A new strategy to select observer (camera) viewpoints for global 3D reconstruction of unknown objects is presented. The method has four steps: local surface feature extraction, shape classification, viewpoint selection and global reconstruction. An active vision system (Biclops) with two cameras aimed by independent pan/tilt axes, extracts 2D and 3D surface features from the scene. These local features are assembled into simple geometric primitives. The primitives are then classified into shapes, which are used to hypothesize the global shape of the object. The next viewpoint is chosen to verify the hypothesized shape. If the hypothesis is verified, some information about global reconstruction of a model can be stored. If not, the data leading up to this viewpoint is re-examined to create a more consistent hypothesis for the object shape. The paper has two main contributions. First, the next viewpoint algorithm uses only the local geometric features of an object. Second, the visibility constraint is not used in the function to compute next viewpoint. Instead it is solved prior to viewpoint selection using volume intersection of prismatic cones generated from camera coordinate center and image plane. The proposed algorithm is demonstrated experimentally by reconstructing the model for simple 3D objects using a two-camera stereo vision system mounted on a 6-DOF manipulator in an uncontrolled (noisy) environment.