A Bayesian approach to subvoxel tissue classification in NMR microscopic images of trabecular bone

NMR microscopy is currently being used as an investigational tool for the evaluation of micromorphometric parameters of trabecular bone as a possible means to assess its strength. Since, typically, the image voxel size is not significantly smaller than individual trabecular elements, partial volume blurring can be a major complication for accurate tissue classification. In this paper, a Bayesian segmentation technique is reported that achieves improved subvoxel tissue classification. Each voxel is subdivided either into eight subvoxels twice the original resolution, or up to four subvoxels along the transaxial direction and the subvoxels optimally classified as volume blurring, the likelihood for the number of marrow subvoxels in each voxel can be computed on the basis of its measured signal. To resolve the ambiguity of the location of the marrow subvoxels, a Gibbs distribution is introduced to model the interaction between the subvoxels. Neighboring subvoxel pairs with the same tissue label are encouraged, and pairs with distinct labels are penalized. The segmentation is achieved by maximizing the a posteriori probability of the label image using the block ICM (iterative conditional mode) algorithm. The potential of the proposed technique is demonstrated in real and synthetic NMR microscopic images.