{"references": ["X. Li, T. ZHANG, and Z. QU, \"Image Segmentation Using Fuzzy\nClustering with Spatial Constraints Based on Markov Random Field via\nBayesian Theory\", IEICE Trans. Fundamental, vol. E91-A, no.3, pp.\n723-729, 2008.", "Y.A. Tolias and S.M. Panas, \"On applying spatial constraints in fuzzy\nimage clustering using a fuzzy rule-based system,\" IEEE Signal Process.\nLett., vol.5, no.10, pp.245-247, 1998.", "D. L. Pham, \"Spatial models for fuzzy clustering,\" Computer Vision and\nImage Understanding, vol.84, no.2, pp.285-297, 2001.", "S. Z. Li, \"Markov Random Field Modeling in Computer Vision\",\nSpringer-Verlag, 1995.", "X. Ye, X. Lin, J. Dehmeshki, G. Slabaugh, and G. Beddoe, \"Shape\nBased Computer Aided Detection of Lung Nodules in Thoracic CT\nImage,\" IEEE Trans. Biomedical Engineering, vol. 56, pp. 1810 - 1820,\n2009.", "O. Demirkaya, M.Hakan Asyali, P. K. Sahoo, \"Image Processing with\nMATLAB Applications in Medicine and Biology,\" CRC Press, 2009.", "N. Nicolaidis, I. Pitas, 3D image processing algorithm. London:wiley;\n2001.", "K. Palagyi, A Kuba, \"A 3D 6-subiteration thinning algorithm for\nextracting medial lines,\" Pattern Recogn Lett, vol. 19, pp. 613-627,\n1998.", "C. Arcelli,G. S. D. Baja, \"A width-independent fast thinning\nalgorithm,\" IEEE Trans PAMI, vol. 7(4), pp. 463-474, 1985.\n[10] P.J. Schneider, D.H. Eberly, Geometric tools for computer graphics,\nMorgan Kaufmann, 2003.\n[11] H. Triebel, Interpolation theory, function spaces, differential operators,\nNorth-Holland Publishing Company , 1978.\n[12] G. Soulez and S.D. Qanadli, \"A multimodality vascular imaging\nphantom with fiducial markers visible in DSA, CTA, MRA, and\nultrasound\", Medical Physics, vol. 31, pp. 1424-1433, 2004.\n[13] H. Scherl, J. Horngger, M. Prummer, M. Lell, \"Semi-automatic level-set\nbased segmentation and stenosis quantification of internal carotid artery\nin 3D CTA data sets,\" Medical Image Analysis, vol. 11, pp. 21-34, 2007.\n[14] Y. Yang, A. Tannenbaum, D. Giddens, \"Knowledge-Based 3D\nSegmentation and Reconstruction of Coronary Arteries Using CT\nImages\", in Proc. 26th Annu. IEEE Conf. Engineering in Medicine and\nBiology Society, Atlanta, GA, USA, 2004.\n[15] C. Metz, M. Schaap, A. Van Der Giessen, T. Van Walsum, W. Niessen,\n\"semi-automatic coronary artery centerline exteraction in computed\ntomography angiography data,\" in Proc. 4th IEEE Int. Symp. Biomed.\nImaging, Arlington, VA, pp. 856-85,2007."]}

Segmentation and quantification of stenosis is an important task in assessing coronary artery disease. One of the main challenges is measuring the real diameter of curved vessels. Moreover, uncertainty in segmentation of different tissues in the narrow vessel is an important issue that affects accuracy. This paper proposes an algorithm to extract coronary arteries and measure the degree of stenosis. Markovian fuzzy clustering method is applied to model uncertainty arises from partial volume effect problem. The algorithm employs: segmentation, centreline extraction, estimation of orthogonal plane to centreline, measurement of the degree of stenosis. To evaluate the accuracy and reproducibility, the approach has been applied to a vascular phantom and the results are compared with real diameter. The results of 10 patient datasets have been visually judged by a qualified radiologist. The results reveal the superiority of the proposed method compared to the Conventional thresholding Method (CTM) on both datasets.