Please use this identifier to cite or link to this item: http://hdl.handle.net/11455/18107
標題: 主動輪廓模型之拓撲研究與數值分析
Topology Study and Numerical Analysis of Active Contour models
作者: 楊志弘
Yang, Chih-Hung
關鍵字: image segmentation
影像分割
active contour models
topology
主動輪廓線
拓撲控制
出版社: 應用數學系所
引用: [1] M. Kass, A. Witkin, and D. Terzopoulos, “Snakes: active contour models.”International Journal of Computer Vision, Vol. 1, No. 4, pp. 321- 331, 1988. [2] D. Terzopoulos, A. Witkin, and M. Kass, “Constraints on deformable models: recovering 3D shape and nonrigid motion.”Artif. Intelligence, Vol. 36, No. 1, pp. 91-123, 1988. [3] F. Leymarie and M.D. Levine, “Tracking deformable objects in the plane using an active contour model.”IEEE Trans. on Pattern Anal. Machine Intell., Vol. 15, No. 6, pp. 617-634, 1993. [4] D. Terzopoulos, and K. Fleischer, “ Deformable models.”The Visual Computer, Vol. 4, No. 6, pp. 306-331, 1988. [5] T. McInerney, and D. Terzopoulos, “On matching deformable models to images.”Medical Image Analysis, Vol. 1, No. 2, pp. 91-108, 1996. [6] D. Terzopoulos, “ Regularization of inverse visual problems involving discontinuities.” IEEE Trans. on Pattern Analysis and Machine Intelligence, Vol. 8, No. 4, pp. 413-424, 1986. [7] D. Terzopoulos, A. Witkin, and M. Kass. “ Symmetry-seeking models and 3D object reconstruction.”International Journal of Computer Vision, Vol. 1, No. 3, pp. 211-221, 1987. [8] T. McInerney and D. Terzopoulos, “ Topologically adaptable snakes.” In Proceedings of the Fifth International Conference on Computer Vision, pp. 840-845, 1995. [9] T. McInerney and D. Terzopoulos, “ Topology adaptive deformable surfaces for medical image volume segmentation”IEEE Transactions on Medical Imaging, Vol. 18, No. 3, pp. 840-850, 1999. [10] R. Malladi, J.A. Sethian, and B.C. Vemuri, “Shape modeling with front propagation: A level set approach.”IEEE Trans. on Pattern Anal.Machine Intell., Vol. 17, No. 2, pp. 158-175, 1995. [11] V. Caselles, “Geometric models for active contours.”In Proceedings of the 1995 IEEE International Conference on Image Processing, Vol. 3, pp. 9-12, 1995. [12] H. Gao, W.C. Siu, and C.H. Hou, “Improved techniques for automatic image segmentation.” IEEE Transactions on Circuits and Systems for Video Technology, Vol. 11, No. 12, pp. 1273-1280, 2001. [13] A.R. Mirhosseini, and H. Yan, “An optimally fast greedy algorithm for active contours.”Proc. of IEEE Int. Symp. Circuits and Systems, Vol. 2, pp. 1189-1192, 1997. [14] J. Liu, and Y.H. Yang, “Multiresolution colorimage segmentation.” IEEE Transactions on Pattern Analysis Machine Intelligence, Vol. 16, No. 7, pp. 689-700, 1994. [15] T. Uchiyama, M.A. Arbib, “ Color image segmentation using competitive learning.”IEEE Transactions on Pattern Analysis Machine Intelligence, Vol.16, No.12, pp.1197-1206, 1994. [16] R.H. Davies, C.J. Twining, T.F. Cootes, J.C. Waterton, and C.J. Taylor, “A minimum description length approach to statistical shape modeling.”IEEE Transactions on Medical Imaging, Vol. 21, No. 5, pp. 525-537, 2002. [17] A. Neumann, “Graphical gaussian shape models and their application to image segmentation.” IEEE Transactions on Pattern Analysis Machine Intelligence, Vol. 25, No. 3, pp. 316-329, 2003. [18] D. Murray, A. Basu, “Motion tracking with an active camera.”IEEE Transactions on Pattern Analysis Machine Intelligence, Vol. 16, No. 5, pp. 449-459, 1994. [19] J.B. Xu, L.M. Po, and C.K. Cheung, “Adaptive motion tracking block matching algorithm for video coding.” IEEE Transactions on Circuits and Systems for Video Technology, Vol. 9, No. 7, pp. 1025-1029,1999. [20] S. Osher, and J.A. Sethian, “Fronts propagating with curvature-dependent speed: algorithms based on hamilton-jacobi formulations.”Journal of Computational Physics, Vol. 79, pp. 12-49,1988. [21] J.A. Sethian, “ Level set methods and fast marching methods: evolving interfaces in computational geometry, fluid mechanics.” Computer