Mobile robots need maps or other forms of geometric information about the environment to navigate. The mobility sensors (LADAR, stereo, etc.) on these robotic vehicles can however populate these maps only up to a distance of a few tens of meters. A navigation system has no knowledge about the world beyond this sensing horizon. As a result, path planners that rely only on this knowledge are unable to anticipate obstacles sufficiently early and have no choice but to resort to an inefficient local obstacle avoidance behavior. However, recent developments in the computer vision community allows us to collect geometric information about the environment far beyond this sensing horizon. The coarse 3D geometric estimation that can be recovered is derived from an appearance-based model. That uses a multiple-hypothesis framework to robustly estimate scene structure from a single image and estimating confidences for each geometric label. This 3D geometric estimation is used with a previously presented navigation strategy that reasons about sensor constraints and plans for measurements while navigating towards the goal. The validity of the sensing method and navigation strategy is supported by results from simulations as well as field experiments with a real robotic platform. These results also show that significant reduction in path length can be achieved by using this framework.