Many recent delineation techniques owe much of their increased effectiveness to path classification algorithms that make it possible to distinguish promising paths from others. The downside of this development is that they require annotated training data, which is tedious to produce.In this paper, we propose an Active Learning approach that considerably speeds up the annotation process. Unlike standard ones, it takes advantage of the specificities of the delineation problem. It operates on a graph and can reduce the training set size by up to 80% without compromising the reconstruction quality.We will show that our approach outperforms conventional ones on various biomedical and natural image datasets, thus showing that it is broadly applicable.