Vector field topology is traditionally visualized by explicit extraction of graphical objects that represent the topological skeleton, including critical points, periodic orbits, and the invariant manifolds converging to those in forward or reverse time. In this work, we present implicit visualization of vector field topology by means of derived scalar fields. We obtain these fields by seeding a forward and a reverse streamline at each of their samples, and determining which critical point, periodic orbit, or solid boundary they converge to. This provides a segmentation of the domain with respect to regions of qualitatively similar streamline behavior, and thus its topological structure.We present an adaptive sampling strategy of the fields, together with an approach to determine their convergence with respect to streamline integration. Using 2D and 3D fields, we exemplify the utility and interpretation of our approach.