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Modeling Cardiovascular Anatomy from Patient-Specific Imaging

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Part of the book series: Computational Methods in Applied Sciences ((COMPUTMETHODS,volume 13))

The importance of modern imaging techniques for capturing detailed structural information of a biological system cannot be understated. Unfortunately images do not reveal the “full functional story” and a spatially realistic computer model is often necessary for a comprehensive understanding of the complicated structural and physiological properties of the biological system's entities under investigation [1]. Deeper insights into structure-to-function relationships of different entities is achieved via finite element simulations of the modeled biomedical process. A 3D (three dimensional) finite element meshed computer model of the biological system is therefore a first step to perform such simulations.

The behavioral attributes of a biological entity or the physiological interaction between different participating components of a biological system are often modeled mathematically via a coupled set of differential and integral equations, and quite often numerically evaluated using finite element (or boundary element) simulations. To further emphasize the premise of cardiac modeling from imaging data, we state a few computational biomedical modeling and simulation examples: 3D computational modeling of the human heart for a quantitative analysis of cyclical electrical conductance on the heart membrane [2–6]; the biomechanical properties (stress-strain, elasticity) of the heart ventricular walls [7–12]; 3D modeling and simulation of pulsatile blood flow through human arteries/veins for vascular by-pass surgery pre-planning on a patient specific basis [13–18]. A finite element decomposition of the geometric domain, capturing the detailed spatial features that can be gleaned from the imaging, is therefore the essential first step toward performing the necessary numerical simulations [19–22].

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References

  1. Winslow, R.L., Scollan, D.F., Greenstein, J.L., Yung, C.K., Jr., W.B., Bhanot, G., Gresh, D.L., Rogowitz, B.E.: Mapping, modeling, and visual exploration of structure-function relationships in the heart. Deep Computing for the Life Sciences 40(2) (2001)

    Google Scholar 

  2. Luo, C., Rudy, Y.: A model of the ventricular cardiac action potential: Depolarization, repo-larization and their interaction. Circulation Research 68(6) (1991) 1501–1526

    Google Scholar 

  3. Luo, C., Rudy, Y.: A dynamic model of the cardiac ventricular action potential: I. simulations of ionic currents and concentration changes. Circulation Research 74(6) (1994) 1071–1096

    Google Scholar 

  4. Hodgkin, A.L., Huxley, A.F.: A quantitative description of membrane current and its application to conduction and excitation in nerve. Journal of Physiology 117(1952) 500–544

    Google Scholar 

  5. Hille, B.: Ionic Channels of Excitable Membranes, 2nd edn. Sinauer Associates, Sunderland, MA (1992)

    Google Scholar 

  6. Winslow, R.L., Scollan, D.F., Holmes, A., Yung, C.K., Zhang, J., Jafri, M.S.: Electrophys-iological modeling of cardiac ventricular function: from cell to organ. Annual Reviews in Biomedical Engineering 2(2000) 119–155

    Article  Google Scholar 

  7. Vetter, F., McCulloch, A., Rogers, J.: A finite element model of passive mechanics and electrical propagation in the rabbit ventricles. Computers in Cardiology (1998) 705–708

    Google Scholar 

  8. Rogers, J.M., McCulloch, A.D.: A collocation-galerkin finite element model of cardiac action potential propagation. IEEE Transactions on Biomedical Engineering 41(1994) 743–757

    Article  Google Scholar 

  9. Rudy, Y., Plonsey, R.: A comparison of volume conductor and source geometry effects on body surface and epicardial potentials. Circulation Research 46(1980) 283–291

    Google Scholar 

  10. Costa, K.D., Hunter, P.J., Wayne, J.S., Waldmann, L.K., Guccione, J.M., McCulloch, A.D.: A three-dimensional finite element method for large elastic deformations of ventricular myocardium: Ii — prolate spheroidal coordinates. Journal of Biomedical Engineering 118(4) (1996) 464–472

    Google Scholar 

  11. Hunter, P., McCulloch, A., Nielsen, P., Smaill, B.: A finite element model of passive ventricular mechanics. ASMS BED 9(1988) 387–397

    Google Scholar 

  12. Sachse, F.B.: Computational Cardiology: Modeling of Anatomy, Electrophysiology, and Mechanics. LNCS 2966. Springer, Berlin, Heidelberg, New York (2004)

    Google Scholar 

  13. Taylor, C., Hughes, T., Zarins, C.: Finite element modeling of blood flow in arteries. Computer Methods in Applied Mechanics and Engineering 158(1–2) (1998) 155–196

