The objective of the Surface Water and Ocean Topography (SWOT) mission is to regularly monitor the height of the earth’s water surfaces. One of the challenges toward obtaining global measurements of these surfaces is to detect small water areas. In this article we introduce a method for the detection of thin water surfaces, such as rivers, in SWOT images. It combines a low-level step (segment detection) with a high-level regularization of these features. The method is then tested on a simulated SWOT image.