在醫院的手術治療前，醫師通常只能透過2D的電腦斷層掃描(Computerized tomography, CT)影像以及個人自身的經驗，來診斷病人的病症位置及狀況，在各式器官手術中，以肝臟最為困難，因為肝臟的血管為人體結構最複雜的部份，一般器官只分為動脈與靜脈，而在肝臟中，還有一組血管稱作肝門靜脈，由於肝臟血管的複雜度極高，所以在手術過程中很容易有不慎切到大型血管的情況，這時會造成手術過程混亂，且流出來的血液很容易蓋住病徵，不僅會使病人陷入危險之中，還會導致手術時間過長。目前醫療影像的拍攝技術仍無法直接輸出完整的立體模型，病人往往無法從影像中想像出自己血管的位置，而醫師也只能憑藉著自身的經驗來判斷大約的位置，這樣很容易造成醫師與病人之間的溝通障礙。
基於上述理由，本論文開發了一套的系統重建出肝臟血管的外型，可以提供醫師做手術前的模擬與講解使用。在影像處理的階段，我們首先利用圖像分割演算法(Graph Cut Algorithm)從斷層掃描影像中，取得肝臟的位置，再利用非局部平均的演算法(Non-Local Means Algorithm)對整張圖片的大範圍進行降噪，最後採取非等向性擴散濾波器(Anisotropic Diffuse Filter)將影像中過度細微的血管去除。在表面重建的階段，我們先利用經過影像處理完的影像，使用傳統取閥值的方式、自適應閥值(Adaptive Threshold)，以及影像二值化來取出血管的部分，再利用電腦斷層掃瞄影像的特性，將平面影像轉變成立體的點雲，最後再利用行進立方體演算法(Marching Cube Algorithm)重建出血管模型，並採用移動最小二乘法(Moving Least Square)的方式平滑血管模型的表面。

Because the structure of liver vessel is the most complicated in anatomy, the surgery on liver is the most difficult medical treatment in hospital. Before surgery in hospital, doctors can only use their personal experience and Computerized Tomography (CT) images to diagnose patient’s disease. There are only two kinds of vessel in general organs, one is artery and another is vein. However, there are three kinds of vessel in liver, which comprise artery, vein, and portal vein. Owing to the complexity of liver vessel, it is possible to accidently cut a large vessel during surgery. If doctors cut the big vessel in surgical procedure, it makes the patient under the risk because the blood flows out quickly and covers the entire organ, and increases the difficulty and time in surgery. The current technique of CT cannot output the model of vessel. Therefore, patients cannot know the actual location of their disease, and doctors can only use their personal experience to find the approximate position, which causes the communication barrier between patients and doctors.
According to the reasons mentioned above, we develop a system of reconstructing liver vessel surface, which is used for preoperative simulation. There are two phases in this system, one is image preprocessing, and another is surface reconstruction. In image preprocessing, we use Graph Cut Algorithm to cut the area of liver first. Next, we adopt Non-Local Means Algorithm to reduce noise in the entire image. The last step in image preprocessing, we use Anisotropic Diffuse filter to remove the vessel which is too small. In surface reconstruction, we use an adaptive threshold method to filter liver vessel in CT images, then we use the characteristic in CT to create the point cloud. Finally, we use Marching Cube algorithm to reconstruct liver vessel surface and Moving Least Square to smooth the liver vessel model.

