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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