Abstract: Vectorization provides a link between raster scans of pencil-and-paper drawings and modern digital processing algorithms that require accurate vector representations. Even when input drawings are comprised of clean, crisp lines, inherent ambiguities near junctions make vectorization deceptively difficult. As a consequence, current vectorization approaches often fail to faithfully capture the junctions of drawn strokes. We propose a vectorization algorithm specialized for clean line drawings that analyzes the drawing's topology in order to overcome junction ambiguities. A gradient-based pixel clustering technique facilitates topology computation. This topological information is exploited during centerline extraction by a new "reverse drawing" procedure that reconstructs all possible drawing states prior to the creation of a junction and then selects the most likely stroke configuration.