Abstract—Image segmentation plays a major role in quantitative image analysis and computer aided detection (CAD) and diagnosis (CADx) for clinical applications. Conventional segmentation assigns a single label to each voxel, neglecting the partial volume (PV) effect. This work presents an EM (Expectation Maximization) framework for segmentation of tissue mixture in each voxel. Image data and tissue mixture models, EM algorithm for mixture quantification, prior model for regularization on the mixtures, and multi-spectral MR (magnetic resonance) data characterization are described in details. Preliminary results from CT (computed tomography) and MR images are reported to demonstrate its potential for clinical use. Keywords—Image segmentation, tissue mixture, maximum a posteriori (MAP) probability, EM algorithm I. I NTRODUCTION Image segmentation is a major component of image processing methodology, facilitating quantitative analysis and visualization of clinical features in medical images toward diagnosis, treatment/surgical planning and follow-up evaluation. Conventional image segmentation assigns a single label to reflect a specific tissue type in each voxel and does not provide the percentage of each tissue type in that voxel. This can result in a significant error in quantitative image analysis [1] . A logical solution is to determine each tissue percentage in each voxel. Quantifying the tissue mixture in each voxel has been attempted in the recent years [2] with a noticeable success. This work presents a framework for mixture segmentation based on the well- established EM (Expectation Maximization) algorithm [3] . II. METHODOLOGY A. Image Data Model Given an acquired image } { i Y = Y , i = 1,2,…,I , over I voxels. Each voxel value i Y is an observation of a random process around a mean i Y and variance 2 i s , i.e., i i i n Y Y = (1) where i n reflects the associated noise with zero mean and variance of 2 i s . Assume that the noise follows a Gaussian distribution, then 2 2 2 2 / ) ( 2 1 ) | ( i i i i Y Y i i e Y P s s p q - - = (2) where i q reflects the model parameters of mean and variance { i Y , 2 i s }. Assume that all voxel values { i Y } are statistically independent from each other, given the mean distribution { i Y }, then we have ) | ( ) | ( 1 i i I i Y P P q = ∏ = Θ Y (3) where Θ = { i q }, i = 1,2,…, I. It is noted that given the mean i Y at voxel i , repeated observations at that voxel will render the variance 2 i s . Therefore, the probability density function in equations (2) and (3) is defined for the given model parameters, which can be utilized to assign an appropriate label for each voxel, given the observed image { i Y } [4] . However, the model parameters describe only the global properties of each voxel as a whole volume and do not consider its substructures or mixture. In many medical imaging applications, each voxel can have more than one tissue types due to the limited spatial resolution. Ignoring the substructures will result in the well-known partial volume (PV) effect. Consideration of the substructures is given below. B. Tissue Mixture Model The acquired image { i Y } reflects K tissue types distributing inside the body. Within each voxel volume, there possibly are K tissue types, where each tissue type has a contribution to the observed voxel value i Y at voxel i . Let ik X be the contribution of tissue type k to the observation i Y . It is clear that ik X is also a random process around a mean ik X and variance 2 ik s , i.e., ik ik ik n X X = (4) where ik n reflects the associated noise with zero mean and variance of 2 ik s . Assume that the noise ik n also follows a Gaussian distribution, then 2 2 2 2 / ) ( 2 1 ) | ( ik ik ik ik X X ik ik e X P s s p q - - = (5) where ik q reflects the model parameters of mean and variance { ik X , 2 ik s }. Assume that all K tissue types have no correlation, then ) | ( ) ˆ | ˆ ( 1 ik ik K k i i X P X P q q = ∏ = (6) where i X ˆ = { ik X } and i q ˆ = { ik q }, k = 1,2,…K, are vectors of length K for voxel i . By the assumption that all voxel variables { i X ˆ }, i = 1,2,…,I , are statistically independent, given the model parameters, then we have ) | ( ) | ( , 1 , ik ik K I k i X P P q = ∏ = Θ X (7) An EM Framework for Segmentation of Tissue Mixture s from Medical Images Zhengrong Liang 1,2 , Xiang Li 1 , Daria Eremina 3 , and Lihong Li 1 Departments of Radiology 1 , Computer Science 2 and Applied mathematics 3 , State University of New York Stony Brook, NY 11794, USA 0 6 E