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Often, in synthetic aperture radar (SAR) images of polar ice, one encounters shadow-like features across the images. Such features make it difficult to classify pixels into ice and water. Accordingly, it becomes a challenge to determine the true size and boundaries of ice floes in an SAR image of polar ice. We develop a simple statistical procedure which classifies pixels of an image by eliminating the effects of shadow-like features. Methodology developed in this paper is illustrated using some noisy SAR images of ice floes in the Arctic sea.