Magnetic resonance (MR) has become the main modality for brain imagingthat facilitates safe, noninvasive assessment and monitoring of patients with neurodegenerative diseases such as Parkinson’s disease, Alzheimer’s disease (AD), epilepsy, schizophrenia, and multiple sclerosis (MS) [

1]–[

6]. The ability to diagnose and characterize these diseases

*in vivo* using MR image data promises exciting developments both toward understanding the underlying pathologies, as well as conducting clinical trials of drug treatments. One important biomarker that is often used to assess patients with neurodegenerative disease is brain tissue volume. The typical rate of global brain atrophy in MS patients has been shown to be 0.6%–0.8% annually, which is two to three times the normal atrophy rate [

7]. Evidence has shown that white matter (WM) and gray matter (GM) atrophy at different rates, and each correlates differently to disability [

8]–[

10]; thus, accurate measurement of the WM and GM brain tissues can provide valuable quantitative indicators of disease progression and, potentially, treatment outcomes [

7], [

11]. Thus, the main goal of this paper is to introduce an automatic algorithm for robust WM, GM, and cerebrospinal fluid (CSF) segmentation to facilitate accurate measurement of brain tissues.

Previously, to measure various tissue volumes in MRI head scans, manual WM and GM segmentations were often performed by skilled experts. Manual segmentation, however, is extremely time-consuming, mostly limited to 2-D slice-based segmentation, and prone to significant intra- and interrater variability [

12]. In particular, manual segmentation cannot be practically and efficiently performed in situations where precise measurements on a large number of scans are required, such as in clinical trials. Therefore, a fully automatic, highly accurate, and robust tissue segmentation technique that provides systematic quantitative analysis of tissue volumes in brain MRI is an invaluable tool in many studies of neurodegenerative diseases. A wide variety of methods have been proposed for automating the segmentation process over the past decade that provided either semi- or fully automated frameworks for the segmentation of brain tissues. A review of some of these methods can be found in [

13] and [

14].

One popular family of brain tissue segmentation methods is based on normalizing the brain scans by registering (or aligning) them to a predefined atlas of brain tissues. One example is the popular statistical parametric mapping (SPM) technique, which relies on voxel-based morphometry (VBM) [

15]. A number of extensions to the original SPM technique have been proposed. For example, SPM is utilized to initialize an expectation–maximization (EM) segmentation framework [

16], which has been extended to nonrigid registration [

17]. Although such atlas-based methods are typically robust to artifacts such as acquisition noise and distortions, concerns and discussion [

18]–[

20] have ensued regarding the use of templates from one population when analyzing data from another population. For example, morphing patient scans with pathologically enlarged ventricles to match a normal template could potentially distort the surrounding tissues in an unpredictable manner. Such structural differences might lead to systematic biases and misregistration errors that are difficult to quantify [

19]. Such concerns introduce yet another level of complications arising from image registration and atlas generation procedures that add to the already nontrivial segmentation problem, especially in the presence of anomalies such as tumors, lesions, and tissue atrophy.

A second family of brain tissue segmentation methods assigns a label for each tissue based on image statistics either by clustering [

21] or by modeling the brain tissue intensity distributions as a finite mixture of distributions such as EM [

22], maximum

*a posteriori* (MAP) [

23], simulated annealing [

24], and Gaussian mixture modeling (GMM) [

25]. Other approaches incorporate additional regional information, which is lacking from these statistical methods, into their segmentation framework. Such methods extend clustering or EM by integrating with fuzzy connectedness [

26], topological constraints [

27], Gibbs random field (GRF) [

28], and hidden Markov random field (HMRF) [

29] in the segmentation task. A common difficulty with many of these methods, particularly the random field approaches, is the requirement for proper parameter settings in a supervised setting.

A third family of brain tissue segmentation methods is based on utilizing geometric information such as deformable models or active contours [

30] that delineates region boundaries using a minimization of an energy functional [

31], [

32]. Deformable models employing level sets [

33] provide an effective implicit representation rather than explicit parameterization of the evolving contour. However, a common problem of directly applying the active contour approach in segmenting brain MR images is leakage through weak or noisy edges that are ubiquitous, especially for edge-based deformable models, e.g., geodesic active contour [

34], which describe the evolution of propagating curve as a function of image gradient features. Some researchers incorporated image statistics into their deformable models in various segmentation applications by utilizing coupled surface principle [

35], [

36] and fuzzy logic [

37], [

38] to achieve better stability. Others employed a region-based model [

39] by utilizing regional homogeneity in a curve evolution perspective and a hierarchical implementation on brain pathology images [

40]. More recently, tissue segmentation was performed and quantitatively evaluated [

41]–[

43] by using the multiphase 3-D level set segmentation (M3DLS) algorithm [

41]. M3DLS utilizes a multiphase extension [

44] of the region-based deformable model [

39] based on the Mumford–Shah functional [

45] by iteratively deforming two closed curves separating four regions. This minimal partitioning approach assumes piecewise constant or piecewise smooth data and optimizes a sum of terms, including the lengths and areas for the two closed curves, and the sums of square intensity differences from the means for all four separated regions. This minimization is also performed in a level set framework [

33] implicitly. Further extending this model to

*N* -phase allows separation of 2

^{N} regions but the number of classes to be segmented is limited to two to the power of the number of closed curves defined. Moreover, complexity increases as more level sets are required and the rate of convergence is typically slow [

46].

In this paper, we propose a MR brain tissue segmentation approach that integrates both geometric and statistical image features into an edge-based deformable model formulation to achieve accurate segmentation results. By utilizing this novel hybrid image feature, we present one solution to the challenging problem of stabilizing the active contour. Similar existing work used a topology preservation principle enforced at non-simple points in a geometric deformable model [

47], or a curve shortening prior for smoothness in a level set framework to minimize leakage [

40], [

48]. Here, we do not explicitly apply any smoothness and topological constraints (e.g., topology preservation at nonsimple points) to the geometric deformable models but rather rely on the proposed hybrid feature to regularize the level sets. Other approaches used prior knowledge such as a distance penalizing term in the level set function between two boundary classes [

35], a fuzzy decision system on contour distance to an anatomical target or atlas [

37], or a dissimilarity measure between the contour and a shape model in the energy term [

49]. Here, we demonstrate our proposed approach in segmenting complex anatomical structures such as WM, GM, and CSF without

*a priori* knowledge. Hence, the proposed approach is truly automated and data-driven in both statistical and geometric sense. Furthermore, we compare the segmentation performance of our proposed edge-based level set method to the region-based M3DLS approach [

41] on real clinical MRI scans. We demonstrate the improved WM, GM, and CSF segmentation accuracy and robustness when using the proposed method.

The paper is organized as follows: In Section II, we introduce our novel hybrid geometric–statistical feature implemented on the edge-based geodesic active contour formulation. Our modified deformable model is then used to design a new automated 3-D brain tissue segmentation algorithm for both single and multiple MR sequence data. In Section III, we present quantitative and qualitative results and analysis obtained on simulated and real clinical MRI images, as well as comparisons to results reported by using M3DLS. We then conclude in Section IV.