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
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)
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
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
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
Hille, B.: Ionic Channels of Excitable Membranes, 2nd edn. Sinauer Associates, Sunderland, MA (1992)
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
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
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
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
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
Hunter, P., McCulloch, A., Nielsen, P., Smaill, B.: A finite element model of passive ventricular mechanics. ASMS BED 9(1988) 387–397
Sachse, F.B.: Computational Cardiology: Modeling of Anatomy, Electrophysiology, and Mechanics. LNCS 2966. Springer, Berlin, Heidelberg, New York (2004)
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
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
Taylor, C., Hughes, T., Zarins, C.: Effect of exercise on hemodynamic conditions in the abdominal aorta. Journal of Vascular Surgery 29(1999) 1077–89
Sahni, O.: Adaptive procedure for efficient blood-flow simulations. PhD thesis, RPI (2005)
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)
Yin, L., Luo, X., Shephard, M.S.: Identifying and meshing thin sections of 3-d curved domains. Technical report, RPI (2005)
Hackbusch, W.: Multi-Grid Methods and Applications. Springer Verlag, Berlin, Heidelberg, New York, Tokyo (1985)
Braess, D.: Towards algebraic multigrid for elliptic problems of second order. Computing 55(1995) 379–393
Brown, P., Byrne, G., Hindmarsh, A.: VODE: a variable-coefficient ode solver. SIAM Journal on Scientific Computation 10(1989) 1038–1057
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
Team, P.E.: Essential Atlas of Anatomy, English edn. Parramon Ediciones, Barcelona, Spain (2001)
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
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
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
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
Park, S.M., Gladish, G.W., Bajaj, C.L.: Artery-vein separation from thoracic CTA scans. IEEE Transactions on Medical Imaging (Submitted)
Park, S.M., Gladish, G.W., Bajaj, C.L.: Automatic pulmonary embolism detection from thoracic CTA scans. IEEE Transactions on Medical Imaging (Submitted)
Schoepf, U.J., Costello, P.: Ct angiography for diagnosis of pulmonary embolism: state of the art. Radiology 230(2) (2004) 329–337
Gonzalez, R., Woods, R.: Digital image processing. Addison-Wesley, New York (1992)
Pratt, W.: Digital Image Processing, 2nd edn. A Wiley-Interscience, New York (1991)
Caselles, V., Lisani, J., Morel, J., Sapiro, G.: Shape preserving local histogram modification. IEEE Transactions on Image Processing 8(2) (1998) 220–230
Stark, J.: Adaptive contrast enhancement using generalization of histogram equalization. IEEE Transactions on Image Processing 9(5) (2000) 889–906
Jobson, D., Rahman, Z., Woodell, G.: Properties and performance of a center/surround retinex. IEEE Transactions on Image Processing 6(3) (1997) 451–462
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
Lu, J., Healy, D., Weaver, J.: Contrast enhancement of medical images using multiscale edge representation. Optical Engineering 33(7) (1994) 2151–2161
Laine, A., Schuler, S., Fan, J., Huda, W.: Mammographic feature enhancement by multiscale analysis. IEEE Transactions on Medical Imaging 13(4) (1994) 725–738
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
Deriche, R.: Fast algorithm for low-level vision. IEEE Transactions on Pattern Recognition and Machine Intelligence 12(1) (1990) 78–87
Young, I., Vliet, L.: Recursive implementation of the gaussian filter. Signal Processing 44(1995) 139–151
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
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
Elad, M.: On the bilateral filter and ways to improve it. IEEE Transactions On Image Processing 11(10) (2002) 1141–1151
Tomasi, C., Manduchi, R.: Bilateral filtering for gray and color images. In: 1998 IEEE International Conference on Computer Vision (1998) 836–846
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
Weickert, J.: Anisotropic Diffusion In Image Processing. ECMI Series, Teubner, Stuttgart, ISBN 3-519-02606-6 (1998)
Donoho, D., Johnson, I.: Ideal spatial adaptation via wavelet shrinkage. Biometrika 81(1994) 425–455
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
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
Hamza, A.B., Krim, H.: Image denoising: A nonlinear robust statistical approach. IEEE Transactions on Signal Processing 49(12) (2001) 3045–3054
Stoschek, A., Hegerl, R.: Denoising of electron tomographic reconstructions using multiscale transformations. Journal of Structural Biology 120(1997) 257–265
Frangakis, A., Hegerl, R.: Noise reduction in electron tomographic reconstructions using nonlinear anisotropic diffusion. Journal of Structural Biology 135(2001) 239–250
Bajaj, C., Wu, Q., Xu, G.: Level set based volumetric anisotropic diffusion. In: ICES Technical Report 301, The University of Texas at Austin (2003)
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
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
