Magnetic Resonance (MR) imaging is a 3-D, multi-slice, radiological technique that acquires multiple intensities corresponding to each voxel. The transverse relaxation time, T$\sb1$, and the axial relaxation time, T$\sb2$, are two commonly obtained intensities that tend to be orthogonal. Automated segmentation of 3-D regions is very difficult because some borders may be delineated only in T$\sb1$ images, while others are delineated only in T$\sb2$ images. Classical segmentation techniques based on either global histogram segmentation or local edge detection often fail due to the non-unique and random nature of MR intensities.
A 3-D, neighborhood based, segmentation method was developed based on both spatial and intensity criteria. The spatial criterion requires that only voxels connected by an edge or face to a voxel known to be in the region be considered for inclusion. Therefore, the region "grows" outward from an initial voxel. An intensity criterion that tries to balance local and global properties must also be satisfied. It determines the vector distance between the intensity of the voxel in question and a characteristic intensity for the neighboring voxels known to be in the region. Voxel intensities within a 95% confidence interval of the characteristic intensity are considered part of the region. The kernel size used to determine the characteristic intensity determines the balance between global and local properties. The segmentation terminates when no additional voxels satisfy both spatial and error criteria.
Some regions, such as the brain compartments, are highly convoluted, resulting in a large number of border voxels containing a mixture of adjoining tissues. A sub-voxel estimate of the fractional composition is necessary for accurate quantification. A least-squares estimator was derived for the fractional composition of each voxel. Additionally, a maximum likelihood estimator was derived to globally estimate the fraction for all mixture voxels. This estimator is a minimum variance estimator in contrast to the least-squares estimator. The estimation methods in conjunction with the 3-D, neighborhood based, segmentation method resulted in an automated, highly accurate, quantification technique shown to be successful even for the brain compartments. Widespread applicability of these methods was further demonstrated by segmentation of kidneys in CT images.