**3. A new non-homogeneous Markov random field model**

As we introduced in Section 2.6.2, Markov random field (MRF) theory (S.Z. Li, 1995) has been widely used in the field of medical image processing with the advantages, including non-supervision, fine stability and satisfied segmentation effect for the image with low SNR. MRF theory provides a convenient and consistent way for modeling context among image pixels. This is achieved through characterizing mutual influences among such entities using conditional MRF distributions. The practical use of MRF models is largely ascribed to the equivalence between MRF and Gibbs distributions established by Hamersley and Clifford (Hammersley & Clifford, 1971) and is further developed by Besag (Besag, 1974) for the joint distribution of MRF. This enables us to model vision problems by a mathematically sound yet tractable means for image segmentation in Bayesian framework (Geman & Geman, 1993; Grenander, 1983).

In traditional MRF model, Gibbs random field (GRF) uses the parameter ߚ to determine spatial correlation among dependent image pixels. The greater the parameter ߚ is, the stronger the spatial correlation would be; the smaller the parameter ߚ is, the weaker the spatial correlation would be. Generally, MRF model is assumed to be homogeneous, which means the parameter ߚ is constant. Plenty of previous researches have offered a series of methods to accurately estimate this parameter, which advance the effect of image segmentation (Deng & Clausi, 2004; Descombes et al., 1999). Due to its own features of medical image, homogeneous MRF model often leads to over-segmentation and induces higher misclassification rate. In this section, we propose a new non-homogeneous MRF model (called Modified-MRF or M-MRF model) using fuzzy membership to accurately estimate the parameter ߚ and the experimental results show our model effectively reduces over-segmentation and enhances segmentation precision (R. Xu & Luo, 2009).

#### **3.1 Fuzzy sets**

Fuzzy sets are sets whose elements have degrees of membership, which firstly were proposed by L.A. Zedeh in 1965 (Zadeh, 1965) as an extension of the classical notion of set. Classical set theory only describes precise phenomenon, because an element belonging to a classic set contains only two cases: yes or no. By contrast, fuzzy set theory permits the gradual assessment of the membership of elements in a set; this is described with the aid of a membership function valued in the real unit interval *[0, 1]*. Fuzzy sets generalize classical sets, since the indicator functions of classical sets are special cases of the membership functions of fuzzy sets, if the latter only take values 0 or 1 (DuBois & Prade, 1980).

*Multispectral segmentation* is a method for differentiating tissue classes having similar characteristics in a single imaging modality by using several independent images of the same anatomical slice in different modalities (e.g., T1, T2, proton density, etc.). As a consequence of different responses of the tissues to particular pulse sequences, this increases the capability of discrimination between different tissues (Fletcher et al., 1993; Vannier et al., 1985). The most common approach for multispectral MR image segmentation is pattern recognition (Bezdek et al., 1993; Suri, Singh, et al., 2002b). These techniques generally appear to be successful particularly for brain MR images (Reddick et al., 1997; Taxt & Lundervold,

As we introduced in Section 2.6.2, Markov random field (MRF) theory (S.Z. Li, 1995) has been widely used in the field of medical image processing with the advantages, including non-supervision, fine stability and satisfied segmentation effect for the image with low SNR. MRF theory provides a convenient and consistent way for modeling context among image pixels. This is achieved through characterizing mutual influences among such entities using conditional MRF distributions. The practical use of MRF models is largely ascribed to the equivalence between MRF and Gibbs distributions established by Hamersley and Clifford (Hammersley & Clifford, 1971) and is further developed by Besag (Besag, 1974) for the joint distribution of MRF. This enables us to model vision problems by a mathematically sound yet tractable means for image segmentation in Bayesian framework (Geman & Geman, 1993;

In traditional MRF model, Gibbs random field (GRF) uses the parameter ߚ to determine spatial correlation among dependent image pixels. The greater the parameter ߚ is, the stronger the spatial correlation would be; the smaller the parameter ߚ is, the weaker the spatial correlation would be. Generally, MRF model is assumed to be homogeneous, which means the parameter ߚ is constant. Plenty of previous researches have offered a series of methods to accurately estimate this parameter, which advance the effect of image segmentation (Deng & Clausi, 2004; Descombes et al., 1999). Due to its own features of medical image, homogeneous MRF model often leads to over-segmentation and induces higher misclassification rate. In this section, we propose a new non-homogeneous MRF model (called Modified-MRF or M-MRF model) using fuzzy membership to accurately estimate the parameter ߚ and the experimental results show our model effectively reduces