Vision and Materials Science. Cambridge University Press, 1988. [22] G. Bonifazi , S. Serranti, F. Volpe, and R. Zuco, “A combined morphological and color based approach to characterize flotation froth bubbles.” Proceedings of the Second International Conference on Intelligent Processing and Manufacturing of Materials, Vol. 1, pp. 465-470, 1999. [23] W.Y. Chung, J.J. Oh, T.K. Kim, J.K. Shin, K.I. Seo, Y.K. Park, and J.T. Kong, “Integrated simulation of equipment and topography for plasma etching in the DRM reactor.” International Conference on Simulation of Semiconductor Processes and Devices, pp. 127-130, 2000. [24] J.M. Berg, “Estimation of parameters appearing in the level set evolution equation.”The Proceedings of the 37th IEEE Conference on Decision and Control, Vol. 2, pp. 2323-2328, 1998. [25] J.M. Berg, “Estimation of parameter values appearing in space and orientation dependent curve evolution process models.”The Proceedings of the 1999 American Control Conference, Vol. 6, pp. 3905-3909, 1999. [26] R. Malladi, and J.A. Sethian, “Level set and fast marching methods in image processing and computer vision.”J. Vac. Sci. Technol. B, Vol. 13, No. 4, pp. 489-492, 1995. [27] R. Malladi and J.A. Sethian, “Level set and fast marching methods in image processing and computer vision.” Proceedings of the 1996 International Conference on Image Processing, Vol. 1, pp. 489-492, 1996. [28] H. Jin, A. Yezzi, and S. Soatto, “Stereoscopic shading: integrating multi-frame shape cues in a variational framework.”Proceedings of the 2000 IEEE Conference on Computer Vision and Pattern Recognition, Vol. 1, pp. 169-176, 2000. [29] R. Hebbar, and M.S. Branicky, “Fast marching for hybrid control.” Proceedings of the 1999 IEEE International Symposium on Computer Aided Control System Design, Vol. 5, pp. 109-114, 1999. [30] M.S. Branicky, R. Hebbar, and G. Zhang, “A fast marching algorithm for hybrid systems.”Proceedings of the 38th IEEE Conference on Decision and Control, Vol. 5, pp. 4897-4902, 1999. [31] Tony F. Chan, and Luminita A. Vese, “Active Contours Without Edges.”IEEE Trans. on Image Processing. Vol. 10, No. 2, pp. 266-277, 2001. [32] D. Mumford and J. Shah, “Optimal approximation by piecewise smooth functions and associated variational problems.”Commun. Pure Appl. Math, Vol. 42, No. 4, pp. 577-685, 1989. [33] C. Xu, and J.L. Prince, “Snakes, shapes, and gradient vector flow.” IEEE Trans. Image Processing, Vol. 7, No. 3, pp. 359-369, 1998. [34] C. Xu, and J.L. Prince, “Global optimality of gradient vector flow.” Proc. of 34th Annual Conference on Information Sciences and Systems, Princeton University, March 2000. [35] D.J. Williams and M. Shah, “A fast algorithm for active contours and curvature estimation.”CVGIP: Image Understanding, Vol. 55, No. 1, pp. 14-26, 1992. [36] K.M. Lam, and H. Yan, “Fast greedy algorithm for active contours” Electronics Lett., Vol. 30, No. 1, pp. 21-23, 1994. [37] K.M. Lam and H. Yan, “Locating head boundary by snakes.”Proc. of Int. Symp. Speech, Image Processing and Neural Networks, Vol. 1, pp.17-20, 1994. [38] A.R. Mirhosseini and H. Yan, “An optimally fast greedy algorithm for active contours.”Proc. of IEEE Int. Symp. Circuits and Systems, Vol. 2, pp. 1189-1192, 1997. [39] W. Gautschi, “Numerical Analysis” , Birkhauser, 1997. [40] D. Adalsteinsson, and J.A. Sethian, “ The fast construction of extension velocities in level set methods.” Journal of Computational Physics, Vol. 148, pp. 2-22, 1999 [41] Osher, S. and J.A. Sethian, “ Fronts propagating with curvature dependent speed: algorithms based on hamilton-jacobi formulations.” Journal of Computational Physics, Vol. 79, pp. 12-49, 1988. [42] G.S. Jiang, and D. Peng, “ Weighted ENO schemes for hamilton jacobi equations.”SIAM J., Comput., Vol. 21, pp. 2126-2143, 2000. [43] C.W. Shu, and S. Osher, “ Efficient Implementation of Essentially Non-Oscillatory Shock Capturing Schemes.”Journal of Computational