Research Article Coronary Arteries Segmentation Based on the 3D Discrete Wavelet Transform and 3D Neutrosophic Transform Shuo-Tsung Chen, 1,2,3 Tzung-Dau Wang, 4 Wen-Jeng Lee, 5 Tsai-Wei Huang, 6 Pei-Kai Hung, 1 Cheng-Yu Wei, 7,8 Chung-Ming Chen, 1 and Woon-Man Kung 7,9 1 Institute of Biomedical Engineering, National Taiwan University, Taipei 10617, Taiwan 2 Department of Applied Mathematics, Tunghai University, Taichung 40704, Taiwan 3 Sustainability Research Center, Tunghai University, Taichung 40704, Taiwan 4 Cardiovascular Center and Division of Cardiology, Department of Internal Medicine, National Taiwan University Hospital, Taipei 10048, Taiwan 5 Department of Medical Imaging, National Taiwan University Hospital, Taipei 10048, Taiwan 6 Department of Nursing, College of Medicine and Nursing, Hungkuang University, Taichung 43302, Taiwan 7 Department of Exercise and Health Promotion, College of Education, Chinese Culture University, Taipei 11114, Taiwan 8 Department of Neurology, Chang Bing Show Chwan Memorial Hospital, Changhua 50544, Taiwan 9 Department of Neurosurgery, Lo-Hsu Foundation, Lotung Poh-Ai Hospital, Luodong, Yilan 26546, Taiwan Correspondence should be addressed to Chung-Ming Chen; chung@ntu.edu.tw and Woon-Man Kung; nskungwm@yahoo.com.tw Received 19 July 2014; Accepted 11 October 2014 Academic Editor: Kuo-Sheng Hung Copyright © 2015 Shuo-Tsung Chen et al. is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Purpose. Most applications in the field of medical image processing require precise estimation. To improve the accuracy of segmentation, this study aimed to propose a novel segmentation method for coronary arteries to allow for the automatic and accurate detection of coronary pathologies. Methods. e proposed segmentation method included 2 parts. First, 3D region growing was applied to give the initial segmentation of coronary arteries. Next, the location of vessel information, HHH subband coefficients of the 3D DWT, was detected by the proposed vessel-texture discrimination algorithm. Based on the initial segmentation, 3D DWT integrated with the 3D neutrosophic transformation could accurately detect the coronary arteries. Results. Each subbranch of the segmented coronary arteries was segmented correctly by the proposed method. e obtained results are compared with those ground truth values obtained from the commercial soſtware from GE Healthcare and the level-set method proposed by Yang et al., 2007. Results indicate that the proposed method is better in terms of efficiency analyzed. Conclusion. Based on the initial segmentation of coronary arteries obtained from 3D region growing, one-level 3D DWT and 3D neutrosophic transformation can be applied to detect coronary pathologies accurately. 1. Introduction Efficient and automatic image segmentation methods are useful for the isolation and visualization of vessels in com- puted tomographic angiography (CTA). ere are many proposed methods for the segmentation of vessels [1–14]. A vessel filter [1] can be used to enhance tubular structure; however, it cannot address the problem of the image force and veins, which can lead to a narrowed or broken seg- mentation of vessels. Parametric shape models [2–5] do not directly allow for the detection of topological changes, and they usually obtain a seriously narrowed segmentation in the neighborhood of a branch point in the vessel. Level-set approaches [6–13] are computationally expensive. ey also suffer from leakage at places where the intensity gradients of the edges are relatively weak and are very sensitive to the placement of the initial contour of the propagating front. Metz et al. [14] used the minimum cost path of the specified start and end points in vessel to detect the coronary arteries centerline. is is not an automatic method; detecting branches is difficult. Friman [15] proposed multiple hypothesis template tracking, which follows the direction of Hindawi Publishing Corporation BioMed Research International Volume 2015, Article ID 798303, 9 pages http://dx.doi.org/10.1155/2015/798303