Fuzzy sets are sets whose elements have degrees of membership, which firstly were proposed by L.A. Zedeh in 1965 (Zadeh, 1965) as an extension of the classical notion of set. Classical set theory only describes precise phenomenon, because an element belonging to a classic set contains only two cases: yes or no. By contrast, fuzzy set theory permits the gradual assessment of the membership of elements in a set; this is described with the aid of a membership function valued in the real unit interval *[0, 1]*. Fuzzy sets generalize classical sets, since the indicator functions of classical sets are special cases of the membership

over-segmentation and enhances segmentation precision (R. Xu & Luo, 2009).

functions of fuzzy sets, if the latter only take values 0 or 1 (DuBois & Prade, 1980).

1994), but much work remains in the area of validation.

Grenander, 1983).

**3.1 Fuzzy sets** 

**3. A new non-homogeneous Markov random field model** 

The fuzzy set is defined as: Given a domain *X*, *x* denotes its element, the mapping �� is defined as �� ��� �0,1�, �������, which means �� confirms a fuzzy set *F* in domain *X*, �� is called *F*'s membership function and ����� is *x*'s membership for *F*. The greater the membership, the greater the degree of one element pertaining to one fuzzy set. As a consequence, *F* is a subset in domain *X*, which does not have undefined border.

#### **3.2 Modified non-homogeneous MRF model**

In terms of the features in brain MR images, the spatial correlation of adjacent pixels varies with the positions of image space, which indicates the parameter � should be a variable changing with space site. Consequently, the corresponding MRF model should be considered as non-homogeneous.

#### **3.2.1 The** � **Function based on fuzzy membership**

Let *y* be the gray value of pixels, and *x* be the classification of pixels in image I. If pixel *i* is marked by class *k* (�� is the clustering center of class *k*, � � 1, � , �), the parameter � will be a decreasing function of ���, which denotes the membership of pixel *i* belonging to class *k*. The smaller the ��� is, the less the degree of pixel *i* in class *k* would be, which implies the attribute of pixel *i* should be decided by the state of neighborhood. The larger the ��� is, the larger the degree of pixel *i* in class *k* would be, which implies the attribute of pixel *i* should be decided by the gray value of itself. Thus, the � function is defined as:

$$
\beta\_i = 1 - 0.8 \cdot u\_{ik} \tag{18}
$$

#### **3.2.2 The modified MRF model (M-MRF model)**

In traditional MRF model (see Section 2.6.2), the parameter � is used to calculate the *energy function* ���� and *clique potentials* ����� over all possible cliques ���, which only depends on the neighborhood of pixel *i*: ����,� � �. According to the � function, the energy function and clique potentials through considering multi-level logistic (MLL) model, second-order neighborhood system and dual potential function, can be modified as

$$\mathcal{U}I(\mathbf{x}) = \sum\_{i \neq I} \sum\_{j \neq \mathcal{S}(i)} V\_c(\mathbf{x}\_i, \mathbf{x}\_j) \tag{19}$$

$$V(\mathbf{x}\_i, \mathbf{x}\_j) = \begin{cases} -\mathcal{J}\_i \, & \text{if } \quad \mathbf{x}\_i = \mathbf{x}\_j \\ \mathcal{J}\_i \, & \text{if } \quad \mathbf{x}\_i \neq \mathbf{x}\_j \end{cases} \tag{20}$$

And the new non-homogeneous MRF (M-MRF) model has been improved into

$$\text{LI}(y \mid \mathbf{x}) = \sum\_{i \in I} \text{LI}(y\_i \mid \mathbf{x}\_i) = \sum\_{i \in I} [\frac{(y\_i - v\_k)^2}{2\sigma\_k^2} + \frac{1}{2}\log(\sigma\_k^2)] \tag{21}$$

Therefore, the segmentation problem is reduced to minimize the above energy function, which is generally solved by iterated conditional modes (ICM) algorithm (Besag, 1986). The algorithm of M-MRF model for image segmentation is designed as follows:

Segmentation of Brain MRI 157

In order to verify the effect of M-MRF model in image segmentation, KFCM algorithm (L. Zhang et al., 2002), traditional MRF model (S.Z. Li, 1995) and M-MRF model are applied in the segmentation of simulated brain MR images. During the experiments, brain MR images are divided into four regions: gray matter (GM), white matter (WM), cerebrospinal fluid (CSF) and background (BG). All experiments are operated by VS.Net 2003 in PC of Intel®

The simulated brain MR images from Brainweb (http://www.bic.mni.mcgill.ca/brainweb/) are applied in the experiments, and we call them gold standard of image segmentation. Each data set is composed of ʹͷͺ ൈ ʹͷͺ pixels, thickness of layer is *1mm*, ܶଵ weighted. Herein, the lay images used in experiments are the ܼ ൌ ͳǤͷ݉݉'s ones of image sequences. Fig. 4 is a comparison of the segmentation results of several algorithms for a simulated brain MRI superposed 9% noise. The experimental results demonstrate that, even for images of lower signal-to-noise ratio (SNR), M-MRF model also achieves more satisfied segmentation results.

(a) (b)

(c) (d)

**3.3 Experimental results** 

Core™2 CPU 6600 @ 2.40GHZ with 2GB memory.


#### **3.2.3 Smoothing of image**

Owing to complexity of brain MR images and their own reasons of segmentation algorithms, segmentation results are often accompanied by burrings, stains, rugged edges, etc. By smoothing, isolated burrings and stains of image can be removed, edges of regions can be smoothed and holes of areal objects can be filled. Sequentially, the quality of segmentation results can be further improved. In the processing of image smoothing, matrix template of ���(*n* is customarily assigned by 3~5) is currently employed to march image via lines and columns. If the image matches successfully, the segmentation result of the pixel in the center of matrix template will be replaced by the same segmentation results around this pixel.

#### **3.2.3.1 Deburring**

The 3�3 deburring matrix in (a) is frequently betaken, where a, b, x � �, � � �(*L* is the set of labels) and *'x'* is arbitrary which figures the segmentation results of *x*'s sites can be left out of account. When the image segmentation results in 3�3 matrix march the deburring matrix in Fig. 3 (a), *'b'* in the center of matrix will become *'a'*.


Fig. 3. The matrix for deburring and smoothing. (a) the deburring matrices; (b) the matrix of smoothing of lines.

#### **3.2.3.2 Smoothing of lines and filling of holes**

The methods of smoothing of lines and filling of holes are the same as that of deburring, just the matrices are different. The 3�3 matrix of smoothing of lines in Fig. 3 (b) is utilized as a rule. In the same way, When the image segmentation results in 3�3 matrix march the 3�3 matrix in Fig. 3 (b), *'b'* in the center of matrix will become *'a'*.

1. Initialize the number of class *K*, the clustering center ��, the smallest error �, and ���; 2. Get the initial segmentation results via KFCM algorithm (L. Zhang et al., 2002), and

3. Segment the initial image based on maximum-likelihood criterion and M-MRF model,

Eq.(19) and Eq.(21), and update the classification of every pixel following the principle

5. Calculate the global energy E of whole image again by the new classification of every

Owing to complexity of brain MR images and their own reasons of segmentation algorithms, segmentation results are often accompanied by burrings, stains, rugged edges, etc. By smoothing, isolated burrings and stains of image can be removed, edges of regions can be smoothed and holes of areal objects can be filled. Sequentially, the quality of segmentation results can be further improved. In the processing of image smoothing, matrix template of ���(*n* is customarily assigned by 3~5) is currently employed to march image via lines and columns. If the image matches successfully, the segmentation result of the pixel in the center of matrix template will be replaced by the same segmentation results around

labels) and *'x'* is arbitrary which figures the segmentation results of *x*'s sites can be left out of account. When the image segmentation results in 3�3 matrix march the deburring

*a a a a a x x x x x a a x a x* 

*a b a a b x a b a x b a a b a* 

*x x x a a x a a a x a a x a x*  (a) (b) Fig. 3. The matrix for deburring and smoothing. (a) the deburring matrices; (b) the matrix of

The methods of smoothing of lines and filling of holes are the same as that of deburring, just the matrices are different. The 3�3 matrix of smoothing of lines in Fig. 3 (b) is utilized as a rule. In the same way, When the image segmentation results in 3�3 matrix march the 3�3

a, b, x

� �, � � �(*L* is the set of

4. Calculate local conditional energy of every pixel for all possible classification by

�� � �, then go to (7), else return (4);

estimate the parameter � by Eq.(18);

of minimizing local conditional energy.

