A system for navigating a medical device through the lumens and cavities in an operating region in a subject, comprising an imaging system for displaying an image of the operating region, including a representation of the distal end of the medical device in the operating region. The system also includes a localization system for determining the position of the medical device in a frame of reference translatable to the displayed image. Finally, the system includes an algorithm for evaluating one or more rotation matrix using a cost function to determine an optimum rotation matrix for performing transformation of a vector in the local frame of the localization system to that of the reference frame of the navigation system. The rotation matrix can then provide a scale invariant transformation or "registration" of the coordinate systems of the localization system and the navigation system. This allows navigation to be performed to a significant extent from the localization system display alone, which avoids the frequent x-ray irradiation that occurs during the use of fluoro imaging for navigation purposes.