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This paper presents a novel technique for automatic edge enhancement and detection in synthetic aperture radar (SAR) images. The characteristics of SAR images justify the importance of an edge enhancement step prior to edge detection. Therefore, this paper presents a robust and unsupervised edge enhancement algorithm based on a combination of wavelet coefficients at different scales. The performance of the method is first tested on simulated images. Then, in order to complete the automatic detection chain, among the different options for the decision stage, the use of geodesic active contour is proposed. The second part of this paper suggests the extraction of the coastline in SAR images as a particular case of edge detection. Hence, after highlighting its practical interest, the technique that is theoretically presented in the first part of this paper is applied to real scenarios. Finally, the chances of its operational capability are assessed.