Registration methods have become an important tool in many medical applications. Existing methods require a good initial estimation (transformation) in order to find a global solution, i.e., if the initial estimation is far from the actual solution, incorrect solution or mismatching is very likely. In contrast, this paper presents a novel approach for globally solving the three dimensional (3D) rigid registration problem. The registration is grounded on a mathematical theory—Lipschitz optimization. It achieves a guaranteed global optimality with a rough initial estimation (e.g., even a random guess). Moreover, Munkres assignment algorithm is used to find the point correspondences. It applies the distance matrix to find an optimal correspondence. Our method is evaluated and demonstrated on MR images from porcine knees and human knees. Compared with state-of-the-art methods, the proposed technique is more robust, more accurate to perform point to point comparisons of knee cartilage thickness values for follow-up studies on the same subject. 
Surface-based rigid registration using a global optimization algorithm for assessment of MRI knee cartilage thickness changes