    Article  MATH  MathSciNet  Google Scholar 

  14. Taylor, C., Hughes, T., Zarins, C.: Finite element modeling of 3-dimensional pulsatile flow in the abdominal aorta: relevance to atherosclerosis. Annals of Biomedical Engineering 26(6) (1998) 1–13

    Article  Google Scholar 

  15. Taylor, C., Hughes, T., Zarins, C.: Effect of exercise on hemodynamic conditions in the abdominal aorta. Journal of Vascular Surgery 29(1999) 1077–89

    Article  Google Scholar 

  16. Sahni, O.: Adaptive procedure for efficient blood-flow simulations. PhD thesis, RPI (2005)

    Google Scholar 

  17. Sahni, O., Mueller, J., Jansen, K.E., Shephard, M.S., Taylor, C.A.: Efficient anisotropic adaptive discretization of the cardiovascular system. Technical report, RPI (2005)

    Google Scholar 

  18. Yin, L., Luo, X., Shephard, M.S.: Identifying and meshing thin sections of 3-d curved domains. Technical report, RPI (2005)

    Google Scholar 

  19. Hackbusch, W.: Multi-Grid Methods and Applications. Springer Verlag, Berlin, Heidelberg, New York, Tokyo (1985)

    MATH  Google Scholar 

  20. Braess, D.: Towards algebraic multigrid for elliptic problems of second order. Computing 55(1995) 379–393

    Article  MATH  MathSciNet  Google Scholar 

  21. Brown, P., Byrne, G., Hindmarsh, A.: VODE: a variable-coefficient ode solver. SIAM Journal on Scientific Computation 10(1989) 1038–1057

    Article  MATH  MathSciNet  Google Scholar 

  22. de Munck, J.: A linear discretization of the volume conductor boundary integral equation using analytically integrated elements. IEEE Transactions on Biomedical Engineering 39(9) (1992) 986–990

    Article  Google Scholar 

  23. Team, P.E.: Essential Atlas of Anatomy, English edn. Parramon Ediciones, Barcelona, Spain (2001)

    Google Scholar 

  24. Zhang, Y., Bazilevs, Y., Goswami, S., Bajaj, C.L., Hughes, T.J.R.: Patient-specific vascular nurbs modeling for isogeometric analysis of blood flow. Computer Methods in Applied Mechanics and Engineering (CMAME) 196(29–30) (2007) 2943–2959

    Article  MATH  MathSciNet  Google Scholar 

  25. Gady Agam, Samuel G. Armato, I., Wu, C.: Vessel tree reconstruction in thoracic ct scans with application to nodule detection. IEEE Transaction on Medical Imaging 24(4) (2005) 486–499

    Article  Google Scholar 

  26. Dehmeshki, J., Ye, X., Wang, F., Lin, X.Y., Abaei, M., Siddique, M., Qanadli, S.: An accurate and reproducible scheme for quantification of coronary artery calcification in ct scans. In: Proceedings of the 26th Annual International Conference of IEEE EMBS, IEEE, The International Society for Optical Engineering (2004) 1918–1921

    Google Scholar 

  27. Yoshitaka Masutani, H.M., Doi, J.: Computerized detection of pulmonary embolism in spiral ct angiography based on volumetric image analysis. IEEE Transaction on Medical Imaging 21(12) (2002) 1517–1523

    Article  Google Scholar 

  28. Park, S.M., Gladish, G.W., Bajaj, C.L.: Artery-vein separation from thoracic CTA scans. IEEE Transactions on Medical Imaging (Submitted)

    Google Scholar 

  29. Park, S.M., Gladish, G.W., Bajaj, C.L.: Automatic pulmonary embolism detection from thoracic CTA scans. IEEE Transactions on Medical Imaging (Submitted)

    Google Scholar 

  30. Schoepf, U.J., Costello, P.: Ct angiography for diagnosis of pulmonary embolism: state of the art. Radiology 230(2) (2004) 329–337

    Article  Google Scholar 

  31. Gonzalez, R., Woods, R.: Digital image processing. Addison-Wesley, New York (1992)

    Google Scholar 

  32. Pratt, W.: Digital Image Processing, 2nd edn. A Wiley-Interscience, New York (1991)

    MATH  Google Scholar 

  33. Caselles, V., Lisani, J., Morel, J., Sapiro, G.: Shape preserving local histogram modification. IEEE Transactions on Image Processing 8(2) (1998) 220–230

    Article  Google Scholar 

  34. Stark, J.: Adaptive contrast enhancement using generalization of histogram equalization. IEEE Transactions on Image Processing 9(5) (2000) 889–906

    Article  Google Scholar 

  35. Jobson, D., Rahman, Z., Woodell, G.: Properties and performance of a center/surround retinex. IEEE Transactions on Image Processing 6(3) (1997) 451–462

