Добавил:
Опубликованный материал нарушает ваши авторские права? Сообщите нам.
Вуз: Предмет: Файл:

Kluwer - Handbook of Biomedical Image Analysis Vol

.2.pdf
Скачиваний:
90
Добавлен:
10.08.2013
Размер:
25.84 Mб
Скачать

262

Frangi, Laclaustra, and Yang

Bibliography

[1]Corretti, M. C., Anderson, T. J., Benjamin, E. J., Celermajer, D., Charbonneau, F., Creager, M. A., Deanfield, J., Drexler, H., GerhardHerman, M., Herrington, D., Vallance, P., Vita, J., Vogel, R., and International Brachial Artery Reactivity Task Force, Guidelines for the ultrasound assessment of endothelial-dependent flow-mediated vasodilation of the brachial artery: A report of the International Brachial Artery Reactivity Task Force, J. Am. Coll. Cardiol., Vol. 39, pp. 257–265, 2002.

[2]Teragawa, H., Kato, M., Kurokawa, J., Yamagata, T., Matsuura, H., and Chayama, K., Endothelial dysfunction is an independent factor responsible for vasospastic angina, Clin. Sci. (London), Vol. 101, pp. 707–713, 2001.

[3]Cooke, J. P., Rossitch, E., Jr, Andon, N. A., Loscalzo, J., and Dzau, V. J., Flow activates an endothelial potassium channel to release an endogenous nitrovasodilator, J. Clin. Invest., Vol. 88, pp. 1663–1671, 1991.

[4]Sinoway, L. I., Hendrickson, C., Davidson, W. R., Jr, Prophet, S., and Zelis, R., Characteristics of flow-mediated brachial artery vasodilation in human subjects, Circ. Res., Vol. 64, pp. 32–42, 1989.

[5]Celermajer, D. S., Sorensen, K. E., Gooch, V. M., Spiegelhalter, D. J., Miller, O. I., Sullivan, I. D., Lloyd, J. K., and Deanfield, J. E., Noninvasive detection of endothelial dysfunction in children and adults at risk of atherosclerosis, Lancet, Vol. 340, pp. 1111–1115, 1992.

[6]Hardie, K. L., Kinlay, S., Hardy, D. B., Wlodarczyk, J., Silberberg, J. S., and Fletcher, P. J., Reproducibility of brachial ultrasonography and flowmediated dilatation (FMD) for assessing endothelial function, Aust. N.Z. J. Med., Vol. 27, pp. 649–652, 1997.

[7]Touboul, P. J., Prati, P., Scarabin, P. Y., Adrai, V., Thibout, E., and Ducimetiere, P., Use of monitoring software to improve the measurement of carotid wall thickness by B-mode imaging, J. Hypertens. Suppl., Vol. 10, pp. S37–S41, 1992.

Computerized Analysis and Vasodilation Parameterization of FMD

263

[8]Gariepy, J., Massonneau, M., Levenson, J., Heudes, D., Simon, A., and Groupe de Prevention Cardio-vasculaire en Medecine du Travail, Evidence for in vivo carotid and femoral wall thickening in human hypertension, Hypertension, Vol. 22, pp. 111–118, 1993.

[9]Selzer, R. H., Hodis, H. N., Kwong-Fu, H., Mack, W. J., Lee, P. L., Liu, C. R., and Liu, C. H., Evaluation of computerized edge tracking for quantifying intima-media thickness of the common carotid artery from B-mode ultrasound images, Atherosclerosis, Vol. 111, pp. 1–11, 1994.

[10]Kozick, R., Detecting interfaces on ultrasound images of the carotid artery by dynamic programming, In: IS&T/SPIE Electronic Imaging Symposium, San Jose, CA, Feb 1996, Vol. 2666, pp. 233–241.

[11]Gustavsson, T., Liang, Q., Wendelhag, I., and Wikstrand, J., A dynamic programming procedure for automated ultrasonic measurement of the carotid artery, In: IEEE Computers Cardiology, IEEE Computer Society, pp. 297–300, 1999.

[12]Sonka, M., Liang, W., and Lauer, R. M., Flow-mediated dilatation in brachial arteries: Computer analysis of ultrasound image sequences, CVD Preven., Vol. 1, pp. 147–55, 1998.

[13]Liang, Q., Wendelhag, I., Wikstrand, J., and Gustavsson, T., A multiscale dynamic programming procedure for boundary detection in ultrasonic artery images, IEEE Trans. Med. Imaging, Vol. 19, pp. 127–142, 2000.

