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This paper presents a novel fuzzy-topology-integrated support vector machine (SVM) (FTSVM) classification method for remotely sensed images based on the standard SVM. Induced threshold fuzzy topology is integrated into the standard SVM. First, the optimal intercorrelation coefficient threshold value is applied to decompose an image class in spectral space into the three parts: interior, boundary, and exterior in fuzzy-topology space. The interior-class pixels are then classified as predefined classes based on maximum likelihood. The exterior-class pixels are ignored. The fuzzy-boundary-class pixels which contain misclassified pixels are reclassified based on the fuzzy-topology connectivity theory. As a result, misclassified pixel problems, to a certain extent, are solved. Two different experiments were performed to evaluate the performance of the FTSVM method, in comparison with standard SVM, maximum likelihood classifier (MLC), and fuzzy-topology-integrated MLC. Experimental results indicate that the FTSVM method performs better than the standard SVM and other methods in terms of classification accuracy, hence providing an effective classification method for remotely sensed images.