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Selecting a threshold from the gradient histogram, a histogram of gradient magnitudes, of an image plays a crucial role in a gradient based edge detection system. In this paper, we propose a methodology to determine this threshold value when the edge detection system is applied to synthetic aperture radar (SAR) images. We consider a SAR image as a random process, perform a transformation, model the gradient histogram of the transformed image using theories of random process and then determine a region of interest in the gradient histogram using certain properties of a probability density function. Standard histogram thresholding techniques are then used within the region of interest to get the threshold value. The proposed methodology provides a systematic solution to the thresholding problem in gradient based edge detection systems for SAR images and hence results in consistently appreciable performance. Extensive experimental results are shown to demonstrate the effectiveness of the proposed methodology.