Given a set of 2D images, we propose a novel approach for the reconstruction of straight 3D line segments that represent the underlying geometry of static 3D objects in the scene. Such an algorithm is especially useful for the automatic 3D reconstruction of man-made environments. The main contribution of our approach is the generation of an improved reconstruction by imposing global topological constraints given by connections between neighbouring lines. Additionally, our approach does not employ explicit line matching between views, thus making it more robust against image noise and partial occlusion. Furthermore, we suggest a technique to merge independent reconstructions, that are generated from different base images, which also helps to remove outliers. The proposed algorithm is evaluated on synthetic and real scenes by comparison with ground truth.