    Article  Google Scholar 

  36. Jobson, D., Rahman, Z., Woodell, G.: A multiscale retinex for bridging the gap between color images and the human observation of scenes. IEEE Transactions on Image Processing 6(7) (1997) 965–976

    Article  Google Scholar 

  37. Lu, J., Healy, D., Weaver, J.: Contrast enhancement of medical images using multiscale edge representation. Optical Engineering 33(7) (1994) 2151–2161

    Article  Google Scholar 

  38. Laine, A., Schuler, S., Fan, J., Huda, W.: Mammographic feature enhancement by multiscale analysis. IEEE Transactions on Medical Imaging 13(4) (1994) 725–738

    Article  Google Scholar 

  39. Yu, Z., Bajaj, C.: A fast and adaptive algorithm for image contrast enhancement. In: Proceedings of IEEE International Conference on Image Processing. (2004) 1001–1004

    Google Scholar 

  40. Deriche, R.: Fast algorithm for low-level vision. IEEE Transactions on Pattern Recognition and Machine Intelligence 12(1) (1990) 78–87

    Article  Google Scholar 

  41. Young, I., Vliet, L.: Recursive implementation of the gaussian filter. Signal Processing 44(1995) 139–151

    Article  Google Scholar 

  42. Barash, D.: A fundamental relationship between bilateral filtering, adaptive smoothing and the nonlinear diffusion equation. IEEE Transactions on Pattern Analysis and Machine Intelligence 24(6) (2002) 844–847

    Article  Google Scholar 

  43. Durand, F., Dorsey, J.: Fast bilateral filtering for the display of high-dynamic-range images. In: ACM Conference on Computer Graphics (SIGGRAPH) (2002) 257–266

    Google Scholar 

  44. Elad, M.: On the bilateral filter and ways to improve it. IEEE Transactions On Image Processing 11(10) (2002) 1141–1151

    Article  MathSciNet  Google Scholar 

  45. Tomasi, C., Manduchi, R.: Bilateral filtering for gray and color images. In: 1998 IEEE International Conference on Computer Vision (1998) 836–846

    Google Scholar 

  46. Perona, P., Malik, J.: Scale-space and edge detection using anisotropic diffusion. IEEE Transactions on Pattern Analysis and Machine Intelligence 12(7) (1990) 629–639

    Article  Google Scholar 

  47. Weickert, J.: Anisotropic Diffusion In Image Processing. ECMI Series, Teubner, Stuttgart, ISBN 3-519-02606-6 (1998)

    Google Scholar 

  48. Donoho, D., Johnson, I.: Ideal spatial adaptation via wavelet shrinkage. Biometrika 81(1994) 425–455

    Article  MATH  MathSciNet  Google Scholar 

  49. Xu, Y., Weaver, J.B., Healy, D.M., Lu, J.: Wavelet transform domain filters: A spatially selective noise filtration technique. IEEE Transactions on Image Processing 3(6) (1994) 747–758

    Article  Google Scholar 

  50. Hamza, A.B., Luque, P., Martinez, J., Roman, R.: Removing noise and preserving details with relaxed median filters. Journal of Mathematical Imaging and Vision 11(2) (1999) 161–177

    Article  MathSciNet  Google Scholar 

  51. Hamza, A.B., Krim, H.: Image denoising: A nonlinear robust statistical approach. IEEE Transactions on Signal Processing 49(12) (2001) 3045–3054

    Article  Google Scholar 

  52. Stoschek, A., Hegerl, R.: Denoising of electron tomographic reconstructions using multiscale transformations. Journal of Structural Biology 120(1997) 257–265

    Article  Google Scholar 

  53. Frangakis, A., Hegerl, R.: Noise reduction in electron tomographic reconstructions using nonlinear anisotropic diffusion. Journal of Structural Biology 135(2001) 239–250

    Article  Google Scholar 

  54. Bajaj, C., Wu, Q., Xu, G.: Level set based volumetric anisotropic diffusion. In: ICES Technical Report 301, The University of Texas at Austin (2003)

    Google Scholar 

  55. Jiang, W., Baker, M., Wu, Q., Bajaj, C., Chiu, W.: Applications of bilateral denoising filter in biological electron microscopy. Journal of Structural Biology 144(2003) 114–122

    Article  Google Scholar 

  56. Yu, Z., Bajaj, C.: A segmentation-free approach for skeletonization of gray-scale images via anisotropic vector diffusion. In: IEEE International Conference on Computer Vision and Pattern Recognition (CVPR'04). Volume 1. (2004) 415–420

