Cartoons are a worldwide popular visual entertainment medium with a long history. Nowadays, with the boom of electronic devices, there is an increasing need to digitize old classic cartoons as a basis for further editing, including deformation, colorization, etc. To perform such editing, it is essential to extract the structure lines within cartoon images. Traditional edge detection methods are mainly based on gradients. These methods perform poorly in the face of compression artifacts and spatially-varying line colors, which cause gradient values to become unreliable. This paper presents the first approach to extract structure lines in cartoons based on regions. Our method starts by segmenting an image into regions, and then classifies them as edge regions and non-edge regions. Our second main contribution comprises three measures to estimate the likelihood of a region being a non-edge region. These measure darkness, local contrast, and shape. Since the likelihoods become unreliable as regions become smaller, we further classify regions using both likelihoods and the relationships to neighboring regions via a graph-cut formulation. Our method has been evaluated on a wide variety of cartoon images, and convincing results are obtained in all cases.