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標題: | 以投影技術重建橢圓與其在血管重建之應用 Elliptical Reconstruction by Projection and Its Applications in Vessel Reconstruction |

作者: | 郭世崇 Kuo, Shye-Chorng |

關鍵字: | Ellipstical Reconstruction;橢圓重建;Stereoscopic Magnetic Resonance Angiography;Vessel Reconstruction;立體磁振造影血管顯像術;血管重建 |

出版社: | 電機工程學系所 |

引用: | [1]P. L. Rosin, “A note on the least squares fitting of ellipses,” Pattern Recognition Letters, vol. 14, no. 10, pp. 799-808, 1993. [2]A. Albano, “Representation of digitized contours in terms of conic arcs and Straight-Line segments,” Computer Graphics and Image Processing, vol. 3, no. 1, pp. 23-33, 1974. [3]T. Ellis, A. Abbood, B. Brillault, “Ellipse detection and matching with uncertainty,” Image and Vision Computing, vol. 10, no. 5, pp. 271-276, 1992. [4]A. Fitzgibbon, M. Pilu, R. Fisher, “Direct least square fitting of ellipses,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 21, no. 5, pp. 476-480, 1999. [5]E. S. Maini, “Enhanced direct least square fitting of ellipses,” International Journal of Pattern Recognition and Artificial Intelligence, vol. 20, no. 6, pp. 939-953, 2006. [6]L. Tian, S. Kamata, “A Two-Stage point pattern matching algorithm using ellipse fitting and dual Hilbert scans,” IEICE Transactions on Information and Systems, vol. E91-D, no. 10, pp. 2477-2484, 2008. [7]X. Bai, C. Sun, F. Zhou, “Splitting touching cells based on concave points and ellipse fitting,” Pattern Recognition, vol. 42, no. 11, pp. 2434-2446, 2009. [8]W. Wu, M. J. Wang, “Elliptical object detection by using its geometric properties,” Pattern Recognition, vol. 26, no. 10, pp. 1499-1509, 1993. [9]G. Watson, “Least squares fitting of circles and ellipses to measured data,” BIT Numerical Mathematics, vol. 39, no. 1, pp. 176-191, 1999. [10]D. Chaudhuri, “Object area-based method for elliptic and circular fit of a two-tone image,” Defence Science Journal, vol. 58, no. 6, pp. 710-714, 2008. [11]D. Chaudhuri, “A simple least squares method for fitting of ellipses and circles depends on border points of a two-tone image and their 3-D extensions,” Pattern Recognition Letters, vol. 31, no. 9, pp. 818-829, 2010. [12]P. L. Rosin, “Assessing error of fit functions for ellipses,” Graphical Models and Image Processing, vol. 58, no. 5, pp. 494-502, 1996. [13]W. Gander, G. H. Golub, R. Strebel, “Least-squares fitting of circles and ellipses,” BIT, vol. 34, no. 4, pp. 558-578, 1994. [14]H. Spath, “Least squares fitting of ellipses and hyperbolas,” Computational Statistics, vol. 12, pp. 329-341, 1997. [15]H. Spath, “Orthogonal distance fitting by circles and ellipses with given area,” Computational Statistics, vol. 12, pp. 343-354, 1997. [16]S. J. Ahn, W. Rauh, H. Warnecke, “Least-squares orthogonal distances fitting of circle, sphere, ellipse, hyperbola, and parabola,” Pattern Recognition, vol. 34, no. 12, pp. 2283-2303, 2001. [17]D. Proffitt, “The measurement of circularity and ellipticity on a digital grid,” Pattern Recognition, vol. 15, no. 5, pp. 383-387, 1982. [18]M. Stricker, “A new approach for robust ellipse fitting,” in: Proc. Intl Conf. Automation, Robotics, and Computer Vision, pp. 940-945, 1994. [19]P. L. Rosin, “Ellipse fitting using orthogonal hyperbolae and Stirling''s oval,” Graphical Models and Image Processing, vol. 60, no. 3, pp. 209-213, 1998. [20]G. Calafiore, “Approximation of n-dimensional data using spherical and ellipsoidal primitives,” IEEE Transactions on Systems, Man and Cybernetics, Part A: Systems and Humans, vol. 32, no. 2, pp. 269-278, 2002. [21]L. G. de la Fraga, I. V. Silva and N. Cruz-Cortes, “Euclidean distance fit of ellipses with a genetic algorithm,” Lecture Notes in Computer Science, vol. 4448, pp. 359-366, 