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Triplet Markov fields (TMF) model is suitable for dealing with multi-class segmentation of non-stationary synthetic aperture radar (SAR) images. In this study, an algorithm using TMF with edge location for fast unsupervised multi-class segmentation of SAR images is proposed. The new segmentation algorithm can locate edge accurately with reasonable computational cost. First for the statistical characteristics of multiplicative speckle noise in SAR image, an edge strength based on the ratio of exponentially weighted averages operator is introduced into the Turbopixels algorithm to obtain a superpixel graph with accurate edge location in SAR images. To enhance the computational efficiency and suppress the speckle, the TMF model on pixel is generalised to that on the superpixel graph. Then, the new corresponding potential energy function and maximisation of posterior marginal segmentation formula are derived. The experimental results on synthetic and real SAR images show that the proposed algorithm can obtain accurate edge location in multi-class segmentation of SAR images, as well as enhance the computational efficiency. Especially when dealing with SAR images in large size, the proposed algorithm can give a robust and efficient result of segmentation.