Global optimization based registration technique for tracking knee cartilage thickness changes in MR images

The objective of this work is to develop and validate a computational method for fast and globally solving the registration problem of the three-dimensional (3-D) bone surface from MR images of knee joint. This technique is used to monitor the local cartilage thickness changes over time. By introducing a "Lipschitzation" process to the traditional cost function, global optimality is guaranteed and a global search over the transformation (translation and rotation) space can be carried out effectively. A fast optimization algorithm to minimize the Lipschitzized cost function is described. We conducted a series of experiments to test and validate the 3-D registration method. Both synthetic realistic MR data and clinical data were used to systematically test and evaluate registration accuracy.