PURPOSE: Point-set registration for interventional tools requires well-defined points to be present on these tools. In this work, an algorithm is proposed which uses planes, lines, and points for registration when point-set registration is not feasible. METHODS: The proposed algorithm matches points, lines, and planes in each coordinate system, uses invariant features for initial registration, and optimizes the registration iteratively. For validation, simulated data with known ground-truth and real surgical tool registration data using point-set registration as ground-truth were created to evaluate the algorithm’s accuracy. RESULTS: The proposed algorithm is equally as accurate as point-set registration, and the difference between the registrations is less than the noise in the tracking system. CONCLUSION: The proposed algorithm is a viable alternative when point-set registration cannot be performed.