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By introducing Gaussian-Gamma-shaped (GGS) bi-windows instead of traditional rectangle bi-windows, a new ratio-based edge detector is proposed to extract thin edges of synthetic aperture radar (SAR) images. As poor 2-D smoothing filters, the rectangle window functions are shown to be apt to incur false-edge pixels near true edges. Using the GGS window functions reduces false-edge pixels near true edges, which can be verified by analyzing effective false maxima in the edge strength maps (ESMs). Operating the nonmaximum suppression and hysteresis thresholding on the ratio-based ESM using GGS bi-windows yields thin edges of SAR images. The receiver-operating-characteristic curve is used to evaluate edge detectors. The experimental results to a synthetic SAR image show that the detector using GGS bi-windows attains better performance than the one using rectangle bi-windows.