The recognition of individual object instances in single monocular images is still an incompletely solved task. In this work, we propose a new approach for detecting and separating vehicles in the context of autonomous driving. Our method uses the fully convolutional network (FCN) for semantic labeling and for estimating the boundary of each vehicle. Even though a contour is in general a one pixel wide structure which cannot be directly learned by a CNN, our network addresses this by providing areas around the contours. Based on these areas, we separate the individual vehicle instances. In our experiments, we show on two challenging datasets (Cityscapes and KITTI) that we achieve state-of-the-art performance, despite the usage of a subsampling rate of two. Our approach even outperforms all recent works w.r.t. several rating scores.