Improved modelling of the human cerebral vasculature

IMPROVED MODELLING OF THE HUMAN CEREBRAL VASCULATURE ZHENG WEILI (M.Eng) A THESIS SUBMITTED FOR THE DEGREE OF DOCTOR OF PHILOSOPHY DEPARTMENT OF MECHANICAL ENGINEERING NATIONAL UNIVERSITY OF SINGAPORE 2007 Acknowledgement Pursuing Ph.D is a harsh journey, the result of which reflects by no means only my efforts and dedication. First of all, I would like to express my deepest gratitude and respect to my supervisors Dr. Chau Fook Siong, Dr. Ang Marcelo H. Jr., and Dr. Wieslaw L. Nowinski for their remarkable guidance, heuristic advice and encouragement. They guided me meticulously through out my research program, and were highly supportive during my initial period of inexperience. Their continuous efforts of encouragement and support derived many benefits in my research work, even in writing this successful dissertation. I would also like to thank Dr. Aamer Aziz, Dr. Ihar Volkau and Dr. Hu Qingmao for their valuable suggestions and creative discussions, which inspired me greatly. Many thanks to the lab officer, Mr. Chiam Tow Jong, and Dr. Fu Yu in the Department of Mechanical Engineering, NUS for their selfless help and cooperation. I would also extend my heartfelt thanks to Ms. Aminah B. B. Abu Bakar, Mr. A. Anand, Mr. Ma Xin, Dr. Liu Jimin, Dr. Qiao Yu and many others in the Biomedical Imaging Lab for solving many technical and administrative problems in the course of this dissertation. Also I would like to thank all my friends who have given support and enthusiasm during the years of my Ph.D. Their friendship greatly stimulated me to carry on through difficult periods. I I would like to thank Biomedical Imaging Lab for sharing the physical vascular phantom data and volunteer data. I would also extend my sincere thanks to the Diagnostic and Interventional Neuroradiology department, University of Saarland, Homburg, Germany, for providing the 17 sets of patient data sets in this dissertation. I am particularly indebted to my parents and parents-in-law for providing constant support and encouragement during my graduate study. Very special thanks to my husband, Huabing, for always helping me to put things into the right perspective. Special thanks also to my little daughter, Tianhui, for bringing a bundle of joy into my life. Because of her, life becomes so meaningful and wonderful. It is impossible to conclude without thanking the Almighty God for all the blessings I received during my Ph.D. studies. Forever, He is the Source of peace and strength. II Table of Contents Acknowledgement………………………………………………………………I Table of contents……………………………………………………………………III Summary……………………………………………………………………VII List of tables………………………………………………………………… .X List of figures………………………………………………………………… .XI List of symbols…….…………………………………………………………… XVI 1. Introduction……………………………………………………………………1 1.1 Human cerebral vasculature……………………………………………3 1.2 Magnetic resonance angiography……………………………………… .4 1.3 Vascular image processing techniques…………………………………5 1.4 Representations of the vasculature……………………………………….6 1.5 Problems statement and contributions……………………………………9 1.5.1 A hybrid strategy………………………………………………….11 1.5.2 Locally adaptive thresholding…………………….…………… .12 1.5.3 Centerline extraction…………………………………………….…13 1.5.4 Elliptical measurement based on affine scale space…………… 14 1.6 Scope of dissertation……………………………………………………….14 2. Vascular modelling……………… …………………………………………….16 2.1 Overview……………………………… .………………………… .16 III 2.2 Deformable models………………… ………………………………18 2.3 Skeletonization strategy…………………… ….……………………20 2.3.1 Angiographic image enhancement…………………………….20 2.3.2 Vessel segmentation………………………………………… 22 2.3.3 Skeletonization……………………………………………….29 2.4 Scale space strategy……………………………………………………33 2.4.1 Scale space theory………………… ……….……… .…… .33 2.4.2 Medialness……………………………………………………35 2.4.3 Scale space centerline extraction………………………………37 2.5 Tracking strategy……………………………………………………….39 2.6 Geometric modelling ………………………………………………….40 2.7 Our solution………………………………………………………………41 3. Locally adaptive thresholding ………………………………………………….43 3.1 Background………………………………………………………… .43 3.2 Experimental Data……………….……………………………………44 3.3 Segmentation with locally adaptive thresholding…………………… .46 3.4 3.3.1 Step 1-Automatice selection of regions of interest (ROIs)….