    Google Scholar 

  57. Bezdek, J.: A convergence theorem for the fuzzy ISODATA clustering algorithm. IEEE Transactions on Pattern Analysis Machine Intelligence 2(1) (1980) 1–8

    Article  MATH  Google Scholar 

  58. Titterington, D.M., Smith, A.F.M., Makov, U.E.: Statistical Analysis of Finite Mixture Dis-trubutions. J. Wiley, Chichester (1985)

    Google Scholar 

  59. Pham, D.L., Prince, J.L.: Adaptive fuzzy segmentation of magnetic resonance images. IEEE Transactions on Medical Imaging 18(9) (1998) 737–752

    Article  Google Scholar 

  60. Pham, D.L., Prince, J.L.: An adaptive fuzzy c-means algorithm for image segmentation in the presence of intensity inhomogeneities. Pattern Recognition Letters 20(1) (1999) 57–68

    Article  MATH  Google Scholar 

  61. Ahmed, M.N., Yamany, S.M., Farag, A.A., Moriarty, T.: A bias field estimation and adaptive segmentation of MRI data using a modified Fuzzy C-Means algorithm. In: Proceedings of 13th International Conference on Computer Assisted Radiology and Surgery (1999)

    Google Scholar 

  62. Ahmed, M.N., Yamany, S.M., Mohamed, N., Farag, A.A.: A modified fuzzy c-means algorithm for bias field estimation and segmentation of MRI data. IEEE Transactions on Medical Imaging 21(3) (2002) 193–199

    Article  Google Scholar 

  63. Gopal, S.S., Hebert, T.J.: Maximum likelihood pixel labeling using a spatially variant finite. IEEE Transaction on Nuclear Science 44(4) (1999) 1578–1582

    Article  Google Scholar 

  64. Laidlaw, D.H., Fleischer, K.W., Barr, A.H.: Bayesian mixture classification of mri data for geometric modeling and visualization. A poster presented at the First International Workshop on Statistical Mixture Modeling, Aussois, France (1995)

    Google Scholar 

  65. Ahmed, M.N., Yamany, S.M., Mohamed, N., Farag, A.A., Moriarty, T.: A modified fuzzy c-means algorithm for bias field estimation and segmentation of mri data. IEEE Transactions on Medical Imaging 21(3) (2002)

    Google Scholar 

  66. Kindlmann, G., Darkin, J.W.: Semi-automatic generation of transfer functions for direct volume rendering. In: Proceedings of 1998 Symposium on Volume Visualization (1998) 79–86

    Google Scholar 

  67. Laidlaw, D.: Geometric Model Extraction from Magnetic Resonance Volume Data (PhD thesis). PhD thesis, CalTech University, Arizona (1995)

    Google Scholar 

  68. Tomasi, C., R.Madcuchi: Bilateral filtering for gray and color images. In: Proceedings of the 1998 IEEE International Conference on Computer Vision, Bombay, India (1998) 839–846

    Google Scholar 

  69. Xu, C., Prince, J.L.: Snakes, shapes, and gradient vector flow. IEEE Transactions on Image Processing 7(3) (1998) 359–369

    Article  MATH  MathSciNet  Google Scholar 

  70. Yu, Z., Bajaj, C.: Normalized gradient vector diffusion and image segmentation. In: Proceedings of European Conference on Computer Vision (2002) 517–530

    Google Scholar 

  71. Bajaj, C., Pascucci, V., Schikore, D.: The contour spectrum. In: Proceedings of IEEE Visualization Conference (1997) 167–173

    Google Scholar 

  72. Park, S., Bajaj, C.: Feature selection of 3d volume data through multi-dimensional transfer functions. Pattern Recognition Letters 28(3) (2007) 367–374

    Article  Google Scholar 

  73. Ellis, R.: Macromolecular crowding: obvious but underappreciated. Trends in Biochemical Sciences 26(10) (2001) 597–604

    Article  Google Scholar 

  74. Hessler, D., Young, S.J., Ellisman, M.H.: A flexible environment for the visualization of three-dimensional biological structures. Journal of Structural Biology 116(1) (1996) 113–119

    Article  Google Scholar 

  75. Kremer, J., Mastronarde, D., McIntosh, J.: Computer visualization of three-dimensional image data using imod. Journal of Structural Biology 116(1996) 71–76

    Article  Google Scholar 

  76. Li, Y., Leith, A., Frank, J.: Tinkerbell-a tool for interactive segmentation of 3d data. Journal of Structural Bioloby 120(3) (1997) 266–275

    Article  Google Scholar 

  77. McEwen, B., Marko, M.: Three-dimensional electron micros-copy and its application to mitosis research. Methods in Cell Biology 61(1999) 81–111

