An accurate and robust method to detect curve structures, such as a vessel branch or a guidewire, is essential for many medical imaging applications. A fully automatic method, although highly desired, is prone to detection errors that are caused by image noise and curve-like artifacts. In this paper, we present a novel method to interactively detect a curve structure in a 2D fluoroscopy image with a minimum requirement of human corrections. In this work, a learning based method is used to detect curve segments. Based on the detected segment candidates, a graph is built to search a curve structure as the best path passing through user interactions. Furthermore, our method introduces a novel hyper-graph based optimization method to allow for imposing geometric constraints during the path searching, and to provide a smooth and quickly converged result. With minimum human interactions involved, the method can provide accurate detection results, and has been used in different applications for guidewire and vessel detections.