A hierarchical genetic algorithm for segmentation of multi-spectral human-brain MRI

Abstract

Magnetic resonance imaging (MRI) segmentation has been implemented by many clustering techniques, such as k-means, fuzzy c-means (FCM), learning-vector quantization (LVQ) and fuzzy algorithms for LVQ (FALVQ). Although these algorithms have been successful in applying MRI segmentation, obtaining the right number of clusters and adapting to different cluster characteristics are still not satisfactorily addressed. This report proposes an optimization technique, a hierarchical genetic algorithm with a fuzzy learning-vector quantization network (HGALVQ), to segment multi-spectral human-brain MRI. Evaluation of this approach is based on a real case with human-brain MRI of an individual suffering from meningioma. The HGALVQ is verified by the comparison with other popular clustering algorithms such as k-means, FCM, FALVQ, LVQ, and simulated annealing. Experimental results show that HGALVQ not only returns an appropriate number of clusters and also outperforms other methods in specificity.

Introduction

Magnetic resonance images (MRI) can produce images of the human anatomy that reveal the structure, metabolism, and function of internal tissues or organs, thereby greatly extending the range of human vision into realms that would otherwise be inaccessible. This process strongly relies on the brain image segmentation which is a procedure in medical applications such as morphological analysis of neurological structures in differential diagnosis, neurosurgical planning, follow-up of a specific treatment or disease evolution and construction of neurological atlases (Valdes-Cristerna, Medina-Banuelos, & Yanez-Suarez, 2004). Several types of medical image segmentation methods can be applied to brain MRI, e.g., edge-based, region-based, and pixel-based (Dhawan, 2003).

The edge-based methods use edge information to determine boundaries of objects to form closed regions belonging to the objects in the image. Some researchers applied these methods to divide MRI into regions with connected boundaries (Long et al., 1991, Tang et al., 2000). However, it suffers from spurious edges and sometimes results in erratic performance. The region-based methods develop a region growing process based on a pre-defined similarity criterion to form closed regions and the pixel-based methods use histogram statistics to define single or multiple thresholds to classify an image pixel-by-pixel. For example, Jimenez-Alaniz, Medina-Banuelos, and Yanez-Suarez (2006) used a mean shift algorithm in the joint spatial-range domain to segment brain MRI. These methods sometimes fail because of they are limited by the difficulties due to intensity inhomogeneities, partial volume effects and susceptibility artifacts. Furthermore, all methods are degraded by noise perturbations in low contrast and low signal-to-noise ratio (SNR) images (Xue et al., 2003). Statistical methods have also been developed, since segmenting images requires a priori statistical assumptions that are rarely satisfied in practice (Cline et al., 1990, Liang, 1993, Marroquin et al., 2002, Prastawa et al., 2004).

In those pixel-based or intensity-based classification methods, clustering techniques are often used for brain image segmentation, such as k-means clustering, fuzzy c-means (FCM) algorithm, neural networks and fuzzy clustering algorithms (Chuang et al., 1999, Dhawan, 2003, Hall et al., 1992, Ozkan et al., 1993, Pham and Prince, 1999, Yen and Langari, 1999). FCM and its variants have been used successfully for MR image segmentation (Hall et al., 1992, Siyal and Yu, 2005, Shen et al., 2005). Neural networks require that a large amount of training data be available, the learning of which usually requires a long time. To complement these difficulties, a family of learning vector quantization (LVQ) has been developed (Karayiammis, 1997, Karayiammis and Pai, 1999). This approach can be used to generate crisp c-partitions of unlabeled data vectors. Pal, Bezdek, and Tsao (1993) identified a close relationship between this algorithm and a clustering procedure, known as the sequential hard c-means algorithm. They also suggested that LVQ could be performed through an unsupervised learning process by using a competitive neural network whose weight vectors represent the prototypes, the formulation of which resulted in the generalized LVQ (GLVQ) algorithm. A batch-learning scheme, namely the fuzzy LVQ (FLVQ), was proposed by Tsao, Bezdek, and Pal (1994). Karayiammis and Pai (1999) proposed a framework for the development of fuzzy algorithms for LVQ (FALVQ), the scheme of which influenced the development of a broad variety of FALVQ algorithms. Recently, a level set algorithm has been successful applied for automatic or semi-automatic segmentation of brain MRI (Wu et al., 2005, Xie et al., 2005).

Although the impact of these imaging techniques on diagnostic radiology has been revolutionary in the last two decades because of its capability to produce anatomical images with unprecedented quality and safety to the patient, obtaining the right number of clusters and adapting to different cluster characteristics are still not satisfactorily addressed. Further, the drawbacks of these techniques include the tedious and time-consuming nature of the segmentation task, and the lack of consistency among persons performing it. Thus, better technology is desirable in order to return an appropriate number of clusters and produce images at a higher speed and resolution.

This report presents an optimization technique, a hierarchical genetic algorithm with a fuzzy learning-vector quantization network (HGALVQ), for segmentation of multi-spectral brain MRIs to achieve this goal. The multi-spectral images are obtained from the magnetic resonance technique which allows for the exploration of different characteristics of the same subject by the adjustment of the acquisition parameters. These produce three pulse sequences in clinical MRI such as T1-weighted, T2-weighted and spin density (SD) images. Each pulse sequence produces images with contrast characteristics that permit specific types of tissue to be visualized. For instance, T1-weighted images provide excellent atomic detail and good tissue contrasts. Cerebrospinal fluid (CSF) is much brighter than the gray and white matter in T2-weighted images. Pathologic lesions are seen very clearly as hyper-intensities in SD images, which also show gray matter/white matter contrasts. These three pulse sequences often provide sufficient contrasts to segment the images into different categories such as white matter, gray matter, CSF, skull, skin, fat, air surrounding, and so on (Brown and Semelka, 1999, Cocosco et al., 2003, Liang and Lauterbur, 2000).

The objective of HGALVQ is to formulate and partition a set of feature vectors of multi-spectral brain MRIs into a relatively small number of clusters, each represented by a vector called a prototype. Each feature vector contains the elements T1, T2, and SD parameters at a certain image location called voxels. Then the HGALVQ searches for the best partition of the feature vectors so that the segmented image is obtained by representing each feature vector by its closest prototype. The objective function is based on the weighted sum of the squared Euclidean distances between each input vector and the prototypes. A fast computation of Euclidean distances using look-up table (LUT) is added to improve the performance of the algorithm over HGALVQ.

The rest of this paper is organized as follows: Section 2 describes in detail the proposed method, including the LVQ network, hierarchical genetic scheme, and hierarchical genetic operation. Section 3 illustrates the experimental results obtained from the algorithm for the segmentation of brain MRIs. Sections 4 Discussion and performance comparison, 5 Conclusion contain the discussion and conclusion.