Physics, Vol. 77, pp. 439-471, 1988. [44] X. Han, C. Xu, and J.L. Prince, “ A topology preserving deformable model using level set.”in Proc. IEEE Conf. CVPR 2001, Vol. 2, pp. 765-770, 2001 [45] G. Hermosillo, O. Faugeras, and J. Gomes, “ Unfolding the cerebral cortex using level set methods.”In: Proc. 2nd Internat. Conf. Scale- Space Theories in Computer Vision, Corfu, Greece. LNCS, Vol. 1682, pp. 58-69, 1999. [46] X. Han, C. Xu, and J.L. Prince, “ A topology preserving level set method for geometric deformable models.”IEEE Trans. Pattern Anal. Machine Intell. Vol. 25, No. 6, pp. 755-768, 2003 [47] C.Y. Hsu, C.H. Yang, and H.C. Wang, “ Segmentation usinggeometric active contours with topology control.”In: 17th IPPR Conf. on Computer Vision, Graphics and Image Processing, Hualien, ROC, 2004 [48] S. Florent, J.P. Pons, F. Bruce, G. Eric, “ A novel active contour framework. Multi-component level set evolution under topology control.” Massachusetts Institute of Technology, Computer Science and Artificial Intelligence Laboratory. Tech., 2005 [49] R.C. Gonzalez, and R.E. Woods, “ Digital image processing.” Addison-Wesley, New York., 2000. [50] A.P. Dhawan, “ Medical image analysis.”John Wiley Publications and IEEE Press, 2003. [51] A.E. Lefohn, J.E. Cates, and R.T. Whitaker, “Interactive, GPU-based level sets for 3D segmentation.” Proceedings of Medical Image Computing and Computer Assisted Intervention (MICCAI), 2003. [52] N. Otsu, “A threshold selection method from gray-level Histograms.”IEEE Transactions on Systems, Man, and Cybernetics, Vol. 9, No. 1, pp. 62-66, 1979. [53] Insight Toolkit (ITK), The National Library of Medicine Insight Segmentation and Registration Toolkit, http://www.itk.org/ [54] J.C. Bezdek, “ Pattern recognition with fuzzy objective function algorithms.”Plenum Press, New York, 1981. [55] J.C. Dunn, “ A fuzzy relative of the ISODATA process and its use in detecting compact well-separated clusters.”Journal of Cybernetics., Vol. 3, Issue. 3, pp. 32-57, 1974. [56] P.C. Teo, G. Sapiro, and B.A. Wandell, “Creating connected representations of cortical grey matter for functional MRI visualization.” IEEE Transactions on Medical Imaging, Vol 16, pp. 852-863, 1997. [57] B. Wandell, S. Chial, and B. Backus, “Visualization and measurement of the cortical surface.”Journal of Cognitive Neuroscience, Vol. 12, No. 5, pp. 739-752, 2000.[58] A.P. Zijdenbos, B.M. Dawant, R.A. Margolin, and A.C. Palmer, “ Morphometric analysis of white matter lesions in MR images: method an validation.”IEEE Trans. Med. Imaging, Vol.13, pp.716-724, 1994. [59] X. Han, C. Xu, J.L. Prince, “ Fast numerical scheme for gradient vector flow computation using a multigrid method.”Image Processing, IET. Vol. 1, Issue 1, pp.48-55,2007. [60] R. P. Fewrenko, “ The speed of convergence of one iterative process.” Journal of Computational Mathematics and Mathematical Physics, Vol. 4, pp. 1092-1096, 1964. [61] A. Brandt, “ Multi-level adaptive technique (MLAT) for fast numerical solution to boundary value problems.”Proceedings of the 3rd Inter. Conf. on Numerical Mech. in Fluid Mech., pp. 82-89,1973. [62] R.A. Nicolaides, “ On multigrid convergence in the indefinite case.” Mathematics of Computation, Vol.32, No.144, pp.1082-1086, 1978. [63] D. Braess and W. Hackbusch, “ A new convergence proof for the multigrid method including the V-cycle.” Society for Industrial and Applied Mathematics, Vol. 20, Issue 5, pp.967-975, 1983. [64] D.J. Mavriplis, “ Unstructured grid techniques.”Annual Review of Fluid Mechanics, Vol. 29, pp.473-514, 1997. [65] S.G. Sheffer, L. Martinelli, and A. Jameson, “ An efficient multigrid algorithm for compressible reactive flows.”Journal of Computational Physics, Vol. 144, No. 2, pp. 484-516, 1998. [66] J.D. Moulton, J.E. Dendy, and J.M. Hyman, “ The black box multigrid numerical homogenization algorithm.” Journal of Computational Physics, Vol. 142, No. 1, pp. 80-108, 1998.
