Detecting and monitoring rivers, specially narrow river trails hold substantial economic, societal, and cultural importance. However, segments of narrow trails of rivers may appear as isolated from remotely sensed images. In this paper, we address the problem of localization of narrow rivers in remote sensing images. As these rivers may be occluded, thin, or under-resolved, pixel-based methods might not be stable enough to ensure satisfying recovery. In this paper, we propose a two-step approach: first, we detect the main river course and larger segment through a pixel-based approach relying on the normalized difference water index. Second, after missing segments are identified, we propose to connect the dots through a Bézier curve adjustment using a dedicated greedy optimization approach. Results on synthetic and real images show the interest of the proposed approach, with respect to pixel-based alternatives.