    Article  Google Scholar 

  78. Harlow, M., Ress, D., Stoschek, A., Marshall, R., McMahan, U.: The architecture of active zone material at the frog's neuromuscular junction. Nature 409(2001) 479–484

    Article  Google Scholar 

  79. Volkmann, N.: A novel three-dimensional variant of the watershed transform for segmentation of electron density maps. Journal of Structural Biology 138(1–2) (2002) 123–129

    Article  Google Scholar 

  80. Frangakis, A.S., Hegerl, R.: Segmentation of two- and three-dimensional data from electron microscopy using eigenvector analysis. Journal of Structural Biology 138(1–2) (2002) 105–113

    Article  Google Scholar 

  81. Zhou, Z.H., Baker, M.L., Jiang, W., Dougherty, M., Jakana, J., Dong, G., Lu, G., Chiu, W.: Electron cryomicroscopy and bioinformatics suggest protein fold models for rice dwarf virus. Nature Structural Biology 8(10) (2001) 868–873

    Article  Google Scholar 

  82. Jiang, W., Li, Z., Baker, M.L., Prevelige, P.E., Chiu, W.: Coat protein fold and maturation transition of bacteriophage p22 seen at subnanometer resolution. Nature Structural Biology 10(2) (2003) 131–135

    Article  Google Scholar 

  83. Marko, M., Leith, A.: Sterecon - three-dimensional reconstructions from stereoscopic contouring. Journal of Structural Biology 116(1) (1996) 93–98

    Article  Google Scholar 

  84. Bajaj, C., Yu, Z., Auer, M.: Volumetric feature extraction and visualization of tomographic molecular imaging. Journal of Structural Biology 145(1) (2004) 168–180

    Article  Google Scholar 

  85. Yu, Z., Bajaj, C.: Automatic ultrastructure segmentation of reconstructed cryoem maps of icosahedral viruses. IEEE Transactions on Image Processing: Special Issue on Molecular and Cellular Bioimaging 14(9) (2005) 1324–1337

    Google Scholar 

  86. Baker, M., Yu, Z., Chiu, W., Bajaj, C.: Automated Segmentation of Molecular Subunits in Electron Cryomicroscopy Density Maps. Journal of Structural Biology (2006) online— version

    Google Scholar 

  87. Malladi, R., Sethian, J.: A real-time algorithm for medical shape recovery. In: IEEE International Conference on Computer Vision (1998) 304–310

    Google Scholar 

  88. Sethian, J.: A marching level set method for monotonically advancing fronts. Proceedings of the National Academy Science 93(4) (1996) 1591–1595

    Article  MATH  MathSciNet  Google Scholar 

  89. Sethian, J.: Level Set Methods and Fast Marching Methods, 2nd edn. Cambridge University Press, Cambridge (1999)

    MATH  Google Scholar 

  90. Sifakis, E., Tziritas, G.: Moving object localization using a multi-label fast marching algorithm. Signal Processing: Image Communication 16(10) (2001) 963–976

    Article  Google Scholar 

  91. Tari, S., Shah, J., Pien, H.: Extraction of shape skeletons from gray-scale images. Computer Vision and Image Understanding 66(2) (1997) 133–146

    Article  Google Scholar 

  92. Chung, D.H., Sapiro, G.: Segmentation-free skeletonization of gray-scale images via pde's. In: International Conference on Image Processing. (2000) 927–930

    Google Scholar 

  93. Lindeberg, T.: Scale-space Theory in Computer Vision. The Kluwer International Series in Engineering and Computer Science, Kluwer, Netherlands (1994)

    Google Scholar 

  94. Pizer, S.M., Eberly, D., Fritsch, D.S., Morse, B.S.: Zoom invariant vision of figural shape: The mathematics of cores. Computer Vision and Image Understanding 69(1) (1998) 55–71

    Article  Google Scholar 

  95. Morse, B.S., Pizer, S.M., Puff, D.T., Gu, C.: Zoominvariant vision of figural shape: Effects on cores of images disturbances. Computer Vision and Image Understanding 69(1) (1998) 72–86

    Article  Google Scholar 

  96. Jang, J.H., Hong, K.S.: A pseudo-distance map for the segmentation-free skeletonization of gray-scale images. In: Proceedings of the International Conference on Computer Vision. (2001) 18–23

    Google Scholar 

  97. Castro, E.D., Morandi, C.: Registartion of translated and rotated images using finite fourier transforms. IEEE Transactions on Patten Analysis and Machine Intelligence 9(5) (1986) 700–703

    Google Scholar 

  98. Kuglin, C.D., Hines, D.C.: The phase correlation image alignment method. In: Proceedings of IEEE International Conference on Cybrnetics and Society. (1975) 163–165