摘要: 近年來,隨著電腦科技的發展,數位化影像的處理與應用漸趨重 要。在許多應用之前,影像分割是一個重要的基本處理,因此影像分割成為影像處理上的一個重要課題。本論文係探討主動輪廓模型之拓撲研究與數值分析應用於影像分割之研究。主動輪廓線可分為兩類,一種為參數式主動輪廓線,另一種為幾何式主動輪廓線。首先,吾人探討參數式主動輪廓線,特別是此模型的一些缺點和優點。為了減輕或解決參數式主動輪廓線的缺點,我們提供了一些採用不同影像能量和數值方法的改進模型於本論文中加以探討。接著,我們將會介紹並討論幾何式主動輪廓線。拓撲改變上的彈性是幾何式主動輪廓線相較於參數式主動輪廓線的一個主要優勢。雖然幾何式主動輪廓線有許多不同的模型,但所有的幾何式主動輪廓線都僅能將輪廓圈選出來,而無法對圈選的輪廓進行拓撲控制。所謂的拓撲控制指的是控制主動輪廓線『分裂或者是合併的能力』以及其『選擇物體的能力』。我們分析一些基本且重要的幾何式主動輪廓線模型並討論他們在拓撲控制上的缺點。最後,在本文中,我們針對這些缺失提供了一些方法去修改這些幾何式主動輪廓線模型並利用一些影像去驗證我們提供的方法。實驗結果顯示,這些修改後的幾何式主動輪廓線在進行影像分割的時候,具備了拓撲控制的能力。
In recent years, with the development of computer technology, digital image processing and its applications have become increasingly important. Image segmentation is a vital yet basic type of processing completed before other higher level applications. This thesis explores the topology study and numerical analysis of active contour models applicable to image segmentation. Active contour models can be classified into two types. One is a parametric active contour model and the other is a geometric active contour model. Firstly, a critical look is focuses on the parametric active contour model. In particular, some drawbacks and advantages of this model are discussed. Aiming to alleviate or solve the drawbacks of parametric active contour model, we present some modified models with a different image force field and numerical methods in this dissertation. Next, we discuss and introduce geometric active contour model. Topological flexibility has been long claimed as the major advantage of geometric active contour model over parametric active contour model. Geometric active contour model has a lot of different models. Although all of the geometric active contour models can segment out the outline of image objects, they cannot carry the function of topology control to the outline segmented. The so-called ability of topology control means that handling the “merging or splitting capability” and “capability of selecting objects” in geometric active contour models. We analyze several basic and important models of geometric active contour models and discuss their drawbacks in topology control. Finally, we present the some ideas that are mainly aimed at those drawbacks to modify those different geometric active contour models in this dissertation. We use some images to verify our proposed methods. The segmentation results of the images show that the modified geometric active contour model to provide the ability of topology control for the segment objects.
URI: http://hdl.handle.net/11455/18107
其他識別: U0005-1507200911393200
文章連結: http://www.airitilibrary.com/Publication/alDetailedMesh1?DocID=U0005-1507200911393200
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