Volumetric partial volume quantification via a statistical model of 3D voxel gradient magnitude

3-D volumetric data sets suffer from partial volume (PV) effects due to the finite bandwidth of the digital sampling process. A variety of approaches have been developed to quantify the PV effect in PET, SPECT, NMR and CT imaging modalities. Amongst these, voxel gradient magnitude information, modeled as a Rician distribution, has been suggested as a useful adjunct for statistical PV correction in 2-1) data. However, many biomedical image acquisition processes provide contiguous image slices arising from an acquisition process, which can be approximated to be 3-D in terms of the digital sampling process. Thus, classifiers using models that utilize extra information from the transverse or third perpendicular direction, in this case 3-D gradient magnitude information, should possess superior performance over algorithms that utilize lower dimensional information (e.g. intensity or 2D gradient features). Therefore, analytically derived probability distributions are presented to describe the 3-D gradient magnitude for 3-D isotropic and anisotropic data sets. A Bayesian classification framework, utilizing the 3-D isotropic and anisotropic gradient magnitude expressions, is compared with other models, illustrating superior performance for 3-D volumetric data.