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Vectorizing line drawing is necessary for the digital workflows of 2D animation and engineering design. But it is challenging due to the ambiguity of topology, especially at junctions. Existing vectorization methods either suffer from low accuracy or cannot deal with high‐resolution images. To deal with a variety of challenging containing different kinds of complex junctions, we propose a two‐phase line drawing vectorization method that analyzes the global and local topology. In the first phase, we subdivide the lines into partial curves, and in the second phase, we reconstruct the topology at junctions. With the overall topology estimated in the two phases, we can trace and vectorize the curves. To qualitatively and quantitatively evaluate our method and compare it with the existing methods, we conduct extensive experiments on not only existing datasets but also our newly synthesized dataset which contains different types of complex and ambiguous junctions. Experimental statistics show that our method greatly outperforms existing methods in terms of computational speed and achieves visually better topology reconstruction accuracy.