…46 3.3.2 Step 2-Local enhancement and adaptive thresholding……… 50 3.3.3 Evaluation…………………………………………………… 55 Results…………………………………………………………….….56 3.4.1 Experiments on a slice………………………………… .……57 3.4.2 Experiments on MRA data sets……………………………… 59 IV 3.4.3 Sensitivity to the width and maximum intensity of a cross section……………………………………… ……………….73 3.5 Discussion……………………………………………………………….74 3.6 Conclusion………………………………………………………….…… 79 4. Centerline model extraction by means of the wave propagation of the marching spheres………………………………………………………………….………80 4.1 Background………………………………………………………… .80 4.2 Centerline extraction procedure………………………………………83 4.3 4.2.1 Initialization………………………………………………….83 4.2.2 Marching procedure …………………………………………87 4.2.3 Procedure of building a tree structure …………………….….…95 4.2.4 Evaluation…………………………………………………… …96 Results…………………………………………………………………….98 4.3.1 Experiments on the simulated data……………… .…………… .98 4.3.2 Studies on the 3D binary cerebral vasculature data sets…… 104 4.4 Discussion…………………………… …………………………………111 4.5 Conclusion…………………………….…………………………………115 5. Building an elliptical centerline model of the cerebral vasculature using model-based affine Gaussian scale space approach………… .117 5.1 Background………………………………………………………….117 5.2 Building an elliptical model of the cerebral vasculature…………….119 5.2.1 Affine medialness function………………………………….119 V 5.3 5.4 5.2.2 Shape adaptation…………………………………………………122 5.2.3 Measurement of elliptical cross sections in 3D vasculature…126 5.2.4 Geometric modelling based on the elliptical centerline model.128 Results and discussion……………………………………………….129 5.3.1 Experiments on the 2D synthetic images……………………129 5.3.2 Applications on 3D MRA data……………………………… 138 Conclusion…………………………………………………………… .143 6. Conclusion and future work….……………………………………….… 144 6.1 Conclusion………………………………………………………… .144 6.2 Future work……………………………………………………….… 146 Bibliography…………………………………………………………………….148 Appendix ….……………………………………….…………………………… .171 A. Evaluation of the segmentation result……………… …… .…… .171 B. Reconstructed 3D cerebral vascular models……………… .………… .172 C. Measured elliptical vessel cross section. ……… …………………….… 173 VI Summary Angiography is a medical imaging technique to visualize blood vessels. Many medical applications need efficient visualization of the vascular angiographic data with topological information to make diagnosis and quantitative analysis of the vasculature. The transition from the volumetric raw data to a representation with topological information which can afford efficient visualization is not trivial. It is especially difficult for cerebral vasculatures which are complicated, tortuous and contain a large number of small vessels. Vascular models generated from the centerline and radius information can provide the tree structure and smooth visualization which suits for these applications. There are generally three strategies to obtain a centerline model: skeletonization strategy, scale space strategy and tracking strategy. From the analysis, none of the strategy is a clear winner under all conditions; rather, each is potentially useful for some set of applications and implementation constraints. This dissertation describes a hybrid strategy which integrated with both skeletonization and scale space strategies. The hybrid strategy by combining the advantages of the above two strategies includes steps. Firstly, the binary data is segmented from three dimensional (3D) time of flight (TOF) magnetic resonance angiography (MRA) data. Then a centerline extraction procedure is applied to VII generate a circular centerline model. A tree structure and 3D data set with vessel voxels labeled with its branch number is also produced. Finally, an elliptical measurement procedure based on affine scale space approach is performed in the original angiographic data for each cross section of the previous circular centerline model. An elliptical centerline model is generated after this procedure. The automation and robustness of this strategy is realized by taking the circular centerline model generated in the second step as initial information for the third step. The accuracy of the final elliptical model is achieved with affine scale space measurement – measuring the size according to its shape. Therefore, it offers more