GAUSSIAN MIXTURE MODEL
Automatic segmentation of brain MRI images to the three main tissue types: white matter (WM), gray matter (GM) and cerebro-spinal fluid (CSF), is a topic of great importance and much research. It is known that volumetric analysis of different parts of the brain is useful in assessing the progress or remission of various diseases, such as alzheimer, epilepsy, sclerosis and schizophrenia.
An automated algorithm for tissue segmentation of noisy, low contrast magnetic resonance (MR) images of the brain is presented. A mixture model composed of a large number of Gaussians is used to represent the brain image. Each tissue is represented by a large number of Gaussian components to capture the complex tissue spatial layout. The intensity of a tissue is considered a global feature and is incorporated into the model through tying of all the related Gaussian parameters. The Expectation-Maximization (EM) algorithm is utilized to learn the parameter-tied, constrained Gaussian mixture model. An elaborate initialization scheme is suggested to link the set of Gaussians per tissue type, such that each Gaussian in the set has similar intensity characteristics with minimal overlapping spatial supports. Segmentation of the brain image is achieved by the affiliation of each voxel to the component of the model that maximized the a-posteriori probability.
The presented algorithm is used to segment 3D, T1-weighted, simulated and real MR images of the brain into three different tissues, under varying noise conditions. Results are compared with state-of-the-art algorithms in the literature. The algorithm does not use an atlas for initialization or parameter learning. Registration processes are therefore not required and the applicability of the framework can be extended to diseased brains and neonatal brains.
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