2007. [22]B. B. Chaudhuri, G. P. Samanta, “Elliptic fit of objects in two and three dimensions by moment of inertia optimization,” Pattern Recognition Letters, vol. 12, no. 1, pp. 1-7, 1991. [23]R. Safaee-Rad, I. Tchoukanov, B. Benhabib, K. C. Smith, “Accurate parameter estimation of quadratic curves from grey-level images,” CVGIP: Image Understanding, vol. 54, no. 2, pp. 259-274, 1991. [24]K. Voss, H. Suesse, “Invariant fitting of planar objects by primitives,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 19, no. 1, pp. 80-84, 1997. [25]P. L. Rosin, “Ellipse fitting by accumulating five-point fits,” Pattern Recognition Letters, vol. 14, no. 8, pp. 661-669, 1993. [26]F. Mai, Y. Hung, H. Zhong, W. Sze, “A hierarchical approach for fast and robust ellipse extraction,” Pattern Recognition, vol. 41, no. 8, pp. 2512-2524, 2008. [27]R. O. Duda, P. E. Hart, “Use of the Hough transformation to detect lines and curves in pictures,” Communications of the ACM, vol. 15, no. 1, pp. 11-15, 1972. [28]N. Guil, E. L. Zapata, “Lower order circle and ellipse Hough transform,” Pattern Recognition, vol. 30, no. 10, pp. 1729-1744, 1997. [29]R. A. McLaughlin, “Randomized Hough transform: Improved ellipse detection with comparison,” Pattern Recognition Letters, vol. 19, no. 3-4, pp. 299-305, 1998. [30]K. U. Kasemir, K. Betzler, “Detecting ellipses of limited eccentricity in images with high noise levels,” Image and Vision Computing, vol. 21, no. 2, pp. 221-227, 2003. [31]S. Zhang, Z. Liu, “A robust, real-time ellipse detector,” Pattern Recognition, vol. 38, no. 2, pp. 273-287, 2005. [32]Y. C. Cheng, “The distinctiveness of a curve in a parameterized neighborhood: extraction and applications,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 28, no. 8, pp. 1215-1222, 2006. [33]V. Wedeen, R. Meuli, R. Edelman, S. Geller, L. Frank, T. Brady and B. Rosen, “Projective imaging of pulsatile flow with magnetic resonance,” Science, vol. 230, no. 4728, pp. 946-948, 1985. [34]D. Atkinson and L. Teresi, “Magnetic resonance angiography,” Magnetic Resonance Quarterly, vol. 10, no. 3, pp. 149-172, 1994. [35]C. L. Dumoulin and H. R. Hart, “Magnetic resonance angiography,” Radiology, vol. 161, no. 3, pp. 717-720, 1986. [36]J. H. Brittain, B. S. Hu, G. A. Wright, C. H. Meyer, A. Macovski and D. G. Nishimura, “Coronary angiography with magnetization-prepared T2 contrast,” Magnetic Resonance in Medicine, vol. 33, no. 5, pp. 689-696, 1995. [37]D. G. Nishimura, A. Macovski, J. M. Pauly and S. M. Conolly, “MR angiography by selective inversion recovery,” Magnetic Resonance in Medicine, vol. 4, no. 2, pp. 193-202, 1987. [38]M. R. Prince, “Gadolinium-enhanced MR aortography,” Radiology, vol. 191, no. 1, pp. 155-164, 1994. [39]J. Kleeeld, G. V. O''Reilly, J. B. Barsotti and M. L. Brooks, “Biplane stereoscopic magnication cerebral angiography,” Radiology, vol. 165, no. 2, pp. 576-577, 1987. [40]B. Movassaghi, V. Rasche, M. Grass, M. A. Viergever and W. J. Niessen, “A quantitative analysis of 3-D coronary modeling from two or more projection images,” IEEE Transactions on Medical Imaging, vol. 23, no. 12, pp. 1517-1531, 2004. [41]J. Yang, Y. Wang, Y. Liu, S. Tang and W. Chen, “Novel approach for 3-D reconstruction of coronary arteries from two uncalibrated angiographic images,” IEEE Transactions on Image Processing, vol. 18, no. 7, pp. 1563-1572, 2009. [42]S.