg10%) may be estimated with small RMS error by setting all pixels to the mean membership for that class (say 5 percent) even though the correlation between observed and estimated memberships is zero. The likelihood of having small memberships per class increases with the number of classes c. The correlation coefficient is insufficient because it is insensitive to bias such that r may be large when the scatterplot lies away from the 1:1 line. A particular problem arises for classes whose memberships are bimodal (i.e., little mixing as is often the case for "water" classes where pixels are either close to 0 percent or 100 percent water but rarely lie between). Then r can be large when the correlation within each "cluster" is zero. Several statistics were evaluated that address these issues including schemes for standardising the RMS error and weighting schemes for estimating overall precision and bias. First, the above issues were explored using fuzzy maps of land cover obtained for four different sites representing different biomes (New Forest, U.K.; Cukurova Deltas, Turkey; BOREAS site, Canada; HAPEX-Sahel site, Niger). These fuzzy maps were obtained from the National Oceanic and Atmospheric Administrationís (NOAA) Advanced Very-High Resolution Radiometer (AVHRR) imagery (trained on classified fine spatial resolution imagery) using a standard feed-forward back-propagation artificial neural network. Second, the proposed statistics were evaluated using simulated data involving classes with different distributions of memberships and different numbers of these classes.