[14]Preik, M., Lauer, T., Heiss, C., Tabery, S., Strauer, B. E., and Kelm, M., Automated ultrasonic measurement of human arteries for the determination of endothelial function, Ultraschall. Med., Vol. 21, pp. 195–198, 2000.

[15]Fan, L., Santago, P., Jiang, H., and Herrington, D. M., Ultrasound measurement of brachial flow-mediated vasodilator response, IEEE Trans. Med. Imaging, Vol. 19, pp. 621–631, 2000.

[16]Fan, L., Santago, P., Riley, W., and Herrington, D. M., An adaptive template-matching method and its application to the boundary detection of brachial artery ultrasound scans, Ultrasound Med. Biol., Vol. 27, pp. 399–408, 2001.

264

Frangi, Laclaustra, and Yang

[17]Mignotte, M. and Meunier, J., A multiscale optimization approach for the dynamic contour-based boundary detection issue, Comput. Med. Imaging Graph., Vol. 25, pp. 265–275, 2001.

[18]Woodman, R. J., Playford, D. A., Watts, G. F., Cheetham, C., Reed, C., Taylor, R. R., Puddey, I. B., Beilin, L. J., Burke, V., Mori, T. A., and Green, D., Improved analysis of brachial artery ultrasound using a novel edge-detection software system, J. Appl. Physiol., Vol. 91, pp. 929–937, 2001.

[19]Sonka, M., Liang, W., and Lauer, R. M., Automated analysis of brachial ultrasound image sequences: Early detection of cardiovascular disease via surrogates of endothelial function, IEEE Trans. Med. Imaging, Vol. 21, pp. 1271–1279, 2002.

[20]Newey, V. R. and Nassiri, D. K., Online artery diameter measurement in ultrasound images using artificial neural networks, Ultrasound Med. Biol., Vol. 28, pp. 209–216, 2002.

[21]Studholme, C., Hill, D. L. G., and Hawkes, D. J., An overlap invariant entropy measure of 3D medical image alignment, Patt. Recogn., Vol. 32, No. 1, pp. 71–86, 1999.

[22]Studholme, C., Hill, D., and Hawkes, D., Automated three-dimensional registration of magnetic resonance and positron emission tomography brain images by multiresolution optimization of voxel similarity measures, Med. Phys., Vol. 24, No. 1, pp. 25–35, 1997.

[23]Kalman, R. E., A new approach to linear filtering and prediction problem, Trans. ASME, J. Basic Eng., Vol. 82 (Series D), pp. 35–45, 1960.

[24]Hayes, M., Statistical Digital Signal Processing and Modelling, Wiley, New York, 1996.

[25]Altman, D., Practical Statistical Research, Chapman & Hall, Boca Raton, FL, 1991.

[26]Bland, J. and Altman, D., Measuring agreement in method comparison studies, Stat. Methods Med. Res., Vol. 8, No. 2, pp. 135–160, 1999.

Computerized Analysis and Vasodilation Parameterization of FMD

265

[27]Bland, J. and Altman, D., Statistical methods for assessing agreement between two methods of clinical measurement, Lancet, Vol. 1, No. 8476,

pp.307–310, 1986.

[28]Vita, J. A. and Keaney, J. F., Jr, Endothelial function: A barometer for cardiovascular risk?, Circulation, Vol. 106, No. 6, pp. 640–642, 2002.

[29]Faulx, M. D., Wright, A. T., and Hoit, B. D., Detection of endothelial dysfunction with brachial artery ultrasound scanning, Am. Heart J., Vol. 145, No. 6, pp. 943–951, 2003.

[30]Widlansky, M. E., Gokce, N., Keaney, J. F., Jr, and Vita, J. A., The clinical implications of endothelial dysfunction, J. Am. Coll. Cardiol., Vol. 42, No. 7, pp. 1149–1160, 2003.

[31]Gokce, N., Keaney, J. F., Jr, Hunter, L. M., Watkins, M. T., Nedeljkovic, Z. S., Menzoian, J. O., and Vita, J. A., Predictive value of noninvasively determined endothelial dysfunction for long-term cardiovascular events in patients with peripheral vascular disease, J. Am. Coll. Cardiol., Vol. 41, No. 10, pp. 1769–1775, 2003.

[32]Jolliffe, I., Principal Component Analysis, 2nd edn., Springer Series in Statistics, Springer-Verlag, New York, 2002.