Bezdek, J.: A convergence theorem for the fuzzy ISODATA clustering algorithm. IEEE Transactions on Pattern Analysis Machine Intelligence 2(1) (1980) 1–8
Titterington, D.M., Smith, A.F.M., Makov, U.E.: Statistical Analysis of Finite Mixture Dis-trubutions. J. Wiley, Chichester (1985)
Pham, D.L., Prince, J.L.: Adaptive fuzzy segmentation of magnetic resonance images. IEEE Transactions on Medical Imaging 18(9) (1998) 737–752
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
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)
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
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
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)
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)
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
Laidlaw, D.: Geometric Model Extraction from Magnetic Resonance Volume Data (PhD thesis). PhD thesis, CalTech University, Arizona (1995)
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
Xu, C., Prince, J.L.: Snakes, shapes, and gradient vector flow. IEEE Transactions on Image Processing 7(3) (1998) 359–369
Yu, Z., Bajaj, C.: Normalized gradient vector diffusion and image segmentation. In: Proceedings of European Conference on Computer Vision (2002) 517–530
Bajaj, C., Pascucci, V., Schikore, D.: The contour spectrum. In: Proceedings of IEEE Visualization Conference (1997) 167–173
Park, S., Bajaj, C.: Feature selection of 3d volume data through multi-dimensional transfer functions. Pattern Recognition Letters 28(3) (2007) 367–374
Ellis, R.: Macromolecular crowding: obvious but underappreciated. Trends in Biochemical Sciences 26(10) (2001) 597–604
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
Kremer, J., Mastronarde, D., McIntosh, J.: Computer visualization of three-dimensional image data using imod. Journal of Structural Biology 116(1996) 71–76
Li, Y., Leith, A., Frank, J.: Tinkerbell-a tool for interactive segmentation of 3d data. Journal of Structural Bioloby 120(3) (1997) 266–275
McEwen, B., Marko, M.: Three-dimensional electron micros-copy and its application to mitosis research. Methods in Cell Biology 61(1999) 81–111
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
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
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
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
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
Marko, M., Leith, A.: Sterecon - three-dimensional reconstructions from stereoscopic contouring. Journal of Structural Biology 116(1) (1996) 93–98
Bajaj, C., Yu, Z., Auer, M.: Volumetric feature extraction and visualization of tomographic molecular imaging. Journal of Structural Biology 145(1) (2004) 168–180
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
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
Malladi, R., Sethian, J.: A real-time algorithm for medical shape recovery. In: IEEE International Conference on Computer Vision (1998) 304–310
Sethian, J.: A marching level set method for monotonically advancing fronts. Proceedings of the National Academy Science 93(4) (1996) 1591–1595
Sethian, J.: Level Set Methods and Fast Marching Methods, 2nd edn. Cambridge University Press, Cambridge (1999)
Sifakis, E., Tziritas, G.: Moving object localization using a multi-label fast marching algorithm. Signal Processing: Image Communication 16(10) (2001) 963–976
Tari, S., Shah, J., Pien, H.: Extraction of shape skeletons from gray-scale images. Computer Vision and Image Understanding 66(2) (1997) 133–146
Chung, D.H., Sapiro, G.: Segmentation-free skeletonization of gray-scale images via pde's. In: International Conference on Image Processing. (2000) 927–930
Lindeberg, T.: Scale-space Theory in Computer Vision. The Kluwer International Series in Engineering and Computer Science, Kluwer, Netherlands (1994)
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
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
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
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
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
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
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
Dutt, A., Rokhlin, V.: Fast fourier transform for nonequispaced data. SIAM Journal of Scientific Computing 14(1993) 1368–1393
Dutt, A., Rokhlin, V.: Fast fourier transform for nonequispaced data ii. Applied and Computational Harmonic Analysis 2(1995) 85–100
Brown, L.G.: A survey of image registration techniques. ACM Computing Surveys 24(4) (1992) 325–376
Bajcsy, R., Kovacic, S.: Multiresolution elastic matching. Computer Vision Graphics and Image Processing 46(1–21) (1989) 1–21
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
Yanovsky, I., Thompson, P., Osher, S., Leow, A.: Large deformation unbiased diffeomorphic nonlinear image registration: Theory and implementation. Technical report, UCLA CAM (2006)
Clarenz, U., Droske, M., Rumpf, M.: Towards fast non-rigid registration. Proceedings of the AMS 313(2002) 67–84
Mumford, D., Shah, J.: Optimal approximations by piecewise smooth functions and associated variational problems. Communications on and Pure Applied Mathematics 42(4) (1989)
Lorensen, W., Cline, H.: Marching Cubes: A High Resolution 3D Surface Construction Algorithm. In: SIGGRAPH. (1987) 163–169
