Purpose: We describe a 3D multi-view perception system for the da Vinci surgical system to enable Operating room (OR) scene understanding and context awareness. Methods: Our proposed system is comprised of four Time-of-Flight (ToF) cameras rigidly attached to strategic locations on the daVinci Xi patient side cart (PSC). The cameras are registered to the robot's kinematic chain by performing a one-time calibration routine and therefore, information from all cameras can be fused and represented in one common coordinate frame. Based on this architecture, a multi-view 3D scene semantic segmentation algorithm is created to enable recognition of common and salient objects/equipment and surgical activities in a da Vinci OR. Our proposed 3D semantic segmentation method has been trained and validated on a novel densely annotated dataset that has been captured from clinical scenarios. Results: The results show that our proposed architecture has acceptable registration error ($3.3\%\pm1.4\%$ of object-camera distance) and can robustly improve scene segmentation performance (mean Intersection Over Union - mIOU) for less frequently appearing classes ($\ge 0.013$) compared to a single-view method. Conclusion: We present the first dynamic multi-view perception system with a novel segmentation architecture, which can be used as a building block technology for applications such as surgical workflow analysis, automation of surgical sub-tasks and advanced guidance systems.