Locating the internal structures of an organ is a critical aspect of many surgical procedures. Minimally invasive surgery, associated with augmented reality techniques, offers the potential to visualize inner structures, allowing for improved analysis, depth perception or for supporting planning and decision systems. Most of the current methods dealing with rigid or non-rigid augmented reality make the assumption that the topology of the organ is not modified. As surgery relies essentially on cutting and dissection of anatomical structures, such methods are limited to the early stages of the surgery. We solve this shortcoming with the introduction of a method for physics-based elastic registration using a single view from a monocular camera. Singularities caused by topological changes are detected and propagated to the preoperative model. This significantly improves the coherence between the actual laparoscopic view and the model and provides added value in terms of navigation and decision-making, e.g., by overlaying the internal structures of an organ on the laparoscopic view. Our real-time augmentation method is assessed on several scenarios, using synthetic objects and real organs. In all cases, the impact of our approach is demonstrated, both qualitatively and quantitatively ( http://www.open-cas.org/?q=PaulusIJCARS16 ). The presented approach tackles the challenge of localizing internal structures throughout a complete surgical procedure, even after surgical cuts. This information is crucial for surgeons to improve the outcome for their surgical procedure and avoid complications.