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.

Accurate thickness measurement of sheet-like structure such as articular cartilage in CT images is required in clinical diagnosis as well as in fundamental research. Using a conventional measurement method based on the zero-crossing edge detection (zero-crossings method), several studies have already analyzed the accuracy limitation on thickness measurement of the single sheet structure that is not influenced by peripheral structures. However, no studies, as of yet, have assessed measurement accuracy of two adjacent sheet structures such as femoral and acetabular cartilages in the hip joint. In this paper, we present a model of the CT scanning process of two parallel sheet structures separated by a small distance, and use the model to predict the shape of the gray-level profiles along the sheet normal orientation. The difference between the predicted and the actual gray-level profiles observed in the CT data is minimized by refining the model parameters. Both a one-by-one search (exhaustive combination search) technique and a nonlinear optimization technique based on the Levenberg-Marquardt algorithm are used to minimize the difference. Using CT images of phantoms, we present results showing that when applying the one-by-one search method to obtain the initial values of the model parameters, Levenberg-Marquardt method is more accurate than zero-crossings and one-by-one search methods for estimating the thickness of two adjacent sheet structures, as well as the thickness of a single sheet structure.