robustness on going over bifurcations than pure scale space strategy and more accurate measurement than pure skeletonization strategy. To demonstrate the advantages of the hybrid strategy, it is also important to show how the image processing techniques can be implemented in each step. The main issues of segmentation, centerline extraction and scale space measurement are explored thoroughly in this dissertation. A novel locally adaptive thresholding segmentation method is proposed in the first step which offers the superiority in accuracy and extraction of finer distal vessels. In the second step, the proposed method by means of wave propagation of the marching spheres can extract the 1-voxel width branches and provide robust bifurcation detection. In the third step, the medialness based on affine Gaussian scale space is extended from the medialness based on linear Gaussian scale space to measure the vessel size. Local shape is VIII efficiently detected by iteratively computing it from the second derivative at the center of the vessel cross section. Our research shows that hybrid strategy is viable and competitive. Its strengths make it a better choice to facilitate automation, provide robust bifurcation detection and generate an elliptical centerline model as a more general and accurate description of vessels. While this dissertation clears the way for the hybrid strategy implementation in each step, there are still many opportunities for further exploration in this area. IX 73. I. Cohen, L.D. Cohen, and N. Ayache, Using deformable surfaces to segment 3D images and infer differential structures, CVGIP: Image Understanding, Vol. 56, No. 2, pp. 242-263, 1992. 74. T. McInernery and D. Terzopoulos, A dynamic finite element surface model for segmentation and tracking in multidimensional medical images with application to cardiac 4D image analysis, Computerized Medical Imaging and Graphics, Vol. 19, No. 1, pp. 69-83, 1995. 75. A. Singh, L. von Kurowski, and M.Y. chiu, Cardiac MR image segmentation using deformable models, Biomedical Image Processing and Biomedical Visualization, SPIE Proceedings, Vol. 1905, pp. 8-28, 1993. 76. I. Carlbom, D. Terzopoulos, and K. Harris, Computer assisted registration, segmentation and 3D reconstruction from images of neuronal tissue sections, IEEE TMI, Vol. 13, No. 2, pp. 351-362, 1994. 77. F. Leitner and P. Cinquim, Complex toplogy 3D objects segmentation, Model-based Vision Development and Tools, SPIE Proceedings, Vol. 1609, pp. 16-26, 1991. 78. H. Delingette, M. Hebert, and K. Ikeuchi, Shape representation and image segmentation using deformable surfaces, Image and Vision Computing, Vol. 10, No. 3, pp. 132-144, 1992. 79. R. Szeliski, D. Tonnesen, and D. Terzopoulos, Modelling surfaces of arbitrary topology with dynamic particles, Proceedings of Conference on Computer Vision and Pattern Recognition (CVPR’93), pp. 82-87, 1993. 158 80. R. Whitaker, Volumetric deformable models, Proceedings of Third Conference on Visualization in Biomedical Computing (VBC’94), SPIE, Vol. 2359, 1994. 81. R. Malladi, R. Kimmel, D. Adalsteinsson, G. Sapiro, V. Caselles, and J.A. Sethian, A geometric approach to segmentation and analysis of 3D medical images, IEEE workshop on Mathematical Methods in Biomedical Image Analysis, pp. 244-252, 1996. 82. J.-O. Lachaud and A. Montanvert, Deformable meshes with automatic topology changes for coarse-to-fine 3D surface extraction, Medical Image Analysis, Vol. 3, No. 2, pp. 187-207, 1999. 83. D. Metaxas and D. Terzopoulos. Shape and nonrigid motion estimation through physics-based synthesis. IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 15, No. 6, 580-591, 1993. 84. R. Malladi, J. Sethian, and B. Vemuri. Shape modelling with front propagation: A level set approach. IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 17, No. 2, pp. 158-175, 1995. 85. V. Caselles, R. Kimmel, G. Sapiro, and C. Sbert. Minimal surfaces based object segmentation.IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 19, No. 4, pp. 394-398, 1997. 86. T. McInerney and D. Terzopoulos. Topologically adaptable snakes, Proc. 5th International Conference of Computer Vision, Cambridge, MA, USA, pp. 840, June 1995. 87. P.J. Yim, J.J. Cebral, R. Mullick, H.B. Marcos, and P.L. Choyke, Vessel surface 159 reconstruction with a tubular deformable model, IEEE Transactions on Medical Imaging, Vol. 20, No.12, pp. 1411 –1421, 2001. 