7. Output image segmentation results and stop.

The 3�3 deburring matrix in (a) is frequently betaken, where

matrix in Fig. 3 (a), *'b'* in the center of matrix will become *'a'*.

**3.2.3.2 Smoothing of lines and filling of holes** 

matrix in Fig. 3 (b), *'b'* in the center of matrix will become *'a'*.

pixel, �����; 6. if �ax ������ � ������

**3.2.3 Smoothing of image** 

this pixel.

**3.2.3.1 Deburring** 

smoothing of lines.

and calculate the global energy *E* of whole image;

#### **3.3 Experimental results**

In order to verify the effect of M-MRF model in image segmentation, KFCM algorithm (L. Zhang et al., 2002), traditional MRF model (S.Z. Li, 1995) and M-MRF model are applied in the segmentation of simulated brain MR images. During the experiments, brain MR images are divided into four regions: gray matter (GM), white matter (WM), cerebrospinal fluid (CSF) and background (BG). All experiments are operated by VS.Net 2003 in PC of Intel® Core™2 CPU 6600 @ 2.40GHZ with 2GB memory.

The simulated brain MR images from Brainweb (http://www.bic.mni.mcgill.ca/brainweb/) are applied in the experiments, and we call them gold standard of image segmentation. Each data set is composed of ʹͷͺ ൈ ʹͷͺ pixels, thickness of layer is *1mm*, ܶଵ weighted. Herein, the lay images used in experiments are the ܼ ൌ ͳǤͷ݉݉'s ones of image sequences. Fig. 4 is a comparison of the segmentation results of several algorithms for a simulated brain MRI superposed 9% noise. The experimental results demonstrate that, even for images of lower signal-to-noise ratio (SNR), M-MRF model also achieves more satisfied segmentation results.

(c) (d)

Segmentation of Brain MRI 159

Due to the inherent technical limitations of the MR image process, uncertainties are inserted into MR images, including random noise, intensity inhomogeneity, and partial volume effect, etc. A more complete and comprehensive coverage of the contributing sources of error inherent in MR images can be found in (Plante & Turkstra, 1991). The image preprocessing techniques reviewed here mainly focus on reducing the detrimental effects of the

It is difficult to remove noise from MR images, which is known to have a *Rician distribution* (Prima et al., 2001), and state-of-art methods in removing noise are substantial. Methods vary from standard filters to more advanced filters, from general methods to specific MR image de-noising methods, such as linear filtering, nonlinear filtering, adaptive filtering, anisotropic diffusion filtering, wavelet analysis, total variation regularization, bilateral filter, trilateral filtering, and non-local means models (NL-means), etc. A worthy survey of image

*Intensity inhomogeneity* (also called bias field, or shading artefact) in MRI, which arises from the imperfections of the image acquisition process, manifests itself as a smooth intensity variation across the image (Fig. 5). Because of this phenomenon, the intensity of the same tissue varies with the location of the tissue within the image. Although intensity inhomogeneity is usually hardly noticeable to a human observer, many medical image analysis methods, such as segmentation and registration, are highly sensitive to the spurious variations of image intensities. This is why a large number of methods for the correction of intensity inhomogeneity in MR images have been proposed in the past (Vovk et al., 2007). Early publications on MRI intensity inhomogeneity correction date back to 1986 (Haselgrove & Prammer, 1986; McVeigh et al., 1986). Since then, sources of intensity inhomogeneity in MRI have been studied extensively (Alecci et al., 2001; Keiper et al., 1998; Liang & Lauterbur, 2000; Simmons et al., 1994) and can be generally divided into two groups: prospective methods and retrospective methods. According to the classification proposed by U. Vovk (Vovk et al., 2007), we may further classify the prospective methods into those that are based on phantoms, multi-coils, and special sequences. The retrospective methods are further classified into filtering, surface fitting, segmentation-based, and histogram-based, etc. Additionally, several valuable reviews about this topic can be found in (Arnold et al., 2001; Belaroussi et al., 2006; Hou, 2006; Sled et al., 1997; Velthuizen et al., 1998; Vovk et al.,

Fig. 5. Intensity inhomogeneity in MR brain image (Images provided courtesy of U. Vovk).

artifacts mentioned for the purpose of applying segmentation methods.

de-noising algorithms can be seen in (Buades et al., 2006).

