在本篇論文中，我們提出了一個系統，將脊椎骨與脊神經等資訊自STIR-MRI影像中切割出來，並且藉由我們提出的三維點群對位方法，估測切割後之CT與STIR-MRI的三維脊椎骨模型之間的轉換關係，以結合STIR-MRI與CT個別節取出之三維脊椎模型。
影像切割的部分，我們採用一種使用者互動的方式，將二維的隨機漫步演算法延伸成三維，並採取分段處理的策略，對三維影像進行切割。取得三維影像之切割結果後，三維的脊椎骨與脊神經模型即可重建。我們接著採用一基於傅立葉動差匹配結合平滑限制之變形對位演算法，對已建立之CT與STIR-MRI之三維脊椎骨模型進行對位。於是我們藉由一線性內插方法，達到局部仿射之轉換，將從STIR-MRI影像取出之三維脊神經模型與自CT影像中重建之三維脊椎骨模型。
在實驗結果中，我們將展示脊椎骨與脊神經之三維影像切割結果，自CT 和STIR-MRI整合後之脊椎骨與脊神經之三維表面模型 ，以及對於我們提出的對位方法之量化評估。

In this thesis, we propose a system for vertebrae, spinal cord and nerve segmentation from STIR-MRI images, and estimate the transformation between the segmented 3D vertebra models in CT and STIR-MRI (Short Tau Inversion Recovery - Magnetic Resonance Imaging) by our 3D point-set registration method to combine the 3D spinal models extracted from STIR-MRI and CT. We present a user interactive segmentation approach for the segmentation from 3D images, which is extended from the 2D random walker method and implemented with a slice-section strategy. After the 3D segmentation result is obtained, the 3D spinal cord and vertebra models are reconstructed. Then we apply a deformable registration algorithm based on the Fourier moment matching in conjunction with smoothness constraint to register the pre-built 3D vertebra models in CT and STIR-MRI. Thus, we apply the local affine transformation to integrate the 3D spinal cord and nerve models extracted from STIR-MRI with the 3D vertebra models reconstructed from CT. This is accomplished by applying a linear interpolation method to achieve local affine transformation. In the experimental results, we show the 3D segmentation results of vertebrae and spinal cord from the STIR-MRI images the integrated 3D surface models of the vertebrae, spinal cord and nerves reconstructed from CT and STIR-MRI, and the quantitative evaluation for our registration approach.

[1]. L. Grady. Random walks for image segmentation. IEEE Trans. on Pattern Analysis and Machine Intelligence, 1768-1783, 2006.
[2]. W. Schroeder, K. Martin, and B. Lorensen. Visualization Toolkit: An Object-Oriented Approach to 3D Graphics, 4th Edition. Kitware, Inc., 2006.
[3]. A. T. Heimann and H. Meinzer. Statistical Shape Models for 3D Medical Image Segmentation: A review, Medical Image Analysis, 13(4): 543-563, 2009.
[4]. P. P. Smyth, C. J. Taylor, and J. E. Adams. Automatic measurement of vertebral shape using active shape models, Image Vis. Comput., 15: 575-581, 1997.
[5]. M. Brejl and M. Sonka. Object localization and border detection criteria design in edge-based image segmentation: Automated learning from examples, IEEE Trans. Med. Imag., 19(10):973-985, Oct. 2000.
[6]. J. Carballido-Gamio, S. J. Belongie, and S. Majumdar. Normalized cuts in 3D for spinal MRI segmentation, IEEE Trans. Med. Imag., 23(1):36-44, Jan. 2004.
[7]. J. Shi and J. Malik. Normalized cuts and image segmentation, IEEE Trans. Pattern Anal. Mach. Intell., 22(8):888-905, Aug. 2000.
[8]. S. H. Huang, Y. H. Chu, S. H. Lai, and C. L. Novak. Learning-Based Vertebra Detection and Iterative Normalized-Cut Segmentation for Spinal MRI, IEEE Trans. Med. Imag., 28(10): 1595-1605 , 2009.
[9]. Y. Y. Cheng, H. M. Chang, H. R. Su, S. H. Lai, K. C. Liu, and C. H. Lin. 3D Liver Segmentation and Model Reconstruction from CT Images, International Conference on Biomedical Engineering and Biotechnology, 654-657, 2012.
[10]. H. R. Su and S. H. Lai. CT-MR Image Registration in 3D K-Space Based on Fourier Moment Matching. PSIVT(2), 299-310, 2011.
[11]. D. D. Patil and S. G. Deore. Medical Image Segmentation: A Review. IJCSMC, 2(1):22-27, 2013.
[12]. P. J. Besl and N. D. McKay. A Method for Registration of 3D Shapes. TPAMI, 14(2):239–256, 1992.
[13]. H. Chui and A. Rangarajan. A new point matching algorithm for non-rigid registration. CVIU, 89:114–141, 2003.
[14]. F. L. Bookstein. Principal Warps: Thin-Plate Splines and the Decomposition of Deformations. PAMI, 11(6):567-585, June 1989.
[15]. A. Myronenko and X. Song. Point Set Registration: Coherent Point Drift. TPAMI, 32(12):2262–2275, 2010.
[16]. M. Fischler and R. Bolles. Random Sample Consensus: A Paradigm for Model Fitting with Applications to Image Analysis and Automated Cartography. Communications ACM, 24(6):381–395, 1981.
[17]. O. Chum and J. Matas. Matching with PROSAC - Progressive Sample Consensus. In Conference on Computer Vision and Pattern Recognition, 1:220–226, June 2005
[18]. C. Yen, H. R. Su, S. H. Lai, K. C. Liu, and R. R. Lee. 3D Spinal Cord and Nerves Segmentation from STIR-MRI. Smart Innovation, Systems and Technologies, 21:383-392, 2013.
[19]. Henderson, A. ParaView Guide, A Parallel Visualization Application. Kitware Inc., 2007.
[20]. M. Kass, A. Witkin, and D. Terzopoulos. Snakes: Active contour models. International journal of computer vision 1(4): 321-331, 1988.
[21]. M. Gastaud, M. Barlaud, and G. Aubert. Combining Shape Prior and Statistical Features for Active Contour Segmentation. IEEE Transactions on Circuits and Systems for Video Technology, 14(5):726-734, 2004.
[22]. L. A. Vese and T. F. Chan. A Multiphase Level Set Framework for Image Segmentation Using the Mumford and Shah Model. International Journal of Computer Vision, 50(3): 271-293, 2002.
[23]. R. Harmouche, F. Cheriet, H. Labelle, and J. Dansereau. Multimodal image registration of the scoliotic torso for surgical planning. BMC Medical Imaging , 13:1, 2013.
[24]. P. Markelj, D. Tomazevic, F. Pernus, and B. Likar. Robust Gradient-Based 3D/2-D Registration of CT and MR to X-Ray Images. IEEE Trans Med Imaging, 27(12):1704-1714, 2008