88. J. Feng, H.H.S. Ip, and S.H. Cheng, A 3D geometric deformable model for tubular structure segmentation, Proceedings of 10th International Multimedia Modelling Conference, pp.174-180, 2004. 89. G. Gerig, O. Kubler, R. Kikinis, and F.A. Jolesz, Nonlinear anisotropic filtering of MRI data, IEEE Trans. Medical Imaging, Vol. 11, No.2, pp. 221--232, 1992. 90. L. Alvarez, F. Guichard, P.L. Lions, and J.M. Morel, Axioms and fundamental equations of image processing, Arch Rational Mechanics, Vol. 123, pp. 200–257, 1993. 91. G. Sapiro and A. Tannenbaum, Affine invariant scale space, International Journal of Computer Vision, Vol. 11, pp. 25–44, 1993. 92. H. Chen and J. Hale, An algorithm for MR angiography image enhancement, Magnetic Resonance in Medicine, Vol. 33, pp. 534–540, 1995. 93. Y. Sun, R.J. Lucariello, and S.A. Chiaramida, Directionsal low-pass filtering for improved accuracy and reproducibility of stenosis quantification in coronary arteriograms, IEEE Transactions Medical Imaging, Vol. 14, pp. 242–248, 1995. 94. Y. Sato, S. Nakajima, N. Shiraga, H. Atsumi, S. Yoshida, T. Koller, G. Gerig, and R. Kikinis, Three-dimensional multi-scale line filter for segmentation and visualization of curvilinear structures in medical images., Medical Image Analysis, Vol. 2, pp. 143–168, 1998. 95. R. Poli and G. Valli, An Algorithm for Real-Time Vessel Enhancement and 160 Detection, Computer Method Methods and Programs in Biomedicine, Vol. 52, No. 1, pp. 1-22, 1997. 96. C.F. Westin, L. Wigstrom, T. Loock, L. Sjokvist, R. Kikinis, and H. Knutsson, Three-dimensional adaptive filtering in magnetic resonance angiography, Journal of Magnetic Resonance Imaging, Vol. 14, pp. 63-71, 2001. 97. E. Meijering, W. Niessen, J. Weickert, and M. Viergever, Diffusion-enhanced visualization and quantification of vascular anomalies in three-dimensional rotational angiography: results of an In-Vitro evaluation, Medical Image Analysis, Vol. 6, No. 3, pp. 215-233, 2002. 98. Y.P. Du, D.L. Parker, and W.L. Davis, Vessel enhancement filtering in three dimensional MR angiography, Journal of Magnetic Resonance Imaging Vol. 5, pp. 353–359, 1995. 99. M.H.F. Wilkinson and M.A. Westenberg, Shape preserving filament enhancement filtering, In W. J. Niessen and M. A. Viergever, editors, Medical Image Computing and Computer-Assisted Intervention - MICCAI 2001, volume LNCS 2208 of Lecture Notes in Computer Science, pp 770-777, Springer, 2001. 100. Perona P, Malik J., Scale space and edge detection using anisotropic diffusion, IEEE Transactions on PAMI; Vol. 12, pp. 629–639, 1990. 101. H.M. Hajj, T.Q. Nguyen, and R.T. Chin, Multiscale edge detection for medical image enhancement, IEEE Transactions on Medical Imaging, Vol. 18. No. 12, pp. 1115-1168, 1999. 102. T.M. Koller, G. Gerig, G. Szekely, and D. Dettwiler, In Proceedings of the Fifth 161 International Conference on Computer Vision, pp. 864--869, 1995. 103. C. Lorenz, I.-C. Carlsen, T. M. Buzug, C. Fassnacht, and J. Weese, Multi-scale line segmentation with automatic estimation of width, contrast and tangential direction in 2D and 3D medical images, in CVRMed-MRCAS'97, J. Troccaz, E. Grimson, R. Mosges (eds.), LNCS, Vol. 1205, pp. 233-242, 1997. 104. B.E. Chapman, D.L. Parker, 3D multi-scale vessel enhancement filtering based on curvature measurements: application to time-of-flight MRA. Medical Image Analysis, Vol. 9, pp. 191-208, 2005. 105. S. Osher and J.A. Sethian, Front propagation with curvature-dependent speed: Algorithm based on halmilton-jacobi formulations, Journal of Computational Physics, pp. 12-49, 1988. 106. L.M. Lorigo, O. Faugeras, W. Grimson, R. Keriven, and R. Kikinis, Segmentation of bone in clinical knee mri using texture-based geodesic active contours. MICAI, October 1998. LNCS, Vol. 1496, pp. 1195-1204, 1998. 107. L.M. Lorigo, O. Faugeras, W.E.L. Grimson, R. Keriven, R. Kikinis, and C-F. Westin. Co-dimension geodesic active contours for MRA segmentation. In Proceedings of the International Conference on Information Processing in Medical Imaging, LNCS, Vol. 1613, pp. 126-139, 1999. 108. L.M. Lorigo, O. Faugeras, W.E. Grimson, R. Keriven, R. Kikinis, A. Nabavi, and C.