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Published on: April 13, 2013
Segmentation of brain MR images through a hidden Markov random field model and the expectation-maximization algorithm
1FMRIB Centre, John Radcliffe Hospital, University of Oxford, UK. yongyue@fmrib.ox.ac.uk
Abstract:
The finite mixture (FM) model is the most commonly used model for statistical segmentation of brain magnetic resonance (MR) images because of its simple mathematical form and the piecewise constant nature of ideal brain MR images. However, being a histogram-based model, the FM has an intrinsic limitation--no spatial information is taken into account. This causes the FM model to work only on well-defined images with low levels of noise; unfortunately, this is often not the the case due to artifacts such as partial volume effect and bias field distortion. Under these conditions, FM model-based methods produce unreliable results. In this paper, we propose a novel hidden Markov random field (HMRF) model, which is a stochastic process generated by a MRF whose state sequence cannot be observed directly but which can be indirectly estimated through observations. Mathematically, it can be shown that the FM model is a degenerate version of the HMRF model. The advantage of the HMRF model derives from the way in which the spatial information is encoded through the mutual influences of neighboring sites. Although MRF modeling has been employed in MR image segmentation by other researchers, most reported methods are limited to using MRF as a general prior in an FM model-based approach. To fit the HMRF model, an EM algorithm is used. We show that by incorporating both the HMRF model and the EM algorithm into a HMRF-EM framework, an accurate and robust segmentation can be achieved. More importantly, the HMRF-EM framework can easily be combined with other techniques. As an example, we show how the bias field correction algorithm of Guillemaud and Brady (1997) can be incorporated into this framework to achieve a three-dimensional fully automated approach for brain MR image segmentation.
Insights
This study introduces a novel hidden Markov random field (HMRF) model for brain MR image segmentation, improving accuracy and robustness over traditional finite mixture (FM) models by incorporating spatial information. The HMRF-EM framework offers a more reliable approach for segmenting noisy and distorted brain images.
Area of Science:
- Medical Imaging
- Computational Neuroscience
- Image Analysis
Background:
- Finite mixture (FM) models are standard for brain MR image segmentation but lack spatial information, leading to inaccuracies with noisy or distorted images.
- Artifacts like partial volume effects and bias fields compromise the reliability of traditional FM-based segmentation methods.
- Existing MRF-based methods often use MRF as a prior within FM models, limiting their full potential.
Purpose of the Study:
- To propose a novel hidden Markov random field (HMRF) model for enhanced statistical segmentation of brain MR images.
- To address the limitations of histogram-based FM models by incorporating spatial information.
- To develop a robust and accurate HMRF-EM framework for brain MR image segmentation, capable of handling image artifacts.
Main Methods:
- Developed a novel hidden Markov random field (HMRF) model, mathematically shown to be a more general form of the FM model.
- Utilized an Expectation-Maximization (EM) algorithm to fit the HMRF model, creating an HMRF-EM framework.
- Integrated bias field correction (Guillemaud and Brady, 1997) into the HMRF-EM framework for a fully automated 3D segmentation approach.
Main Results:
- The proposed HMRF-EM framework achieves accurate and robust brain MR image segmentation.
- The model effectively incorporates spatial information through the interactions of neighboring image sites.
- Demonstrated the framework's flexibility by successfully combining it with bias field correction for automated 3D segmentation.
Conclusions:
- The HMRF-EM framework provides a significant advancement over traditional FM models for brain MR image segmentation.
- This approach enhances segmentation reliability, particularly in the presence of noise and artifacts.
- The framework's modularity allows for easy integration with other image processing techniques, paving the way for fully automated analysis.
