This paper provides a method for recognizing 3D objects in a single camera image and for determining their 3D poses. A model is trained solely based on the geometry information of a 3D CAD model of the object. We do not rely on texture or reflectance information of the object's surface, making this approach useful for a wide range of industrial and robot applications and complementary to descriptor-based approaches. A view-based approach that does not show the drawbacks of previous methods is applied: It is robust to noise, occlusions, clutter, and contrast changes. Furthermore, the 3D pose is determined with high accuracy. The high robustness of an exhaustive search is combined with an efficient hierarchical search, a high percentage of which can be computed offline, making our method suitable even for time-critical applications. The method is especially suited for, but not limited to, the recognition of untextured objects like metal parts, which are often used in industrial envi...