-F. Westin. Codimension-two geodesic active contours for the segmentation of tubular structure. In IEEE Conference on Computer Vision and Pattern Recognition, pp. 444-451, 2000. 162 109. L.M. Lorigo, O.D. Faugeras, W.E. Grimson, R. Keriven, R Kikinis, A Nabavi, and C.F. Westin, CURVES: curve evolution for vessel segmentation, Medical Image Analysis, Vol. 5, pp. 195-206, 2001. 110. S. Loncaric, M. Subasic and E. Sorantin, 3-D deformable model for abdominal aortic aneurysm segmentation from CT images, IEEE International Workshop on Image and Signal Processing and Analysis, pp. 139-144, 2000. 111. K.C. Wang, R.W. Dutton, and C.A. Taylor, Improving geometric model construction for blood flow modelling, IEEE Engineering in Medicine and Biology Magazine, Vol. 18, No. 6, pp. 58-69, 1999. 112. K.C. Wang, Level sets methods for computational prototyping with application to hemodynamic modelling, Ph.D thesis, Department of Electrical Engineering, Stanford University, USA, 2001. 113. D. Magee, A. Bulpitt, and E. Berry, 3D automated segmentation and structural analysis of vascular trees using deformable models. IEEE Workshop on Variational and Level Set Methods in Computer Vision, pp. 119-126, 2001. 114. D. Nain, A. Yezzi, and G. Turk, Vessel segmentation using a shape driven flow, MICCAI, pp.51-59, 2004. 115. J. Chen, and A.A. Amini, Quantifying 3-D vascular structures in MRA images using hybrid PDE and geometric deformable models, IEEE TMI, Vol. 23, No. 10, pp. 1251-1262, 2004. 116. P. Yan and A.A. Kassim, Segmentation of volumetric MRA images by suing capillary active contour, Medical Image Analysis, Vol. 10, pp. 317-329, 2006. 163 117. R. Jain, R. Kasturi, and B.G. Schunck, Machine Vision, McGH, 1995. 118. R. Adams and L. Bischof, Seeded region growing. IEEE Trans. PAMI, Vol. 16, No. 6, pp. 641- 647, 1994. 119. N. Passat, C. Ronse, J. Baruthio, J. P. Armspach, C. Maillot, and C. Jahn, Region-growing segmentation of brain vessels: An atlas-based automatic approach, Journal of Magnetic Resonance Imaging, Vol. 21, pp. 715-725, 2005. 120. N. Passat, C. Ronse, J. Baruthio, J.P. Armspach, C. Maillot, Magnetic resonance angiography: from anatomical knowledge modelling to vessel segmentation. Vol. 10, pp. 259-274, 2006. 121. N. Passat, C. Ronse, J. Baruthio, J.-P. Armspach, and J. Foucher, Using watershed and multimodal data for vessel segmentation: application to the superior sagittal sinus. In: Proceedings of ISMM, Paris, France, pp. 419–428, 2005. 122. H. Sekiguchi, N. Sugimoto, S. Eiho, T. Hanakawa, and S. Urayama, Blood vessel segmentation for head MRA using branch-based region growing, Systems and Computers in Japan, Vol. 36, No. 5, pp. 80-88, 2005. 123. P.J. Yim, P.L. Choyke, and R.M. Summers, Gray-scale skeletonization of small vessels in magnetic resonance angiography, IEEE Transactions on Medical Imaging, , Vol. 19, No. , pp. 568-576, 2000. 124. H. Schmitt, M. Grass, V. Rasche, O. Schramm, S. Haehnel, and K. Sartor, An x-ray-based method for the determination of the contrast agent propagation in 3-d vessel structures, IEEE Transactions on Medical Imaging, Vol. 21, pp. 164 251–262, 2002. 125. J. F. OBrien and N. F. Ezquerra, Automated segmentation of coronary vessels in angiographic image sequences utilizing temporal, spatial structural constraints, in Proc. SPIE Conf. Visualization in Biomed. Computing, 1994. 126. W.E. Higgins, W.J.T. Sypra, R.A. karwoski, and E.L. Ritman, System for analyzing higresolution three-dimensional coronary angiograms, IEEE Transactions on Medical Imaging, Vol. 15, pp. 377–385, June 1996. 127. M. Donizelli, Region-oriented segmentation of vascular structures from DSA images using mathematical morphology and binary region growing, vol. 0, 0. 128. A.D. Dempster, N.M. Larid, and D.B. Rubin, Maximum likelihood from the incomplete data via the EM algorithm, J. R. Statist. Soc. Vol. 39, pp. 1-37, 1977. 129. A.C.S. Chung, J.A. Noble, and P. Summers, Fusing speed and phase information for vascular segmentation of phase contrast MR angiograms, Medical Image Analysis, Vol. 6, No. 2, pp. 109–128, 2002. 130. M.S. Hassouna, A.A Farag., S. Hushek, and T. Moriarty, Cerebrovascular segmentation from TOF using stochastic models, Medical Image Analysis, Vol. 10, pp.2-18, 2006. 131. A. El-Baz, A.A Farag., G. Gimel’farb, and M.A. El-Ghar, A new adaptive probabilistic model of blood vessels for segmentation MRA images, MICCAI, LNCS, Vol. 4191, pp. 799-806, 2006. 