    Google Scholar 

  99. Lehmann, T.M.: A two stage algorithm for model-based registration of medical images. In: Proceedings of the International Conference on Pattern Recognition ICPR'98. (1998) 344–352

    Google Scholar 

  100. Araiza, R., Averill, M., Keller, G., Starks, S., Bajaj, C.: 3D image registration using Fast Fourier Transform, with potential applications to geoinformatics and bioinformatics. In: Proceedings of the International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems IPMU06. (2006) 817–824

    Google Scholar 

  101. Dutt, A., Rokhlin, V.: Fast fourier transform for nonequispaced data. SIAM Journal of Scientific Computing 14(1993) 1368–1393

    Article  MATH  MathSciNet  Google Scholar 

  102. Dutt, A., Rokhlin, V.: Fast fourier transform for nonequispaced data ii. Applied and Computational Harmonic Analysis 2(1995) 85–100

    Article  MATH  MathSciNet  Google Scholar 

  103. Brown, L.G.: A survey of image registration techniques. ACM Computing Surveys 24(4) (1992) 325–376

    Article  Google Scholar 

  104. Bajcsy, R., Kovacic, S.: Multiresolution elastic matching. Computer Vision Graphics and Image Processing 46(1–21) (1989) 1–21

    Article  Google Scholar 

  105. Christensen, G.E., Rabbitt, R.D., Miller, M.I.: Deformable templates using large deformation kinematics. IEEE Transaction on Image Processing 5(10) (1996) 1435–1447

    Article  Google Scholar 

  106. Yanovsky, I., Thompson, P., Osher, S., Leow, A.: Large deformation unbiased diffeomorphic nonlinear image registration: Theory and implementation. Technical report, UCLA CAM (2006)

    Google Scholar 

  107. Clarenz, U., Droske, M., Rumpf, M.: Towards fast non-rigid registration. Proceedings of the AMS 313(2002) 67–84

    MathSciNet  Google Scholar 

  108. Mumford, D., Shah, J.: Optimal approximations by piecewise smooth functions and associated variational problems. Communications on and Pure Applied Mathematics 42(4) (1989)

    Google Scholar 

  109. Lorensen, W., Cline, H.: Marching Cubes: A High Resolution 3D Surface Construction Algorithm. In: SIGGRAPH. (1987) 163–169

    Google Scholar 

  110. Lopes, A., Brodlie, K.: Improving the robustness and accuracy of the marching cubes algorithm for isosurfacing. In: IEEE Transactions on Visualization and Computer Graphics. Volume 9. (2003) 16–29

    Article  Google Scholar 

  111. Dey, T.K.: Curve and Surface Reconstruction: Algorithms with Mathematical Analysis. Cambridge Monographs on Applied and Computational Mathematics (2006)

    Google Scholar 

  112. Dey, T.K., Goswami, S.: Tight cocone: A water-tight surface reconstructor. In: Proceedings of the 8th ACM Symposium on Solid Modeling and Applications. (2003) 127–134

    Google Scholar 

  113. Zhao, H., Osher, S., Fedkiw, R.: Fast surface reconstruction using the level set method. In: 1st IEEE Workshop on Variational and Level Set Methods. (2001) 194–202

    Google Scholar 

  114. Bajaj, C., Xu, G., Zhang, X.: Bio-Molecular surface constructions via a higher-order level-set method. In: Proceedings of the 14th CAD/CG International Conference, 2007, Beijing, China

    Google Scholar 

  115. Cheng, S.W., Wang, Y., Wu, Z.: Provable dimension detection using principal component analysis. In: Proceedings of the Symposium on Computational Geometry (2005) 208–217

    Google Scholar 

  116. Dey, T.K., Giesen, J., Goswami, S., Zhao, W.: Shape dimension and approximation from samples. Discrete and Computaional Geometry 29(2003) 419–434

    Article  MATH  MathSciNet  Google Scholar 

  117. Siersma, D.: Voronoi diagrams and morse theory of the distance function (1999)

    Google Scholar 

  118. Dey, T.K., Giesen, J., Goswami, S.: Shape segmentation and matching with flow discretization. In: Dehne, F., Sack, J.R., Smid, M., eds.: Proceedings of Workshop Algorithms Data Structures (WADS 03). LNCS 2748, Berlin, Germany (2003) 25–36

    Google Scholar 

  119. Bajaj, C., Gillette, A., Goswami, S.: Topology based selection and curation of level sets. In: TopoInVis 2007, edited by A. Wiebel and H. Hege and K. Polthier and G. Scheuermann (Accepted)