**4. Image pre-processing** 

2007).

Fig. 4. A comparison of the segmentation results for several algorithms. (a) a simulated brain MR image; (b) a simulated brain MR image superposed 9% noise; (c) ground truth; (d) the results of KFCM method; (e) the results of MRF model; (f) the results of M-MRF model.

Table 1 presents MCRs of several algorithms for simulated brain MRIs superposed noise of distinct intensity in image segmentation (see the definition of MCR in Section 1.3), whose data are average segmentation results of 20 images. From table 1, MCRs of M-MRF model for all simulated brain MRIs are lower than other algorithms. In addition, segmentation effect of M-MRF model for simulated brain MRI superposed 7% and 9% noise is obviously better than other algorithms, while segmentation effect of M-MRF model for simulated brain MRI superposed 3% and 5% noise only has slight ascendancy compared with other algorithms. For this reason, the stronger the intensity of noise in image is, the better the segmentation performance of M-MRF model would be.


Table 1. MCRs (%) of images superposed noise of distinct intensity

In consideration of its own traits of brain MRIs, a new non-homogeneous MRF model (M-MRF model) is put forward for reducing over-segmentation, where the parameter ߚ is estimated to an inch by fuzzy membership, so that the spatial relativities among each pixel will be reasonably set up. The experimental results prove our model not only inherits the superiorities of traditional MRF model, e.g., non-supervision, fine stability and satisfied robustness for image of low signal-to-noise ratio (SNR), but also significantly enhance the accuracy of image segmentation. Meanwhile, the algorithm of this new model is also simple and feasible and it is easy to be applied into clinical application by fusing de-bias field model.

(e) (f)

Fig. 4. A comparison of the segmentation results for several algorithms. (a) a simulated brain MR image; (b) a simulated brain MR image superposed 9% noise; (c) ground truth; (d) the results of KFCM method; (e) the results of MRF model; (f) the results of M-MRF model.

Table 1 presents MCRs of several algorithms for simulated brain MRIs superposed noise of distinct intensity in image segmentation (see the definition of MCR in Section 1.3), whose data are average segmentation results of 20 images. From table 1, MCRs of M-MRF model for all simulated brain MRIs are lower than other algorithms. In addition, segmentation effect of M-MRF model for simulated brain MRI superposed 7% and 9% noise is obviously better than other algorithms, while segmentation effect of M-MRF model for simulated brain MRI superposed 3% and 5% noise only has slight ascendancy compared with other algorithms. For this reason, the stronger the intensity of noise in image is, the better the

The intensity of noise(%) 3% 5% 7% 9% MCRs of KFCM(%) 4.88 5.65 6.64 8.19 MCRs of MRF(%) 4.21 5.24 6.30 7.64 MCRs of M-MRF(%) 4.06 5.00 5.80 6.67

In consideration of its own traits of brain MRIs, a new non-homogeneous MRF model (M-MRF model) is put forward for reducing over-segmentation, where the parameter ߚ is estimated to an inch by fuzzy membership, so that the spatial relativities among each pixel will be reasonably set up. The experimental results prove our model not only inherits the superiorities of traditional MRF model, e.g., non-supervision, fine stability and satisfied robustness for image of low signal-to-noise ratio (SNR), but also significantly enhance the accuracy of image segmentation. Meanwhile, the algorithm of this new model is also simple and feasible and it is easy to be applied into clinical application by fusing

segmentation performance of M-MRF model would be.

de-bias field model.

Table 1. MCRs (%) of images superposed noise of distinct intensity

## **4. Image pre-processing**

Due to the inherent technical limitations of the MR image process, uncertainties are inserted into MR images, including random noise, intensity inhomogeneity, and partial volume effect, etc. A more complete and comprehensive coverage of the contributing sources of error inherent in MR images can be found in (Plante & Turkstra, 1991). The image preprocessing techniques reviewed here mainly focus on reducing the detrimental effects of the artifacts mentioned for the purpose of applying segmentation methods.