132. S. Kobashi, N. Kamiura, Y. Hata, and F. Miyawaki: Fuzzy information granulation on blood vessel extraction from 3D TOF MRA image. IJPRAI, Vol. 165 14, No. 4, pp. 409-425, 2000. 133. J. K. Udupa and S. Samarasekera, Fuzzy connectedness and object delineation: Theory, algorithm, and applications in image segmentation, Graph. Models Image Processing, Vol. 58, No. 3, pp. 246–261, 1996. 134. J. K. Udupa, D. Odhner, J. Tian, G. Holland, and L. Axel, Automatic clutter free volume rendering for MR angiography using fuzzy connectedness, SPIE, Vol. 3034, pp. 114–119, 1997. 135. B.E. Chapman, J.O. Stapelton, D.L. Parker, Intracranial vessel segmentation from time of flight MRA using pre-processing of the MIP Z-buffer: accuracy of the ZBS algorithm, Medical Image Analysis, Vol. 8, pp. 113-126, 2004. 136. H. Blum, A transformation for extracting new descriptors of shape. In Models for the Perception of Speech and Visual Form. W. Wathen-Dunn, Ed., MIT Press, Cambridge, Mass., pp. 362-380, 1967. 137. A. Okbe, B. Boots and K. Sugihara, Spatial Tesselations, Concepts and Applications of Voronoi Diagrams, John Wiley and Sons, 1992 138. R. L. Ogniewicz and O. Kubler Hierarchic Voronoi skeletons, Pattern recognition, Vol. 28, No. 3, pp. 343-359, 1995. 139. G. Bertrand and G. Malandain, A new characterization of three-dimensional simple points, Pattern recognition Letters, Vol. 15, pp. 169-175, 1994. 140. T. Lee, R. Kashyap and C. Chu, Building skeleton models via 3D medial face/axis thinning algorithms, Computer Vision Graphics Image Processing (CVGIP): Graphical models and image processing, Vol. 56, No. 6, pp. 462-478, 166 1994. 141. G. Bertrand, A parallel thinning algorithm for medial surfaces, Pattern recognition Letters, Vol. 16, pp. 97-98, 1995. 142. I. Nystrom, Skeletonization applied to magnetic resonance angiography images, Medical imaging 1998: Image processing, SPIE, Vol. 3338, pp. 693-701, 1998. 143. K. Pal´agyi, J. Tschirren, and M. Sonka, Quantitative analysis of three-dimensional tubular tree structures, Medical Imaging, Proceedings of SPIE, Vol. 5032, pp. 277–287, 2003. 144. G. Borggefors, Distance transformation in arbitrary dimensions, Computer Vision, Graphics, and Image Processing, Vol. 27, pp. 321-345, 1984. 145. F.A. Zampirolli and R.A. Lotufo, Classification of the distance transformation algorithms under the morphological approach. IEEE Proceedings of the 13th Brazilian symposium on computer graphics and image processing, pp. 292-299, 2000. 146. Q.M. Hu, Two and Three Dimensional Skeletonization, PCT patent application. Int. Pub. No. WO 02/058008, 2002. 147. S. Bouix, K. Siddiqi, and A. Tannenbaum. Flux Driven Fly Throughs. International Conference on Computer Vision and Pattern Recognition, 2003. 148. N. Gagvani and D. Silver, Technical report, CAIP-TR-216, Parameter Controlled skeletonization of 3D Objects, June 1997. 149. F. Leymaire and M. D. Levine, Simulating the grassfire transform using an active contour model. IEEE Transactions on Pattern Analysis and Machine 167 Intelligence, Vol. 14, No. 1, pp. 56-75, 1992. 150. Y. Zhou and W. Toga, Efficient skeletonization of volumetric objects, IEEE Transactions on Visualization and Computer Graphics, Vol. 5, No. 3, pp. 196-209, 1999. 151. M. Sato, I. Bitter, M.A. Bender, A.E. Kaufman, and M. Nakajima, TEASAR: tree structure extraction algorithm for accurate and robust skeletons, IEEE Eighth Pacific Conference on Computer Graphics and Applications, pp. 281, 2000. 152. I. Bitter, M. Sato, M.A. Bender, K.T. McDonnel, A. Kaufman, and M. Wan, CEASAR: A smooth, accurate and robust centerline extraction algorithm. Visualization 2000, pp. 45-52, 2000. 153. Z. Chen and S. Molloi, Automatic 3D vascular tree construction in CT angiography. CMIG, Vol. 27, pp. 469-479, 2003. 154. T. Lindeberg and B. M. ter Haar Romeny. Linear scale-space: I. basic theory. II. early visual operations, In B. M. ter Haar Romeny, editor, Geometry-Driven Diffusion in Computer Vision, Computational Imaging and Vision, pp. 1-38, 39-72. Kluwer Academic Publishers, Dordrecht, the Netherlands, 1994. 155. B. M. ter Haar Romeny and L. M. J. Florack. A multiscale geometric model of human vision. In William R. Hendee and Peter N. T. Wells, editors, Perception of Visual Information, chapter 4, pp. 73–114. Springer-Verlag, Berlin, 1993. Second edition 1996. 