-K. Chang and C. K. Chow, “The reconstruction of three-dimensional objects from two orthogonal projections and its application to cardiac cineangiography,” IEEE Transactions on Computers, vol. 22, no. 1, pp. 18-28, 1973. [43]C. H. Slump and J. J. Gerbrands, “A network flow approach to reconstruction of the left ventricle from two projections,” Computer Graphics and Image Processing, vol. 18, no. 1, pp. 18-36, 1982. [44]Y. Bresler and A. Macovski, “Three-dimensional reconstruction from projections with incomplete and noisy data by object estimation,” IEEE Transactions on Acoustics, Speech and Signal Processing, vol. 35, no. 8, pp. 1139-1152, 1987. [45]G. P. M. Prause and D. G. W. Onnasch, “Binary reconstruction of the heart chambers from biplane angiographic image sequences,” IEEE Transactions on Medical Imaging, vol. 15, no. 4, pp. 532-546, 1996. [46]Y. Wang, P. A. Heng and F. M. Wahl, “Image reconstructions from two orthogonal projections,” International Journal of Imaging Systems and Technology, vol. 13, no. 2, pp. 141-145, 2003. [47]R. Medina, M. Garreau, J. Toro, J.-L. Coatrieux and D. Jugo, “Three-dimensional reconstruction of the left ventricle from two angiographic views: an evidence combination approach,” IEEE Transactions on Systems, Man and Cybernetics, Part A, vol. 34, no. 3, pp. 359-370, 2004. [48]R. Medina, M. Garreau, J. Toro, H. L. Breton, J.-L. Coatrieux and D. Jugo, “Markov random field modeling for three-dimensional reconstruction of the left ventricle in cardiac angiography,” IEEE Transactions on Medical Imaging, vol. 25, no. 8, pp. 1087-1100, 2006. [49]L. Fillatre and I. Nikiforov, “Non-Bayesian detection and detectability of anomalies from a few noisy tomographic projections,” IEEE Transactions on Signal Processing, vol. 55, no. 2, pp. 401-413, 2007. [50]C. Soussen and J. Idier, “Reconstruction of three-dimensional localized objects from limited angle x-ray projections: an approach based on sparsity and multigrid image representation,” Journal of Electronic Imaging, vol. 17, no. 3, pp. 033011-19, 2008. [51]S. J. Chen and J. D. Carroll, “3-D reconstruction of coronary arterial tree to optimize angiographic visualization,” IEEE Transactions on Medical Imaging, vol. 19, no. 4, pp. 318-336, 2000. [52]S.-Y. J. Chen, J. D. Carroll and J. C. Messenger, “Quantitative analysis of reconstructed 3-D coronary arterial tree and intracoronary devices,” IEEE Transactions on Medical Imaging, vol. 21, no. 7, pp. 724-740, 2002. [53]S.-Y. J. Chen and J. D. Carroll, “Kinematic and deformation analysis of 4-D coronary arterial trees reconstructed from cine angiograms,” IEEE Transactions on Medical Imaging, vol. 22, no .6, pp. 710-721, 2003. [54]K. Sprague, M. Drangova, G. Lehmann, P. Slomka, D. Levin, B. Chow and R. deKemp, “Coronary x-ray angiographic reconstruction and image orientation,” Medical Physics, vol. 33, no. 3, pp. 707-718, 2006. [55]K. Kitamura, J. M. Tobis and J. Sklansky, “Estimating the 3D skeletons and transverse areas of coronary arteries from biplane angiograms,” IEEE Transactions on Medical Imaging, vol. 7, no. 3, pp. 173-187, 1988. [56]T. Kayikcioglu, A. Gangal and M. Ozer, “Reconstructing ellipsoids from three projection contours,” Pattern Recognition Letters, vol. 21, no. 11, pp. 959-968, 2000. [57]T. Kayikcioglu, A. Gangal and M. Turhal, “Reconstructing coronary arterial segments from three projection boundaries,” Pattern Recognition Letters, vol. 22, no. 6-7, pp. 611-624, 2001. [58]J.-R. Liao, J.-J. Jou and S.-H. Huang, “Three-dimensional reconstruction of blood vessels from stereoscopic magnetic resonance angiography,” Proc. SPIE Medical Imaging, San Diego, CA, pp. 700-707, 2002. [59]J.-R. Liao, S.-C. Kuo, L.-S. Kuo, S.-H. Huang and J.-J. Jou, “Three dimensional reconstruction of blood vessels from stereoscopic magnetic resonance angiography,” Journal of Medical and Biological Engineering, vol. 24, no. 2, pp. 109-114, 2004. [60]W. C. Karl, G. C. Verghese and A. S. Willsky, “Reconstructing ellipsoids from projections,” CVGIP: Graphical Models and Image Processing, vol. 56, no. 2, pp. 124-139, 1994. |