It is difficult to remove noise from MR images, which is known to have a *Rician distribution* (Prima et al., 2001), and state-of-art methods in removing noise are substantial. Methods vary from standard filters to more advanced filters, from general methods to specific MR image de-noising methods, such as linear filtering, nonlinear filtering, adaptive filtering, anisotropic diffusion filtering, wavelet analysis, total variation regularization, bilateral filter, trilateral filtering, and non-local means models (NL-means), etc. A worthy survey of image de-noising algorithms can be seen in (Buades et al., 2006).

*Intensity inhomogeneity* (also called bias field, or shading artefact) in MRI, which arises from the imperfections of the image acquisition process, manifests itself as a smooth intensity variation across the image (Fig. 5). Because of this phenomenon, the intensity of the same tissue varies with the location of the tissue within the image. Although intensity inhomogeneity is usually hardly noticeable to a human observer, many medical image analysis methods, such as segmentation and registration, are highly sensitive to the spurious variations of image intensities. This is why a large number of methods for the correction of intensity inhomogeneity in MR images have been proposed in the past (Vovk et al., 2007). Early publications on MRI intensity inhomogeneity correction date back to 1986 (Haselgrove & Prammer, 1986; McVeigh et al., 1986). Since then, sources of intensity inhomogeneity in MRI have been studied extensively (Alecci et al., 2001; Keiper et al., 1998; Liang & Lauterbur, 2000; Simmons et al., 1994) and can be generally divided into two groups: prospective methods and retrospective methods. According to the classification proposed by U. Vovk (Vovk et al., 2007), we may further classify the prospective methods into those that are based on phantoms, multi-coils, and special sequences. The retrospective methods are further classified into filtering, surface fitting, segmentation-based, and histogram-based, etc. Additionally, several valuable reviews about this topic can be found in (Arnold et al., 2001; Belaroussi et al., 2006; Hou, 2006; Sled et al., 1997; Velthuizen et al., 1998; Vovk et al., 2007).

Fig. 5. Intensity inhomogeneity in MR brain image (Images provided courtesy of U. Vovk).

Segmentation of Brain MRI 161

The future researches in the segmentation of human brain MRI will focus upon improving the accuracy, precision, and execution speed of segmentation methods, as well as reducing the amount of manual interaction. Accuracy and precision can be improved by incorporating prior information from atlases and by the fusion of different methods. For the sake of advancing execution efficiency, multi-scale processing, graphic processing unit (GPU) technique and parallelizable methods such as neural networks can be used promisingly. In order to raise the current acceptance of routine clinical applications for segmentation methods, extensive efficient validation is required. Furthermore, one must be able to demonstrate some significant performance advantage (e.g. more accurate diagnosis or earlier detection of pathology) over traditional methods to guarantee the less cost of training and equipment. It is impossible that automated methods will replace the

physicians, but they are likely to become crucial elements in medical image analysis.

for their valuable suggestions for improving this manuscript.

pp.299, DOI: 10.1117/12.274098.

Special thanks to go the group of Ohya Laboratory, Global Information and Telecommunication Studies (GITS), Waseda University, Japan, and the group of the Laboratory of Image Science and Technology (LIST), School of Computer Science and Engineering, Southeast University, China, for their contribution and discussion on various aspects and projects associated with image segmentation. The authors would like to thank the reviewers

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**6. Acknowledgment** 

**7. References** 

126.

1522-2594.

0269-2821.

*Partial volume effect (PVE)* means artefacts that occur where multiple tissue types contribute to a single pixel, resulting in a blurring of intensity across boundaries, which is common in medical images, particularly for 3D MRI data. Fig. 6 illustrates how the sampling process can result in PVE, leading to ambiguities in structural definitions. In Fig. 6 (Right), it is difficult to precisely determine the boundaries of the two objects. The most common approach to addressing partial volume effect is to produce segmentations that allow regions or classes to overlap, called soft segmentations. Standard approaches use 'hard segmentations' that enforce a binary decision on whether a pixel is inside or outside the object. Soft segmentations, on the other hand, retain more information from the original image by allowing for uncertainty (such as membership for every pixel) in the location of object boundaries. Generally, membership functions can be derived by fuzzy clustering and classifier algorithms (Herndon et al., 1996; Pham & Prince, 1999) or statistical algorithms, in which case the membership functions are probability functions (Wells III et al., 1996), or can be computed as estimates of partial volume fractions (Choi et al., 1991). Soft segmentations based on membership functions can be easily converted to hard segmentations by assigning a pixel to its class with the highest membership value (Pham et al., 2000). The growing attention have been given to estimate partial volume effect in the last decade (Choi et al., 1991; Gage et al., 1992; Gonzalez Ballester et al., 2002; Roll et al., 1994; Soltanian-Zadeh et al., 1993; Thacker et al., 1998; Tohka et al., 2004).