156. B. M. ter Haar Romeny. Applications of scale-space theory. In J. Sporring, M. Nielsen, L. Florack, and P. Johansen, editors. Gaussian Scale-Space Theory. 168 Kluwer Academic Publishers, Dordrecht, The Netherlands, 1997. 157. M. Xu, The multiscale medial properties of interfering image structures. Pattern Recognition Letters, Vol. 25, No.1, pp. 21-34, 2004. 158. A. Almansa and T. Lindeberg. Fingerprint enhancement by shape adaptation of scale-space operators with automatic scale-selection. IEEE Transactions on Image Processing, Vol. 9, No. 12, pp. 2027-2042, 2000. 159. H.J. Noordmans, A.W.M. Smeulders, M.A.Viergever, Accurate tracking of blood vessels and EEG electrodes by Consecutive Cross-Section Matching, SPIE, Vol. 3661. pp. 1637-1645, 1999. 160. H. Tek, D. Comaniciu and J. Williams. Vessel detection by mean-shift based on ray propagation, IEEE workshop on Mathematical Methods in Biomedical Image Analysis, 2001. 161. N. Flasque, M. Desvignes, J.M. Constans, and M. Revenu, Acquisition, segmentation and tracking of the cerebral vascular tree on 3D magnetic resonance angiography images. Medical Image Analysis, Vol. 5, pp. 173-183, 2001. 162. M. Hernandez Hoyos, P. Oriowski, E. Piatkowska-Janko, P. Bogorodzki, M. Orkisz, Vascular centerline extraction in 3D MR angiograms for phase contrast MRI blood flow measurement, Int. J. CARS, Vol. 1, pp. 51-61, 2006. 163. B. Jähne Digital Image Processing, 6Th Rev. and Ext. Ed. Berlin; New York: Springer Science & Business Media, 2005. 164. Walter Rudin, Functional analysis. Singapore, McGraw-Hill, 1991. 169 165. S. Huang, R. Baimouratov, I. Volkau, and W.L. Nowinski, IVEM: A tool for editing, manipulation, quantification, and labeling of cerebrovascular models, Computerized Medical Imaging and Graphics, Vol. 30, No. 3, pp. 187-195, 2006. 166. 3DView free visualization software, available at: http://www.i10.org.uk/pooled/articles/BF_WEBART/view.asp?Q=BF_WEBART _136905 167. W.L. Nowinski, A. Thirunavuukarasuu, I.Volkau, V.M. Runge, N. Salamon, G. Salamon, Atlas of cerebral vasculature, 92 Radiological Society of North America Scientific Assembly and Annual Meeting, RSNA, Chicago USA 2006. 168. V.H. Patel, MRI of the brain: normal anatomy and normal variants, V.H. Patel, L.Friedman. Phildelphia: W.B. Saunders, 1997. 169. B. Johnson and B. Shneiderman, Tree-maps: A space-filling approach to the visualization of hierarchical information structures, in Proceedings of IEEE Visualization (VIS), pp. 284-291, 1991. 170. P.J. Yim, J.J. Cebral, R. Mullick, H.B. Marcos, P.L. Choyke. Vessel surface reconstruction with a tubular deformable model, IEEE Transactions on Medical Imaging, Vol. 20, No. 12, pp. 1411 –1421, 2001. 170 Appendix A. Evaluation of the segmentation result True positive rate False positive rate W-N Local adaptive W-N Local adaptive Av 73.56% 74.92% 3.72% 11.44% Std 9.11% 5.71% 3.28% 7.29% Table A-1 True positive rate and false positive rate of the segmented data evaluated based on the ground truth edited by an anatomist. True positive rate False positive rate W-N Local adaptive W-N Local adaptive Av 70.10% 84.55% 12.81% 18.45% Std 7.16% 9.37% 2.56% 9.56% Table A-2 True positive rate and false positive rate of the segmented branchings evaluated based on the ground truth anatomy edited by an anatomist. 171 B. Reconstructed 3D cerebral vascular models Figure B-1 3D cerebral vascular models reconstructed from 1T (raw and 2) and1.5T (raw and 4) MRA data. Column is MIP images of original data; column is reconstructed from ground truth edited by an anatomist; column is reconstructed from our segmented data; column is reconstructed from W-N result. 172 C. Measured elliptical vessel cross section Figure C-1. The circular cross section (green) after centerline extraction procedure and the elliptical cross section (red) after elliptical measurement 173 [...]