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A new edge localisation technique for step edges in images with signal-dependent Rician noise in MRI is proposed. Dependent noise can not only affect the detection of true edges in an image but also their position. Inaccurate localisation of an edge can lead to insufficient segmentation and reduce the overall accuracy of any edge detection method. The proposed technique uses higher-order moments of the noise function to determine the correction factor for localisation and thus reduce the overall mean square error for true edge localisation due to noise. The proposed technique offers significant improvement in edge localisation for an image as compared with Canny and Sobel methods.