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.

To determine the thickness from MR images, segmentation, that is, boundary detection, of the two adjacent thin structures (e.g., femoral cartilage and acetabular cartilage in the hip joint) is needed before thickness determination. Traditional techniques such as zero-crossings of the second derivatives are not suitable for the detection of these boundaries. A theoretical simulation analysis reveals that the zero-crossing method yields considerable biases in boundary detection and thickness measurement of the two adjacent thin structures from MR images. This paper studies the accurate detection of hip cartilage boundaries in the image plane, and a new method based on a model of the MR imaging process is proposed for this application. Based on the newly developed model, a hip cartilage boundary detection algorithm is developed. The in-plane thickness is computed based on the boundaries detected using the proposed algorithm. In order to correct the image plane thickness for overestimation due to oblique slicing, a three-dimensional (3-D) thickness computation approach is introduced. Experimental results show that the thickness measurement obtained by the new thickness computation approach is more accurate than that obtained by the existing thickness computation approaches.