Computer-aided medical systems, e.g. in the fields of medical robotics or image-based assistance, are continuously investigated to overcome human limitations concerning perception, memory or dexterity. A common requirement of such systems is the availability of a digital model describing the patient's position and morphology during a procedure. Operational complexity and technical limitations of established 3D imaging methods leave clinical settings in need of a method for the fast acquisition of a three-dimensional body surface representation. For this purpose, we propose an unsupervised and efficient body registration pipeline based on the markerless elastic registration and completion of single-view stereo range images of the body surface with statistical parametric body shape templates. Initial results show a promising representative quality of the models generated through the registration process with submillimetric fitting accuracy and realistic surface morphology, indicating the general feasibility of our approach as an instant body registration method for automated medical and biometric applications.