    Google Scholar 

  120. Dey, T.K., Zhao, W.: Approximate medial axis as a Voronoi subcomplex. Computer Aided Design 36(2) (2003) 195–202

    Article  Google Scholar 

  121. Chazal, F., Lieutier, A.: The λ-medial axis. Graphical models 67(4) (2005) 304–331

    Article  MATH  Google Scholar 

  122. Cocone: Tight Cocone Software for surface reconstruction and medial axis approximation. http://www.cse.ohio-state.edu/?tamaldey/cocone.html (2003)

  123. Borgefors, G., Nystrom, I., Baja, G.D.: Computing skeletons in three dimensions. Pattern Recognition 32(7) (1999)

    Google Scholar 

  124. Bitter, I., Kaufman, A., Sato, M.: Penalized distance volumetric skeleton algorithm. IEEE TVCG 7(3) (2001)

    Google Scholar 

  125. Bouix, S., Siddiqi, K., Tannenbaum, A.: Flux driven fly throughs. In: IEEE Conference on Computer Vision and Pattern Recognition. (2003) 449–454

    Google Scholar 

  126. Hassouna, M.S., Farag, A.A.: Robust centerline extraction framework using level sets. In: IEEE Conference on Computer Vision and Pattern Recognition. (2005) 458–465

    Google Scholar 

  127. Zhou, Y., Toga, A.: Efficient skeletonization of volumetric objects. IEEE Transactions on Visualization and Computer Graphics 5(3) (1999) 196–209

    Article  Google Scholar 

  128. Cornea, N., Silver, D., Yuan, X., Balasubramaniam, R.: Computing hierarchical curveskele-tons of 3D objects. The Visual Computer 21(11) (2005) 945–955

    Article  Google Scholar 

  129. Dey, T.K., Sun, J.: Defining and computing curve-skeletons with medial geodesic functions. In: Symposium on Geometry Processing. (2006) 143–152

    Google Scholar 

  130. Costa, L.: Multidimensional scale space shape analysis. In: IWSNHC3DI. (1999) 214–217

    Google Scholar 

  131. Ogniewicz, R.L., Kubler, O.: Hierachic voronoi skeletons. Pattern Recognition 28(3) (1995) 343–359

    Article  Google Scholar 

  132. Verroust, A., Lazarus, F.: Extracting skeletal curves from 3D scattered data. The Visual Computer 16(2000) 15–25

    Article  MATH  Google Scholar 

  133. Cornea, N., Silver, D., Min, P.: Curve skeleton applications. In: IEEE Visualization. (2005) 95–102

    Google Scholar 

  134. Goswami, S., Dey, T.K., Bajaj, C.L.: Identifying flat and tubular regions of a shape by unstable manifolds. In: Proceedings of the 11th Symposium Solid and Physical Modeling. (2006) 27–37

    Google Scholar 

  135. Eckstein, I., Joshi, A.A., Kuo, C.J., Leahy, R., Desbrun, M.: Generalized surface flows for deformable registration and cortical matching. In: MICCAI. (2007) 183–192

    Google Scholar 

  136. Amenta, N., Choi, S., Kolluri, R.: The power crust, unions of balls, and the medial axis transform. Computational Geometry: Theory and Applications 19(2–3) (2001) 127–153

    MATH  MathSciNet  Google Scholar 

  137. Tama, F., Miyashita, O., Brooks, C.: Flexible multi-scale fitting of atomic structures into low-resolution electron density maps with elastic network normal mode analysis. Journal of Molecular Biology 337(2004) 985–999

    Article  Google Scholar 

  138. Zhang, Y., Bajaj, C.: Adaptive and quality quadrilateral/hexahedral meshing from volumetric data. Computer Methods in Applied Mechanics and Engineering (CMAME) 195(9–12) (2006) 942–960

    Article  MATH  MathSciNet  Google Scholar 

  139. Ju, T., Losasso, F., Schaefer, S., Warren, J.: Dual contouring of hermite data. In: SIGGRAPH 2002, Computer Graphics Proceedings, ACM Press / ACM SIGGRAPH. (2002) 339–346

    Google Scholar 

  140. Farin, G.: Curves and Surfaces for CAGD: A Practical Guide. 5th edn. Morgan-Kaufmann, San Francisco, CA (2002)

    Google Scholar 

  141. Catmull, E., Clark, J.: Recursively generated b-spline surfaces on arbitrary topological surfaces. Computer-Aided Design 10(6) (1978) 350–355

    Article  Google Scholar 

  142. Doo, D.: A subdivision algorithm for smoothing down irregularly shaped polyhedrons. In: Proceedings on Interactive Techniques in Computer Aided Design. (1978) 157–165