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
Dey, T.K.: Curve and Surface Reconstruction: Algorithms with Mathematical Analysis. Cambridge Monographs on Applied and Computational Mathematics (2006)
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
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
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
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
Dey, T.K., Giesen, J., Goswami, S., Zhao, W.: Shape dimension and approximation from samples. Discrete and Computaional Geometry 29(2003) 419–434
Siersma, D.: Voronoi diagrams and morse theory of the distance function (1999)
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
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)
Dey, T.K., Zhao, W.: Approximate medial axis as a Voronoi subcomplex. Computer Aided Design 36(2) (2003) 195–202
Chazal, F., Lieutier, A.: The λ-medial axis. Graphical models 67(4) (2005) 304–331
Cocone: Tight Cocone Software for surface reconstruction and medial axis approximation. http://www.cse.ohio-state.edu/?tamaldey/cocone.html (2003)
Borgefors, G., Nystrom, I., Baja, G.D.: Computing skeletons in three dimensions. Pattern Recognition 32(7) (1999)
Bitter, I., Kaufman, A., Sato, M.: Penalized distance volumetric skeleton algorithm. IEEE TVCG 7(3) (2001)
Bouix, S., Siddiqi, K., Tannenbaum, A.: Flux driven fly throughs. In: IEEE Conference on Computer Vision and Pattern Recognition. (2003) 449–454
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
Zhou, Y., Toga, A.: Efficient skeletonization of volumetric objects. IEEE Transactions on Visualization and Computer Graphics 5(3) (1999) 196–209
Cornea, N., Silver, D., Yuan, X., Balasubramaniam, R.: Computing hierarchical curveskele-tons of 3D objects. The Visual Computer 21(11) (2005) 945–955
Dey, T.K., Sun, J.: Defining and computing curve-skeletons with medial geodesic functions. In: Symposium on Geometry Processing. (2006) 143–152
Costa, L.: Multidimensional scale space shape analysis. In: IWSNHC3DI. (1999) 214–217
Ogniewicz, R.L., Kubler, O.: Hierachic voronoi skeletons. Pattern Recognition 28(3) (1995) 343–359
Verroust, A., Lazarus, F.: Extracting skeletal curves from 3D scattered data. The Visual Computer 16(2000) 15–25
Cornea, N., Silver, D., Min, P.: Curve skeleton applications. In: IEEE Visualization. (2005) 95–102
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
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
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
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
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
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
Farin, G.: Curves and Surfaces for CAGD: A Practical Guide. 5th edn. Morgan-Kaufmann, San Francisco, CA (2002)
Catmull, E., Clark, J.: Recursively generated b-spline surfaces on arbitrary topological surfaces. Computer-Aided Design 10(6) (1978) 350–355
Doo, D.: A subdivision algorithm for smoothing down irregularly shaped polyhedrons. In: Proceedings on Interactive Techniques in Computer Aided Design. (1978) 157–165
Doo, D., Sabin, M.: Behavior of recursive division surfaces near extraordinary points. Computer-Aided Design 10(6) (1978) 356–360
Loop, C.: A g 1 triangular spline surface of arbitrary topological type. Computer Aided Geometric Design 11(3) (1994) 303–330
Krishnamurthy, V., Levoy, M.: Fitting smooth surfaces to dense polygon meshes. In: Proceedings of SIGGRAPH. (1996) 313–324
Eck, M., Hoppe, H.: Automatic reconstruction of b-spline surfaces of arbitrary topological type. In: Proceedings of SIGGRAPH. (1996) 325–334
Cohen-Steiner, D., Alliez, P., Desbrun, M.: Variational shape approximation. In: Proceedings of SIGGRAPH. (2004) 905–914
Dong, S., Bremer, P.T., Garland, M., Pascucci, V., Hart, J.: Spectral surface quadrangulation. ACM Transactions on Graphics 25(3) (2006) 1057–1066
Ying, L., Zorin, D.: A simple manifold-based construction of surfaces of arbitrary smoothness. ACM Transactions on Graphics 23(3) (2004) 271–275
Bajaj, C., Chen, J., Xu, G.: Modeling with cubic A-patches. ACM Transactions on Graphics 14(2) (1995) 103–133
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
Bajaj, C., Xu, G., Holt, R., Netravali, A.: Hierarchical multiresolution reconstruction of shell surfaces. Computer Aided Geometric Design 19(2002) 89–112
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
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
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
Rogers, D.F.: An Introduction to NURBS With Historical Perspective. Academic, San Diego, CA (2001)
Piegl, L., Tiller, W.: The NURBS Book (Monographs in Visual Communication), 2nd edn. Springer, New York (1997)
Thompson, J.F., Soni, B.K., Weatherill, N.P.: Grid Generation. CRC Press LLC, Boca Raton, FL (1999)
Gursoy, H.N.: Tetrahedral finite element mesh generation from nurbs solid models. Engineering with Computers 12(19) (1996) 211–223
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)
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
Hughes, T.J., Cottrell, J.A., Bazilevs, Y.: Isogeometric analysis: CAD, finite elements, NURBS, exact geometry, and mesh refinement. CMAME 194(2005) 4135–4195
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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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