摘要: | 在本論文中，我們提出了利用影像的投影資訊來重建橢圓形物件的新方法，並且應用這些方法在立體磁振造影的血管重建上。論文中的第一個部份(第三章)，我們介紹了橢圓重建的新方法，從實驗的結果中，可以看出我們所提出的新方法比最小二平方法的方法來得好。在論文的第二個部份(第四章至第八章)，我們提出兩個橢圓重建的新方法應用在立體磁振造影血管顯像術上，我們假定血管為傾斜某個角度的直圓柱，則傾斜血管切面的幾何形狀為橢圓形，而橢圓形的表示式，可以用參數式或是矩陣式來表示，因此基於此兩種表示式，我們提出兩個演算法來重建橢圓形。在我們的立體血管重建的實驗中，以參數式演算法來做重建，所得的平均誤差為0.066像素，而以矩陣式演算法來做重建，所得的平均誤差為0.014像素。 In this dissertation, we propose new methods to reconstruct elliptical objects from the projections of an image and apply these methods in reconstructing blood vessel from stereoscopic magnetic resonance angiography. In the first part of this dissertation (Chapter 3), we introduce the new elliptical reconstruction method. Through experiments, we show that our new method gives better results as compared to the popular least square fitting method. In the second part of this dissertation (Chapter 4-8), we propose two elliptical reconstruction algorithms for stereoscopic magnetic resonance angiography. The basic assumption we make is that the blood vessels are tilting circular tubes and the shape of the vessel on every cross-section is an ellipse. Since an ellipse can be represented either in parametric form or in algebraic form, we propose two algorithms that reconstruct the ellipses by representing them in these two forms. In our experiments, the average estimation error for the parametric algorithm is 0.066 pixels. The average error for the algebraic algorithm is 0.014 pixels. |

URI: | http://hdl.handle.net/11455/8983 |

其他識別: | U0005-2801201107421800 |

Appears in Collections: | 電機工程學系所 |

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