Fig. 6. Illustration of partial volume effect. (Left) Ideal image; (Right) Acquired image (Images provided courtesy of D.L. Pham).

## **5. Conclusion**

A great number of medical image segmentation techniques have been used for analysis of MRI data of human brain, whose performance is affected by the characteristics of MRI data, which include a number of artifacts, such as random noise, intensity inhomogeneity and partial volume effect, etc. On the other hand, the inherent multispectral character of MRI gives it a distinct advantage over other imaging techniques. Many of the approaches described here explore ways to correct the artifacts in MRI and to fully exploit the multispectral character of this imaging modality. In this chapter, we have given a brief introduction to the fundamental concepts of these techniques, and presented our work on brain MR image segmentation, as well as a descripted the pre-processings such as denoising, the correction of intensity inhomogeneity and the estimation of partial volume effect.

*Partial volume effect (PVE)* means artefacts that occur where multiple tissue types contribute to a single pixel, resulting in a blurring of intensity across boundaries, which is common in medical images, particularly for 3D MRI data. Fig. 6 illustrates how the sampling process can result in PVE, leading to ambiguities in structural definitions. In Fig. 6 (Right), it is difficult to precisely determine the boundaries of the two objects. The most common approach to addressing partial volume effect is to produce segmentations that allow regions or classes to overlap, called soft segmentations. Standard approaches use 'hard segmentations' that enforce a binary decision on whether a pixel is inside or outside the object. Soft segmentations, on the other hand, retain more information from the original image by allowing for uncertainty (such as membership for every pixel) in the location of object boundaries. Generally, membership functions can be derived by fuzzy clustering and classifier algorithms (Herndon et al., 1996; Pham & Prince, 1999) or statistical algorithms, in which case the membership functions are probability functions (Wells III et al., 1996), or can be computed as estimates of partial volume fractions (Choi et al., 1991). Soft segmentations based on membership functions can be easily converted to hard segmentations by assigning a pixel to its class with the highest membership value (Pham et al., 2000). The growing attention have been given to estimate partial volume effect in the last decade (Choi et al., 1991; Gage et al., 1992; Gonzalez Ballester et al., 2002; Roll et al., 1994; Soltanian-Zadeh et al.,

Fig. 6. Illustration of partial volume effect. (Left) Ideal image; (Right) Acquired image

A great number of medical image segmentation techniques have been used for analysis of MRI data of human brain, whose performance is affected by the characteristics of MRI data, which include a number of artifacts, such as random noise, intensity inhomogeneity and partial volume effect, etc. On the other hand, the inherent multispectral character of MRI gives it a distinct advantage over other imaging techniques. Many of the approaches described here explore ways to correct the artifacts in MRI and to fully exploit the multispectral character of this imaging modality. In this chapter, we have given a brief introduction to the fundamental concepts of these techniques, and presented our work on brain MR image segmentation, as well as a descripted the pre-processings such as denoising, the correction of intensity inhomogeneity and the estimation of partial volume

1993; Thacker et al., 1998; Tohka et al., 2004).

(Images provided courtesy of D.L. Pham).

**5. Conclusion** 

effect.

The future researches in the segmentation of human brain MRI will focus upon improving the accuracy, precision, and execution speed of segmentation methods, as well as reducing the amount of manual interaction. Accuracy and precision can be improved by incorporating prior information from atlases and by the fusion of different methods. For the sake of advancing execution efficiency, multi-scale processing, graphic processing unit (GPU) technique and parallelizable methods such as neural networks can be used promisingly. In order to raise the current acceptance of routine clinical applications for segmentation methods, extensive efficient validation is required. Furthermore, one must be able to demonstrate some significant performance advantage (e.g. more accurate diagnosis or earlier detection of pathology) over traditional methods to guarantee the less cost of training and equipment. It is impossible that automated methods will replace the physicians, but they are likely to become crucial elements in medical image analysis.
