Component analysis approach to estimation of tissue intensity distributions of 3D images

Many segmentation problems in medical imaging rely on accurate modeling and estimation of tissue intensity probability density functions. Gaussian mixture modeling, currently the most common approach, has several drawbacks, such as reliance on a specific model and iterative optimization. It also does not take advantage of substantially larger amount of data provided by 3D acquisitions, which are becoming standard in clinical environment. We propose a novel completely non-parametric algorithm to estimate the tissue intensity probabilities in 3D images. Instead of relying on traditional framework of iterating between classification and estimation, we pose the problem as an instance of a blind source separation problem, where the unknown distributions are treated as sources and histograms of image subvolumes as mixtures. The new approach performed well on synthetic data and real magnetic resonance (MR) scans, robustly capturing intensity distributions of even small image structures and partial volume voxels.