We describe a technique for the registration of three dimensional (3D) knee femur surface points from MR image data sets; it is a technique that can track local cartilage thickness changes over time. In the first coarse registration step, we use the direction vectors of the volume given by the cloud of points of the MR image to correct for different knee joint positions and orientations in the MR scanner. In the second fine registration step, we propose a global search algorithm that simultaneously determines the optimal transformation parameters and point correspondences through searching a six dimensional space of Euclidean motion vectors (translation and rotation). The present algorithm is grounded on a mathematical theory - Lipschitz optimization. Compared with the other three registration approaches (ICP, EM-ICP, and genetic algorithms), the proposed method achieved the highest registration accuracy on both animal and clinical data.