    Google Scholar 

  143. Doo, D., Sabin, M.: Behavior of recursive division surfaces near extraordinary points. Computer-Aided Design 10(6) (1978) 356–360

    Article  Google Scholar 

  144. Loop, C.: A g 1 triangular spline surface of arbitrary topological type. Computer Aided Geometric Design 11(3) (1994) 303–330

    Article  MATH  MathSciNet  Google Scholar 

  145. Krishnamurthy, V., Levoy, M.: Fitting smooth surfaces to dense polygon meshes. In: Proceedings of SIGGRAPH. (1996) 313–324

    Google Scholar 

  146. Eck, M., Hoppe, H.: Automatic reconstruction of b-spline surfaces of arbitrary topological type. In: Proceedings of SIGGRAPH. (1996) 325–334

    Google Scholar 

  147. Cohen-Steiner, D., Alliez, P., Desbrun, M.: Variational shape approximation. In: Proceedings of SIGGRAPH. (2004) 905–914

    Google Scholar 

  148. Dong, S., Bremer, P.T., Garland, M., Pascucci, V., Hart, J.: Spectral surface quadrangulation. ACM Transactions on Graphics 25(3) (2006) 1057–1066

    Article  Google Scholar 

  149. Ying, L., Zorin, D.: A simple manifold-based construction of surfaces of arbitrary smoothness. ACM Transactions on Graphics 23(3) (2004) 271–275

    Article  Google Scholar 

  150. Bajaj, C., Chen, J., Xu, G.: Modeling with cubic A-patches. ACM Transactions on Graphics 14(2) (1995) 103–133

    Article  Google Scholar 

  151. Bajaj, C., Xu, G.: Smooth shell construction with mixed prism fat surfaces. Brunett, G., Bieri,H., Farin, G. (eds.), Geometric Modeling Computing Supplement 14(2001) 19–35

    Google Scholar 

  152. Bajaj, C., Xu, G., Holt, R., Netravali, A.: Hierarchical multiresolution reconstruction of shell surfaces. Computer Aided Geometric Design 19(2002) 89–112

    Article  MATH  MathSciNet  Google Scholar 

  153. Goswami, S., Gillette, A., Bajaj, C.: Efficient Delaunay mesh generation from sampled scalar function. In: Proceedings of the 16th International Meshing Roundtable. (2007) 495–511

    Google Scholar 

  154. Zhang, Y., Bajaj, C., Sohn, B.S.: 3D finite element meshing from imaging data. The special issue of Computer Methods in Applied Mechanics and Engineering (CMAME) on Unstructured Mesh Generation 194(48–49) (2005) 5083–5106

    MATH  Google Scholar 

  155. Zhang, Y., Bajaj, C., Xu, G.: Surface smoothing and quality improvement of quadrilat-eral/hexahedral meshes with geometric flow. In: Proceedings of 14th International Meshing Roundtable. (2005) 449–468

    Google Scholar 

  156. Rogers, D.F.: An Introduction to NURBS With Historical Perspective. Academic, San Diego, CA (2001)

    Google Scholar 

  157. Piegl, L., Tiller, W.: The NURBS Book (Monographs in Visual Communication), 2nd edn. Springer, New York (1997)

    Google Scholar 

  158. Thompson, J.F., Soni, B.K., Weatherill, N.P.: Grid Generation. CRC Press LLC, Boca Raton, FL (1999)

    MATH  Google Scholar 

  159. Gursoy, H.N.: Tetrahedral finite element mesh generation from nurbs solid models. Engineering with Computers 12(19) (1996) 211–223

    Article  Google Scholar 

  160. Anderson, C.W., Crawford-Hines, S.: Fast generation of nurbs surfaces from polygonal mesh models of human anatomy. In: Technical Report CS-99-101, Colorado State University. (2000)

    Google Scholar 

  161. Yu, T.Y., Soni, B.K.: Nurbs evaluation and utilization for grid generation. In: 5th International Conference on Numerical Grid Generation in Computational Field Simulations. (1996) 323–332

    Google Scholar 

  162. Hughes, T.J., Cottrell, J.A., Bazilevs, Y.: Isogeometric analysis: CAD, finite elements, NURBS, exact geometry, and mesh refinement. CMAME 194(2005) 4135–4195

    MATH  MathSciNet  Google Scholar 

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Bajaj, C., Goswami, S. (2009). Modeling Cardiovascular Anatomy from Patient-Specific Imaging. In: Tavares, J.M.R.S., Jorge, R.M.N. (eds) Advances in Computational Vision and Medical Image Processing. Computational Methods in Applied Sciences, vol 13. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-9086-8_1

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