The ready availability of satellite and other images of the Earth together with increasing societal interest in coastal processes and morphology make it desirable to have a consistent way of defining and mapping shorelines from images. The obvious choice, the land-water interface, is inadequate because it includes the back sides of islands and the edges of river and tidal channels that are not directly exposed to open water. On complex coasts, inclusion of these portions of the land-water interface would significantly affect quantitative measures of shoreline geometry. Here we propose a method to map shorelines consistently while accounting for ambiguity. The Opening Angle Method (OAM) uses a visibility criterion to define the shoreline. First a region of unambiguous open water is defined. Next, the shoreline is defined as the locus of points for which the sum of viewing angles extending to open water, unobstructed by land, exceeds a specified critical value. Shorelines defined by the OAM follow the land-water interface where the shoreline is unambiguous, and in more complex cases OAM shorelines are consistent with the idea that the shoreline is that part of the land-water interface that is directly exposed to open water.