Visualizing 3D flow fields intrinsically suffers from problems of clutter and occlusion. A common practice to alleviate these issues is to restrict the visualization to feature surfaces that capture important characteristics of the underlying data. However, this often comes at costs of losing information due to the inherent projection of the 3D field on a 2D surface, which may limit the technique's ability to provide insight and impede fast exploration of the three-dimensional flow. In this paper we present a combination of 2D and 3D flow visualization techniques in order to capture the flow field's behavior on the feature surface as well as in its vicinity. We introduce surface-guided streamlines to complement 2D dense vector field visualization on the surface. Image-based seeding strategies are used to achieve an importance-driven distribution of streamline seed points on the surface that adapts to local flow properties as well as to characteristics of the feature surfaces...