Multiplicative versus additive bias field models for unified partial-volume segmentation and inhomogeneity correction in brain MR images

It has been widely accepted that for brain MR images, both the image density inhomogeneity (slowly-varying intensity changes across the field of view) and partial-volume effect (PVE) (more than one tissue type present in a single voxel) considerably reduce the accuracy and reliability of quantitative analysis for various clinical purposes. This paper presents a unified expectation-maximization (EM) approach, where PVE and intensity inhomogeneity are combined together into a built-in-one statistical model in additive and multiplicative formats. It assumes that each tissue type follows a conditionally-independent normal distribution, based on which the summation of all tissue contributions multiplied or added by the bias term leads to mean density value at each voxel. Meanwhile, the summation of all the tissue mixtures, which is unobservable but could be estimated via EM framework (many-to-one mapping), multiplied or added by the bias term would lead to the observed image density at each voxel. In doing so, both the inhomogeneity and tissue mixtures are updated voxel-by-voxel until the convergence of a stable solution. Comprehensive tests on simulated brain MR images strongly demonstrated the feasibilities of additive/multiplicative bias models and the effectiveness of the unified EM approach. In addition, additive and multiplicative bias field models reflect advantages in terms of stability and robustness.