[1] G. T. Herman, Image Reconstruction from Projections, Springer, Berlin, Germany, 1979.
[2] Y. Z. Zeng et al., “Liver vessel segmentation based on extreme learning machine,” Physica Medica, vol. 32, no.5, pp. 709-716, 2016.
[3] Y. Z. Zeng et al., “Liver vessel segmentation and identification based on oriented flux symmetry and graph cuts,” Computer Methods and Programs in Biomedicine, vol. 150, no.3, pp. 31-39, 2017.
[4] M. Zou et al., “Topology-constrained surface reconstruction from cross-sections,” ACM Transactions on Graphics (TOG), vol. 34, no. 4, pp. 128:1-128:10, 2015.
[5] Roee Lazar et al., “Robust optimization for topological surface reconstruction,” ACM Transactions on Graphics, vol. 37, no. 4, pp. 46:1–46:10, 2018.
[6] D. Lesagea and G. Funka-Leaa, “A review of 3D vessel lumen segmentation techniques: Models features and extraction schemes,” Medical Image Analysis, vol. 13, pp. 819-845, 2009
[7] A. F. Frangi et al., “Multiscale vessel enhancement filtering,” in Proceedings of the International Conference on the Computer Science, Berlin, Germany, pp. 130-137, 1998.
[8] T. Jerman et al., “Beyond Frangi: An improved multiscale vesselness filter,” in Proceedings of the SPIE Medical Imaging, Orlando, Florida, pp. 94132A-11, 2015.
[9] K. Krissian et al., “Model-based detection of tubular structures in 3D images,” Computer Vision and Image Understanding, vol. 80, no. 2, pp. 130-171, 2000
[10] C. Xiao et al., “Multiscale Bi-Gaussian filter for adjacent curvilinear structures detection with application to vasculature images,” IEEE Transactions on Image Processing, vol. 22, no. 1, pp. 174-188, 2013.
[11] A. Vasilevskiy and K. Siddiqi, “Flux-maximizing geometric flows,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 24, no. 12, pp. 1565-1578, 2002.
[12] M. W. Law and A. C. Chung, “Three dimensional curvilinear structure detection using optimally oriented flux,” in Proceedings of the 10th European Conference on Computer Vision: Part IV, Berlin, Germany, pp. 368-382, 2008.
[13] E. Turetken et al., “Detecting irregular curvilinear structures in gray scale and color imagery using multi-directional oriented flux,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, Sydney, Australia, pp. 1553-1560, 2013.
[14] L. M. Lorigo et al., “Curves: curve evolution for vessel segmentation,” Medical Image Analysis, vol. 5, no. 3, pp. 195-206, 2001.
[15] Y. Shang et al., “Vascular active contour for vessel tree segmentation,” IEEE Transactions on Biomedical Engineering, vol. 58, no. 4, pp. 1023-1032, 2011.
[16] C. Bauer et al., “Segmentation of interwoven 3D tubular tree structures utilizing shape priors and graph cuts,” Medical Image Analysis, vol. 14, no. 2, pp. 172-184, 2010.
[17] S. Esneault, C. Lafon, and J. L. Dillenseger, “Liver vessels segmentation using a hybrid geometrical moments/graph cuts method,” IEEE Transactions on Biomedical Engineering, vol. 57, no. 2, pp. 276-283, 2010.
[18] H. Hemmatia et al., “Semi-automatic 3D segmentation of carotid lumen in contrast-enhanced computed tomography angiography images,” Physica Medica, vol. 31, no. 8, pp. 1098-1104, 2015.
[19] F. Conversano et al., “Hepatic vessel segmentation for 3D planning of liver surgery: Experimental evaluation of a new fully automatic algorithm,” Academic Radiology, vol. 18, no. 4, pp. 461-470, 2011.
[20] X. C. Pan et al., “3D liver vessel reconstruction from CT images,” in Proceedings of the Second International Conference on 3D Vision, Tokyo, Japan, pp. 75-81, 2014.
[21] E. Keppel, “Approximating complex surfaces by triangulation of contour lines,” IBM Journal of Research and Development, vol. 19, no. 2, pp. 2-11, 1975.
[22] H. Fuchs, Ζ. M. Kedem, and S. P. Uselton, “Optimal surface reconstruction from planar contours,” ACM SIGGRAPH Computer Graphics, vol. 20, no. 10, pp. 693-702, 1977
[23] D. Meyers, S. Skinner, and K. Sloan, “Surfaces from contours,” ACM Transactions on Graphics, vol. 11, no. 3, pp. 228-258, 1992.
[24] T. Ju et al., “Building 3D surface networks from 2D curve networks with application to anatomical modeling,” Visual Computer, vol. 21, no. 8, pp. 764-773, 2005.
[25] L. Liu et al., “Surface reconstruction from non-parallel curve networks,” Computer Graphics Forum, vol. 27, no. 2, pp. 155-163, 2008.
[26] G. Barequet and A. Vaxman, “Reconstruction of multi-label domains from partial planar cross-sections,” Computer Graphics Forum, vol. 28, no. 5, pp. 1327-1337, 2009.
[27] J. D. Boissonnat and P. Memari, “Shape reconstruction from unorganized cross-sections,” in Proceedings of the Symposium on Geometry Processing, Barcelona, Spain, pp. 89-98, 2007.
[28] W. Lorensen and H. Cline, “Marching Cubes: A high resolution 3D surface construction algorithm,” Computer Graphics, vol. 21, no. 4, pp. 163-170, 1987.
[29] E. Chernyaev, “Marching Cubes 33: construction of topologically correct iso surfaces,” Technical Report, no. CERN-CN-95-17, Petersburg, Russian Federation, 1995.
 
[30] P. Cignoni et al., “Reconstruction of topologically correct and adaptive trilinear surfaces,” Computers and Graphics, vol. 24, no. 3, pp. 399-418, 2000.
[31] F. Velasco et al., “Adaptive cube tessellation for topologically correct isosurfaces,” in Proceedings of the Computer Graphics Theory and Applications, Barcelona, Spain, pp. 220-227, 2007.
[32] L. Custodio, “Practical considerations on Marching Cubes 33 topological correctness,” Computers and Graphics, vol. 37, no. 7, pp. 840-850, 2013.
[33] Y. T. Hsieh, “CT Images segmentation using deep convolution neural network”, Master Thesis, Department of Electronic and Computer Engineering, National Taiwan University of Science Technology, Taipei, Taiwan, 2019.
[34] L. Huang, M. Weng, and F. Gao, “Automatic liver segmentation from CT images using single-block linear detection,” BioMed Research International, vol. 2016, no. 6, pp. 1-11, 2016.
[35] Y. Boykov and M. P. Jolly, “Interactive organ segmentation using graph cuts,” in the Proceedings of the Medical Image Computing and Computer-Assisted Intervention, Pittsburgh, Pennsylvania, vol. 1935, pp. 276-286, 2000.
[36] R. Duda, P. Hart, and D. Stork, Pattern Classification, 2nd Ed, Wiley Interscience, New York, New York, 2001.
[37] Y. Boykov and V. Kolmogorov, “An experimental comparison of Min-Cut/Max-flow algorithms for energy minimization in vision,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 26, no. 9, pp. 1124-1137, 2004
[38] A. Buades, B. Coll, and J.M. Morel, “A non-local algorithm for image denoising,” in Proceedings of the IEEE Computer Vision and Pattern Recognition, San Diego, California, pp.60-65, 2005.
 
[39] P. Perona and J. Malik, “Scale space and edge detection using anisotropic diffusion,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 12, no. 7, pp. 629-639, 1990.
[40] F. H. Y. Chan, F. K. Lam, and H. Zhu, “Adaptive thresholding by variational method,” IEEE Transactions on Image Processing, vol. 7, no. 3, pp. 468-473, 1998.
[41] D. Bradley and G. Roth, “Adaptive thresholding using the integral image,” Journal of Graphics, Gpu, & Game Tools, vol. 12, no. 2, pp. 13-21, 2007.