... arteries in the chest Two carotids cerebral circulations consist of connected sets of vessels that supply the front and top of the head The vertebral arterial circulation supplies the rest of the brain such as brainstem, cerebellum, the occipital, lobe of the cerebrum, and parts of the thalamus At the base of the brain, the carotid and vertebral arteries form a circle referred to as the circle of Willis... Characteristic of 3D TOF MRA data of a healthy volunteer………….60 Figure 3-8 MIPs from a sagittal view of the complete vasculature of the healthy volunteer………………………………………………………………61 Figure 3-9 MIPs of the volunteer’s vasculature after manually removing part of the venous system and vessels in the skull……………………………… 62 Figure 3-10 Difference of the left internal carotid artery (ICA) siphon and some distal vessels of. .. skeleton (or centerline) of vasculature from the binary data as concise representation of the vasculature [16] The skeleton of a 3D object could be defined as the locus of centers 5 of all maximal spheres inscribed in the object, thus touching its boundary at least at 2 points [1] The major difficulties in processing the cerebral vascular angiographic data can be listed as the following [17]: 1) Vessel... efficient than the previous methods Local shape is detected by iteratively computing it from the second derivative at the center of the vessel cross section Thus, the size of the vessel can be more accurately measured according to its shape than using the linear medialness The convergence of the iterative procedure is proven in this dissertation The superiority of the elliptical model generated from the angiographic... into animations, thus creating the illusion of rotation 3D volume model represents the vasculature with volume data The vasculature firstly needs to be segmented from the angiography data [16] Then it may be viewed by directly rendering the volume as a block of data or by rendering the isosurface extracted from the volume with a fixed threshold determining the locations of the surface Volume rendering... Figure 4-19 Anterior cerebral arteries (ACAs) (1) and the Circle of Willis (2) in the 3D displays………………………………………………………… 108 Figure 4-20 Internal carotid arteries (ICA) (1) and the vertebral arteries (2)….…109 Figure 4-21 3D displays of the cerebral vasculature of a patient (Data ID: GD_1T_05) scanned under 1T Siemens scanner……………… ….110 Figure 4-22 3D displays of the cerebral vasculature of a patient (Data... through three communicating arteries It is an important anatomy of the cerebral vasculature If one of the main arteries (carotids or vertebral) is occluded, the brain can still function normally, since the distal smaller arteries, supplied by the occluded arteries can still receive blood from the other two circulations Figure 1-2 Anatomy of human cerebral vaculature 3 1.2 Magnetic Resonance Angiography Main... further accurate measurement Then, the hybrid strategy goes back to the Gray-scale image to measure the cross section with scale space method under the guidance of previous circular centerline model It takes advantage of the tree structure produced by the skeletonization approach, so that the elliptical measurement procedure in the third step could stably go over bifurcation and go through the whole vasculature. .. processing techniques (the shaded block in Figure 1-1) to generate a representation of cerebral vasculature for efficient visualization in medical applications Figure 1-1 Procedures to generate a visualization of vasculature 2 1.1 Human Cerebral Vasculature The brain receives blood from two pairs of large vessels [14]: the internal carotid arteries, which arise from arteries in the neck, and the vertebral arteries,... images to the circular model generated from binary data is demonstrated 1.6 Scope of Dissertation The dissertation begins with a literature review of the geometric models of vasculature in Chapter 2 It categorizes the related works in two groups based on deformable models and the centerline models In each group, the fundamental theories and the state of art techniques are reviewed in detail 14 The main . IMPROVED MODELLING OF THE HUMAN CEREBRAL VASCULATURE ZHENG WEILI (M.Eng) A THESIS SUBMITTED FOR THE DEGREE OF DOCTOR OF PHILOSOPHY DEPARTMENT OF MECHANICAL. from the 3D TOF MRA data of a volunteer…58 Figure 3-7 Characteristic of 3D TOF MRA data of a healthy volunteer………….60 Figure 3-8 MIPs from a sagittal view of the complete vasculature of the. 4-21 3D displays of the cerebral vasculature of a patient (Data ID: GD_1T_05) scanned under 1T Siemens scanner……………… ….110 Figure 4-22 3D displays of the cerebral vasculature of a patient (Data