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images [1–5], while color image segmentation techniques have been created much later than its gray-level counterpart because of the computational complexity involved with the latter. However, the availability of fast digital processors in recent times allows easy implementations of such complex algorithms. Most of the segmentation techniques applied to gray-level images can also be extended to color images [6, 7].

Clustering is a pattern recognition technique that has been frequently used in image segmentation [8, 9]. Similar to the variety of approaches in image segmentation, there are numerous clustering techniques based on statistics, fuzzy logic [10, 11], neural network, or an integration of these [12]. This chapter applies two recently developed advanced clustering algorithms, namely, deterministic annealing (DA) [13] and adaptive fuzzy leader clustering (AFLC) [14] and compares their performances with other standard well-known algorithms in efficient segmentation of medical images. DA is designed on a statistical frame work, while AFLC has a neural network structure embedded with fuzzy optimization. The performances of these two algorithms have been compared with classical clustering techniques such as k-means [15], and fuzzy C-means (FCM) [16]. These clustering algorithms have been applied to segment a few diverse types of medical images. All operations are performed on images in the spatial domain, i.e., pixel intensity will be used as the only feature. For gray-scale images, such as MRI, the feature will be 1D, while for color images, such as the retinal image, the classification is 3D (red, green, and blue components for each pixel).

The major advantage of using clustering for medical image segmentation is that these unsupervised techniques for data partitioning do not require a training set, which is not easy to find in most clinical datasets. The two clustering techniques, namely AFLC and DA, used in our study to investigate the effectiveness and accuracy of these techniques in medical image segmentation can be considered as optimization processes. Both AFLC and DA do not require an initial guess of the actual number of clusters present in a dataset and thus do not suffer from the instability inherent to traditional and well-known clustering algorithms such as k-means.

Several types of medical images are selected and used as examples of clustering application. The first modality we used is MRI. We compared the segmentation of anatomical structures such as gray matter, white matter, and cerebrospinal fluid from simulated MRI. Pathological segmentation of multiple sclerosis with both simulated and real MRI is also performed. The second imaging

modality involves stereo retinal imaging for evaluating structural damage in the retina. We demonstrated delineation of blood vessels in these images with DA and applied the result to 3-D disparity mapping and segmentation of optic disk/cup. Traditional 2-D segmentation of the optic disk/cup is also presented and compared with manually segmented optic disk/cup by ophthalmologists. The third imaging modality is direct optical (color) imaging used to investigate precancerous lesions in the cervix. Traditionally, an abnormal Pap smear finding is followed by Cervicographic and Colposcopic examination of the cervix by a gynecologist/oncologist to determine the severity of the lesions and identify the location for a biopsy probe. Segmentation of lesions using selected clustering algorithms is carried out for comparison.

The chapter is organized as follows: A brief description of image segmentation is given in section 6.2. Selected clustering techniques, traditional and advanced, are introduced in section 6.3. In section 6.4, results of applying these techniques for precise segmentation of various modalities of medical images are presented. Section 6.5 contains discussions and conclusions.

6.2 Image Segmentation

Image segmentation can be defined as separating the image into similar constituent parts. Given an image I, segmentation of I is a partition P of I into a

set of N regions Rn, n = 1, . . . , N, such that 0N Rn = I. The separated regions

n=1

should be homogeneous and meaningful to the application intended. According to Pham et al. [1] image segmentation techniques can be classified into several categories, such as thresholding, region growing, classifiers, clustering, Markov random field, artificial neural network, fuzzy logic, deformable models, and atlas-guided approaches. The performance efficiency of each approach, however, varies and is dependent on specific application and image modality. When a practical application is concerned, sometimes integration of these techniques is needed to achieve better performance. A number of review papers on image segmentation in general and specifically on medical image segmentation are already available [1–7, 9]. In this chapter, we have focused on the impact of recent advanced clustering algorithms in precise segmentation of medical images.

Most of the common medical images such as MRI, positron emission tomography (PET), computed tomography (CT), and ultrasound images are

monochromatic. Some of these types of images can be pseudocolored. As mentioned earlier in section 6.1, most of the segmentation techniques developed for gray scale images can be extended to color images. There are quite a few color models [17] that are commonly used in image processing, mainly to comply with color video standards and human perception. RGB (red, green, blue), HSI (hue, saturation, intensity), and CIE L a b are color models that have been frequently used in segmentation. RGB is hardware oriented while HSI and L a b representations are compatible with human visual perception. What is more, perceptual uniformity of the L a b color space is advantageous over RGB and HSI in that the human perception of color difference can be represented as the euclidean distance between color points, a useful property can be used in error functions of some segmentation algorithms. Most color images, such as the ones used in our examples, the color retinal stereo images and the color cervix images, are captured in RGB. If processing in other color space is preferred, color transformation is needed [6, 7].

To verify the efficiency of a segmentation method, segmentation result is compared with the “truth model.” Truth models for practical images are often obtained by manual segmentation. In medical imaging, manual segmentation is usually performed by trained medical professionals. However, such truth models are not as accurate since they are prone to subjective variability, and often poor repeatability, leading to some ambiguities in diagnosis. Therefore, as far as validation is concerned, computer-simulated phantoms are preferred. The phantoms are simplified mimics of the real images. Quantative statistics such as the number of misclassified pixels or shape differences can be obtained by comparison segmented result with the phantom in a straightforward manner. Unfortunately, phantoms are not available for all image modalities. In our examples, we used both computer-simulated phantoms (MRI) as well as manual segmentations (stereo retinal image and color cervix images) to validate the clustering algorithms.

6.3 Clustering Methods

Clustering is a natural way for image segmentation since partitions of similar intensity or texture can be seen as different clusters, the same way human beings perceive objects. Let xi, i = 1, . . . , N, be a sample of the input space, and let c j C, j = 1, . . . , M, be one class of a total of M classes. A clustering

algorithm determines the classes C and assigns every sample xi into one of

the classes. For hard clustering, a sample belongs to only one class, meaning

1

Ck C j = φ, k = j. For fuzzy clustering, a sample can be classified into more than one class with different membership values (a degree of similarity) [11]. The sum of all membership values of one sample is unity. Categorization and summary of most clustering techniques can be found in [12, 18, 19].

k-means (or c-means) and its fuzzy version FCM are two well-known classical clustering algorithms used for image segmentation. A comparative study of k-means and FCM is presented in [20]. Application of these algorithms and their variations on image segmentation can be found in [21–25].

The clustering techniques discussed below, namely, AFLC, DA, k-means, and FCM, can be regarded as optimization processes that seek to reduce misclassification by minimizing specific cost functions or system energy functions. Contrary to the classical Bayesian classifier that needs training, these clustering techniques are unsupervised. The complexity of these algorithms, however, varies. k-means and FCM are relatively simple and easier to implement but not as effective when compared to DA and AFLC, as will be demonstrated in the next section. The main problem inherent to both k-means and FCM is that the initial guess of the actual number of clusters present in a dataset is crucial to the convergence of the algorithms.

6.3.1 Adaptive Fuzzy Leader Clustering

AFLC is an integrated neural-fuzzy clustering algorithm that can be used to learn cluster structure embedded in complex datasets in a self-organizing manner. The algorithm has a two-layer structure as illustrated in Fig. 6.1. The first layer uses a self-organizing neural network similar to ART1 [26–28] to find hard clusters. Let C be the current number of centroids and vi(i = 1, . . . , C) representing the centroids. When a new sample xk comes in, it is normalized and then initially classified into the cluster on which it has the largest projection (a winner-take-all or MAXNET [29, 30] learning rule):

n

where i is the index of the winning centroid.