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In this paper, we put forward a novel approach for change detection in synthetic aperture radar (SAR) images. The approach classifies changed and unchanged regions by fuzzy c-means (FCM) clustering with a novel Markov random field (MRF) energy function. In order to reduce the effect of speckle noise, a novel form of the MRF energy function with an additional term is established to modify the membership of each pixel. In addition, the degree of modification is determined by the relationship of the neighborhood pixels. The specific form of the additional term is contingent upon different situations, and it is established ultimately by utilizing the least-square method. There are two aspects to our contributions. First, in order to reduce the effect of speckle noise, the proposed approach focuses on modifying the membership instead of modifying the objective function. It is computationally simple in all the steps involved. Its objective function can just return to the original form of FCM, which leads to its consuming less time than that of some obviously recently improved FCM algorithms. Second, the proposed approach modifies the membership of each pixel according to a novel form of the MRF energy function through which the neighbors of each pixel, as well as their relationship, are concerned. Theoretical analysis and experimental results on real SAR datasets show that the proposed approach can detect the real changes as well as mitigate the effect of speckle noises. Theoretical analysis and experiments also demonstrate its low time complexity.