Quantification of MR brain images by mixture density and partial volume modeling

Abstract

The problem of automatic quantification of brain tissue by utilizing single-valued (single echo) magnetic resonance imaging (MRI) brain scans is addressed. It is shown that this problem can be solved without classification or segmentation, a method that may be particularly useful in quantifying white matter lesions where the range of values associated with the lesions and the white matter may heavily overlap. The general technique utilizes a statistical model of the noise and partial volume effect together with a finite mixture density description of the tissues. The quantification is then formulated as a minimization problem of high order with up to six separate densities as part of the mixture. This problem is solved by tree annealing with and without partial volume utilized, the results compared, and the sensitivity of the tree annealing algorithm to various parameters is exhibited. The actual quantification is performed by two methods: a classification-based method called Bayes quantification, and parameter estimation. Results from each method are presented for synthetic and actual data.

Fast and robust parameter estimation for statistical partial volume models in brain MRI

“…Other applications that gain from modeling of PVE have been as well considered within brain MRI. Santago and Gage (1993) apply information about partial volume voxels to improve tissue quantification. González Ballester et al (2002) study the asymmetry of temporal horns taking PVE into account, and in an earlier work (González Ballester et al, 2000), they suggest that PVE and discrete sampling at boundary locations can lead to volume measurement errors in the range 20 -60%.…”

“…The method involves maximum-likelihood estimation of the PVCs for each voxel that model PV fractions of pure tissue types. Some authors have studied the identification of voxels containing PVE based on the mixel or a closely related model without trying to estimate the PVCs for each voxel (Laidlaw et al, 1998;Ruan et al, 2000;Santago and Gage, 1993). Our interest in this study is in estimating PVCs and not in merely identifying voxels containing PVE.…”

“…In general, there are three approaches to the parameter estimation problem: histogram analysis (Santago and Gage, 1993), simultaneous parameter, and partial volume estimation by expectation maximization (EM)-like algorithms (Noe and Gee, 2001), and estimation based on a hard segmentation of the image (Shattuck et al, 2001). These three approaches, however, each have their drawbacks.…”

“…If a standard nonlinear optimization algorithm aimed at local minimization (e.g., LevenbergMarquee algorithm used commonly for curve fitting) is used, the initialization for the algorithm has to be chosen carefully to avoid convergence to a poor local minimum. These considerations call for the use of advanced global optimization algorithms, for example, Santago and Gage (1993) propose to use the treeannealing method (Bilbro and Snyder, 1991). The problem with global optimization methods is that they are usually far more time consuming than local optimization methods.…”

Three validation metrics for automated probabilistic image segmentation of brain tumours

“…In discriminant imaging analysis, mixture models such as normal, normal mixture, or histograms are used. For example flexible histogram approach [8,9], classifications of several target features may be conducted by treating pixels as a set of independent samples drawn from a mixture distribution [10]. A distribution of feature vectors using Parzen windows was modelled.…”