Image Processing Reference

In-Depth Information

contrasts based on the three MR parameters ρ, T1, and T2. Therefore, majority of research

in medical image segmentation concerns MR images (Suetens, 2002).

Conventionally, the brain MR images are interpreted visually and qualitatively by ra-

diologists. Advanced research requires quantitative information, such as the size of the

brain ventricles after a traumatic brain injury or the relative volume of ventricles to brain.

Fully automatic methods sometimes fail, producing incorrect results and requiring the in-

tervention of a human operator. This is often true due to restrictions imposed by image

acquisition, pathology and biological variation. So, it is important to have a faithful method

to measure various structures in the brain. One of such methods is the segmentation of

images to isolate objects and regions of interest.

Many image processing techniques have been proposed for MR image segmentation, most

notably thresholding (Lee, Hun, Ketter, and Unser, 1998; Maji, Kundu, and Chanda, 2008),

region-growing (Manousakes, Undrill, and Cameron, 1998), edge detection (Singleton and

Pohost, 1997), pixel classification (Pal and Pal, 1993; Rajapakse, Giedd, and Rapoport,

1997) and clustering (Bezdek, 1981; Leemput, Maes, Vandermeulen, and Suetens, 1999;

Wells III, Grimson, Kikinis, and Jolesz, 1996). Some algorithms using the neural network

approach have also been investigated in the MR image segmentation problems (Cagnoni,

Coppini, Rucci, Caramella, and Valli, 1993; Hall, Bensaid, Clarke, Velthuizen, Silbiger, and

Bezdek, 1992). One of the main problems in medical image segmentation is uncertainty.

Some of the sources of this uncertainty include imprecision in computations and vagueness

in class definitions. In this background, the possibility concept introduced by the fuzzy

set theory (Zadeh, 1965) and rough set theory (Pawlak, 1991) have gained popularity in

modeling and propagating uncertainty. Both fuzzy set and rough set provide a mathematical

framework to capture uncertainties associated with human cognition process (Dubois and

H.Prade, 1990; Maji and Pal, 2007b; Pal, Mitra, and Mitra, 2003). The segmentation of MR

images using fuzzy c-means has been reported in (Bezdek, 1981; Brandt, Bohan, Kramer,

and Fletcher, 1994; Hall et al., 1992; Li, Goldgof, and Hall, 1993; Xiao, Ho, and Hassanien,

2008). Image segmentation using rough sets has also been done (Mushrif and Ray, 2008;

Pal and Mitra, 2002; Widz, Revett, and Slezak, 2005a,b; Widz and Slezak, 2007; Hassanien,

2007).

In this chapter, a hybrid algorithm called rough-fuzzy c-means (RFCM) algorithm is pre-

sented for segmentation of brain MR images. Details of this algorithm have been reported

in (Maji and Pal, 2007a,c). The RFCM algorithm is based on both rough sets and fuzzy

sets. While the membership function of fuzzy sets enables e
cient handling of overlapping

partitions, the concept of lower and upper approximations of rough sets deals with uncer-

tainty, vagueness, and incompleteness in class definition. Each partition is represented by

a cluster prototype (centroid), a crisp lower approximation, and a fuzzy boundary. The

lower approximation influences the fuzziness of the final partition. The cluster prototype

(centroid) depends on the weighting average of the crisp lower approximation and fuzzy

boundary. However, an important issue of the RFCM based brain MR image segmentation

method is how to select initial prototypes of different classes or categories. The concept of

discriminant analysis, based on the maximization of class separability, is used to circumvent

the initialization and local minima problems of the RFCM, and enables e
cient segmenta-

tion of brain MR images (Maji and Pal, 2008). The effectiveness of the RFCM algorithm,

along with a comparison with other c-means algorithms, is demonstrated on a set of brain

MR images using some standard validity indices.

The chapter is organized as follows: Section 2.2 briefly introduces the necessary notions

of fuzzy c-means and rough sets. In Section 2.3, the RFCM algorithm is described based on

the theory of rough sets and fuzzy c-means. While Section 2.4 deals with pixel classification

problem, Section 2.5 gives an overview of the feature extraction techniques employed in seg-

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