An integrated method of adaptive enhancement for unsupervised segmentation of MRI brain images☆
Introduction
Segmentation of brain tissues in MRI (Magnetic Resonance Imaging) images plays a crucial role in three-dimensional (3-D) volume visualization, quantitative morphometric analysis and structure-function mapping for both scientific and clinical investigations. For instance, in order to be able to combine EEG (ElectroEncephaloGram) data and MRI images for the localization of epileptic sources within the brain, an anatomic head model is required; this model describes the brain in terms of segments of CSF (CerebroSpinal Fluid), GM (Gray Matter), WM (White Matter), skull and scalp which have significantly different electric conductivities (Van Hoey et al., 2000). In this paper, we deal with the segmentation of CSF, GM and WM in MRI brain images.
Numerous MRI segmentation methods have been reported (Bezdek et al., 1993; Zijdenbos and Dawant, 1994; Clarke et al., 1995; Niessen et al., 1999; Pham et al., 2000; Ruan et al., 2000; Xue et al., 2001; Ruan et al., 2002). Niessen et al. (1999) roughly grouped these methods into three main categories: classification methods, region-based methods and boundary-based methods. Just as pointed out in (Niessen et al., 1999), the methods in the first two categories are limited by the difficulties due to intensity inhomogeneities, partial volume effects and susceptibility artifacts, while those in the last category suffer from spurious edges. Furthermore, all methods are degraded by noise perturbations in low contrast and low SNR (Signal-to-Noise Ratio) images, e.g., the images used in EEG/MRI analysis where the slices are thin and the measuring time is short.
In this context, we propose an integrated method to achieve an adaptive enhancement for the unsupervised global-to-local segmentation of CSF, GM and WM. In our method, a region-based global algorithm (minimum error thresholding) and an unsupervised local classification algorithm (Fuzzy C-Means clustering) are used for segmentation. In order to remove noise and artifacts, a versatile filter (Pizurica et al., 2003) based on wavelet domain techniques, and locally adaptive 3-D weighted median and average filters based on clustering results are also proposed and embedded into our method. Only single-channel (T1-weighted) MRI images are addressed. In this paper, we do not pay much attention to the image registration. Nevertheless, the proposed method can be extended to work on registered multiple pulse sequences, like T1-, T2- and Proton-Density-weighted MRI images.
The contribution of this paper is the integration of locally adaptive image enhancement and global-to-local segmentation in a 3-D framework, which achieves a more robust and accurate segmentation.
This paper is organized as follows: Section 2 outlines the proposed method. Section 3 presents the versatile wavelet-based de-noising algorithm. 4 Minimum error thresholding, 5 Segmentation with FCM describe the minimum error thresholding and the FCM (Fuzzy C-Means) clustering-based on a feature space of pairs (intensity, 3-D locally averaged intensity), respectively. The clustering-based locally adaptive enhancement scheme is proposed in Section 6. Section 7 validates our proposed method with an MRI brain phantom and real images. Section 8 gives a summary and makes conclusions.
Section snippets
Outline of proposed integrated method
First, we de-noise the images using the versatile wavelet-based filter. Second, we segment the images with minimum error global thresholding. Third, we classify the voxels (counterpart of pixels in a 3-D volume) into three brain tissues through FCM clustering, using the global thresholding result to initialize the FCM parameters. The feature space is constructed by intensity pairs (intensity, 3-D locally averaged intensity) associated with each of the voxels in the MRI images. Subsequently, we
Versatile wavelet-based de-noising
In medical image enhancement, a trade off between noise reduction and the preservation of actual image features has to be made in a way that enhances the diagnostically relevant image content. To achieve a good performance in this respect, a de-noising algorithm has to adapt to image discontinuities. The wavelet representation naturally facilitates the construction of such spatially adaptive algorithms. It compresses the essential information in an image into relatively few, large coefficients;
Minimum error thresholding
In our integrated global-to-local method, we use FCM clustering (Bezdek, 1981) to achieve spatially adaptive segmentation. FCM has been applied widely to MRI segmentation (Bezdek et al., 1993; Clark et al., 1994, Clarke et al., 1995), and regarded as one of the most promising methods (Clarke et al., 1995). As an unsupervised clustering method, the performance of FCM, particularly its validity and speed of convergence, depends on the initialization of its parameters, e.g., the centers
Segmentation with FCM
Consider a dataset where q is the dimension of the desired feature space, denotes the feature vector of kth voxel; furthermore, consider a set of fuzzy clusters {Fi}i=1C in with its corresponding crisp version {Hi}i=1C.
Given a fuzzy cluster Fi, FCM assigns to each voxel in the dataset X a degree of membership to the cluster Fi which is denoted as (hereinafter abbreviated as uik). uik∈[0,1], and ∑i=1Cuik=1,∀k∈{1,…,n}.
The optimal assignment is accessed via minimizing
Adaptive enhancement for segmentation
Conventional linear/non-linear filters always employ fixed-shape and fixed-size templates in a sliding window (here denoted as ) to perform convolutions (Astola and Kuosmanen, 1997). The voxel to be filtered is generally the center voxel (denoted as ) of . The entries in the templates can be selected in a non-linear manner using statistics calculated from . Normally stationarity is assumed in the sliding window . However, this assumption is not always true for MRI images, especially
Quantitative validation
To quantitatively validate our method, test images with known “ground truth” are required. For this purpose, we used a realistic digital brain phantom (Kwan et al., 1999) considering the partial volume effects. A discrete anatomical model of three brain tissues is derived from the phantom by assigning the voxel a label of the tissue which contributes the most to that voxel. This model serves as the “ground truth” in our quantitative validation.
Based on the above phantom, four realistic MRI
Conclusion
In this paper, we have presented an integrated method of the adaptive enhancement for the unsupervised global-to-local segmentation of three brain tissues (CSF, GM and WM) in single-channel 3-D MRI images. To enable the effective and robust implementation of such an enhancement and segmentation, we have first integrated a versatile wavelet de-noising algorithm with the minimum error thresholding based on a global intensity threshold, then combined an FCM clustering using 3-D spatial context
Acknowledgements
The authors wish to thank all the reviewers for their insightful and constructive comments on the earlier version of this manuscript. We are also grateful to Dr. Su Ruan (GREYC-ISMRA, France) for her help in the brain extraction from MRI volumes.
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This work was financially supported by the Flemish Fund for Scientific Research through the project G.0037.00 and by Ghent University through the project 12.0513.98.