Abstract: Primates are very good at recognizing objects independently of viewing angle or retinal position and outperform existing computer vision systems by far. But invariant object recognition is only one prerequisite for successful interaction with the environment. An animal also needs to assess an object's position and relative rotational angle. We propose here a model that is able to extract object identity, position, and rotation angles, where each code is independent of all others. We demonstrate the model behavior on complex three-dimensional objects under translation and in-depth rotation on homogeneous backgrounds. A similar model has previously been shown to extract hippocampal spatial codes from quasi-natural videos. The rigorous mathematical analysis of this earlier application carries over to the scenario of invariant object recognition.