We present an integrated approach for perception of unknown articulated objects. To robustly perceive objects and understand interactions, our method tightly integrates pose tracking, shape reconstruction, and the estimation of their kinematic structure. The key insight of our method is that these sub-problems complement each other: for example, tracking is greatly facilitated by knowing the shape of the object, whereas the shape and the kinematic structure can be more easily reconstructed if the motion of the object is known. Our combined method leverages these synergies to improve the performance of perception. We analyze the proposed method in average cases and difficult scenarios using a variety of rigid and articulated objects. The results show that our integrated solution achieves better results than solutions for the individual problems. This demonstrates the benefits of approaching robot perception problems in an integrated manner.