[33]Hubert, M., Rousseeuw, P., and van den Branden, K., ROBPCA: A new approach to robust principal component analysis, Technical Report, Department of Mathematics, Katholieke Universiteit Leuven, 2003.

[34]The National Cholesterol Education Program (NCEP), Executive summary of the third report of The National Cholesterol Education Program (NCEP) expert panel on detection, evaluation, and treatment of high blood cholesterol in adults (Adult Treatment Panel III), JAMA, Vol. 285,

pp.2486–2497, 2001.

[35]Ross, R., The pathogenesis of atherosclerosis: A perspective for the 1990s, Nature, Vol. 362, pp. 801–809, 1993.

[36]Friedewald, W. T., Levy, R. I., and Fredrickson, D. S., Estimation of the concentration of low-density lipoprotein cholesterol in plasma, without

266

Frangi, Laclaustra, and Yang

use of the preparative ultracentrifuge, Clin. Chem., Vol. 18, pp. 499–502,

1972.

[37]Roberts, W. C., The Friedewald-Levy-Fredrickson formula for calculating low-density lipoprotein cholesterol, the basis for lipid-lowering therapy, Am. J. Cardiol., Vol. 62, pp. 345–346, 1988.

[38]Kuvin, J. T., Patel, A. R., Sidhu, M., Rand, W. M., Sliney, K. A., Pandian, N. G., and Karas, R. H., Relation between high-density lipoprotein cholesterol and peripheral vasomotor function, Am. J. Cardiol., Vol. 92,

pp.275–279, 2003.

[39]Aggoun, Y., Bonnet, D., Sidi, D., Girardet, J. P., Brucker, E., Polak, M., Safar, M. E., and Levy, B. I., Arterial mechanical changes in children with familial hypercholesterolemia, Arterioscler Thromb. Vasc. Biol., Vol. 20, pp. 2070–2075, 2000.

[40]Toikka, J. O., Ahotupa, M., Viikari, J. S., Niinikoski, H., Taskinen, M., Irjala, K., Hartiala, J. J., and Raitakari, O. T., Constantly low HDLcholesterol concentration relates to endothelial dysfunction and increased in vivo LDL-oxidation in healthy young men, Atherosclerosis, Vol. 147, pp. 133–138, 1999.

[41]Holubkov, R., Karas, R. H., Pepine, C. J., Rickens, C. R., Reichek, N., Rogers, W. J., Sharaf, B. L., Sopko, G., Merz, C. N., Kelsey, S. F., McGorray, S. P., and Reis, S. E., Large brachial artery diameter is associated with angiographic coronary artery disease in women, Am. Heart J., Vol. 143,

pp.802–807, 2002.

Chapter 6

Statistical and Adaptive Approaches for Optimal Segmentation in Medical Images

Shuyu Yang1 and Sunanda Mitra1

6.1 Introduction

Image analysis techniques have been broadly used in computer-aided medical analysis and diagnosis in recent years. Computer-aided image analysis is an increasingly popular tool in medical research and practice, especially with the increase of medical images in modality, amount, size, and dimension. Image segmentation, a process that aims at identifying and separating regions of interests from an image, is crucial in many medical applications such as localizing pathological regions, providing objective quantative assessment and monitoring of the onset and progression of the diseases, as well as analysis of anatomical structures.

Generally speaking, segmentation techniques are application specific and nonuniversal. There exists no approach that works best for all types of images. In fact, some approaches work better on one type of image than others, depending on the modality of the image. For example, images acquired by magnetic resonance imaging (MRI) and radiographic X-ray imaging are quite different from retinal images. In the former, the images are represented by intensity variations proportional to radiation absorption or RF signal amplitude mapped into gray-level values, while for the latter, the images are chromatic and generated optically. Numerous segmentation techniques have been developed for gray scale

1 Department of Electrical and Computer Engineering, Texas Tech University Lubbock,

TX 79409-3102

267

268

Yang and Mitra

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

Statistical and Adaptive Approaches for Optimal Segmentation

269

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

270

Yang and Mitra

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

Statistical and Adaptive Approaches for Optimal Segmentation

271

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

 

=

 

i {

 

} =

 

i

 

 

 

 

=

 

 

yi

 

max

yi

 

 

max

bij

x

kj

i

 

1, . . . , C

(6.1)

 

 

 

vij

 

 

 

 

 

 

xkj

j=1

 

 

 

 

bij =

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

xkj =

 

 

 

 

 

 

 

 

vi

 

xk

 

 

 

 

 

 

 

where i is the index of the winning centroid.