
This Article  
 
Share  
Bibliographic References  
Add to:  
Digg Furl Spurl Blink Simpy Del.icio.us Y!MyWeb  
Search  
 
ASCII Text  x  
Sang Wook Yoo, JoonKyung Seong, MinHyuk Sung, Sung Yong Shin, Elaine Cohen, "A TriangulationInvariant Method for Anisotropic Geodesic Map Computation on Surface Meshes," IEEE Transactions on Visualization and Computer Graphics, vol. 18, no. 10, pp. 16641677, Oct., 2012.  
BibTex  x  
@article{ 10.1109/TVCG.2012.29, author = {Sang Wook Yoo and JoonKyung Seong and MinHyuk Sung and Sung Yong Shin and Elaine Cohen}, title = {A TriangulationInvariant Method for Anisotropic Geodesic Map Computation on Surface Meshes}, journal ={IEEE Transactions on Visualization and Computer Graphics}, volume = {18}, number = {10}, issn = {10772626}, year = {2012}, pages = {16641677}, doi = {http://doi.ieeecomputersociety.org/10.1109/TVCG.2012.29}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  JOUR JO  IEEE Transactions on Visualization and Computer Graphics TI  A TriangulationInvariant Method for Anisotropic Geodesic Map Computation on Surface Meshes IS  10 SN  10772626 SP1664 EP1677 EPD  16641677 A1  Sang Wook Yoo, A1  JoonKyung Seong, A1  MinHyuk Sung, A1  Sung Yong Shin, A1  Elaine Cohen, PY  2012 KW  Measurement KW  Equations KW  Surface treatment KW  Approximation algorithms KW  Least squares approximation KW  shape analysis. KW  Geodesic KW  anisotropy KW  surface mesh KW  HamiltonJacobiBellman KW  curvature minimization KW  curvature variation minimization VL  18 JA  IEEE Transactions on Visualization and Computer Graphics ER   
[1] S. Katz and A. Tal, "Hierarchical Mesh Decomposition Using Fuzzy Clustering and Cuts," Proc. ACM SIGGRAPH '03, pp. 954961, 2003.
[2] T. Funkhouser, M. Kazhdan, P. Shilane, P. Min, W. Kiefer, A. Tal, S. Rusinkiewicz, and D. Dobkin, "Modeling by Example," ACM Trans. Graphics, vol. 23, no. 3, pp. 652663, 2004.
[3] G. Zigelman, R. Kimmel, and N. Kiryati, "Texture Mapping Using Surface Flattening via Multidimensional Scaling," IEEE Trans. Visualization and Computer Graphics, vol. 8, no. 2, pp. 198207, Apr.June 2002.
[4] K. Zhou, J. Synder, B. Guo, and H.Y. Shum, "IsoCharts: StretchDriven Mesh Parameterization Using Spectral Analysis," Proc. Eurographics/ACM SIGGRAPH Symp. Geometry Processing (SGP '04), pp. 4554, 2004.
[5] G. Peyré and L.D. Cohen, "Geodesic Remeshing Using Front Propagation," Int'l J. Computer Vision, vol. 69, no. 1, pp. 145156, 2006.
[6] O. Sifri, A. Sheffer, and C. Gotsman, "GeodesicBased Surface Remeshing," Proc. 12th Int'l. Meshing Roundtable, pp. 189199, 2003.
[7] Q. Du and D. Wang, "Anisotropic Centroidal Voronoi Tessellations and Their Applications," SIAM J. Scientific Computing, vol. 26, no. 3, pp. 737761, 2005.
[8] A. Elad and R. Kimmel, "Bending Invariant Representations for Surfaces," Proc. IEEE CS Conf. Computer Vision and Pattern Recognition, vol. 1, pp. 168174, 2001.
[9] M. Hilaga, Y. Shinagawa, T. Kohmura, and T.L. Kunii, "Topology Matching for Fully Automatic Similarity Estimation of 3D Shapes," Proc. ACM SIGGRAPH '01, pp. 203212, 2001.
[10] A.M. Bronstein, M.M. Bronstein, and R. Kimmel, "Generalized Multidimensional Scaling: A Framework for IsometryInvariant Partial Surface Matching," Proc. Nat'l Academy of Sciences of USA, vol. 103, no. 5, pp. 11681172, 2006.
[11] E. Pichon, C.F. Westin, and A. Tannenbaum, "A HamiltonJacobiBellman Approach to High Angular Resolution Diffusion Tractography," Proc. Eighth Int'l Conf. Medical Image Computing and ComputerAssisted Intervention (MICCAI '05), pp. 180187, 2005.
[12] S. Rusinkiewicz, "Estimating Curvatures and Their Derivatives on Triangle Meshes," Proc. Second Int'l Symp. 3D Data Processing, Visualization and Transmission, pp. 486493, Sept. 2004.
[13] J.A. Sethian and A.M. Popovici, "3D Traveltime Computation Using the Fast Marching Method," Geophysics, vol. 64, no. 2, pp. 516523, 2006.
[14] R. Kimmel and J. Sethian, "Computing Geodesic Paths on Manifolds," Proc. Nat'l Academy of Sciences of USA, vol. 95, no. 15, pp. 84318435, 1998.
[15] J.A. Sethian and A. Vladimirsky, "Ordered Upwind Methods for Static HamiltonJacobi Equations: Theory and Algorithms," SIAM J. Numerical Analysis, vol. 41, no. 1, pp. 325363, 2003.
[16] J.S.B. Mitchell, D.M. Mount, and C.H. Papadimitriou, "The Discrete Geodesic Problem," SIAM J. Computing, vol. 16, no. 4, pp. 647668, 1987.
[17] V. Surazhsky, T. Surazhsky, D. Kirsanov, S.J. Gortler, and H. Hoppe, "Fast Exact and Approximate Geodesics on Meshes," ACM Trans. Graphics, vol. 24, no. 3, pp. 553560, 2005.
[18] D. Bommes and L. Kobbelt, "Accurate Computation of Geodesic Distance Fields for Polygonal Curves on Triangle Meshes," Proc. VMV '07, pp. 151160, 2007.
[19] J. Klein and G. Zachmann, "Point Cloud Surfaces using Geometric Proximity Graphs," Computers and Graphics, vol. 28, no. 6, pp. 839850, 2004.
[20] M. Hofer and H. Pottmann, "EnergyMinimizing Splines in Manifolds," ACM Trans. Graphics, vol. 23, no. 3, pp. 284293, 2004.
[21] M.R. Ruggeri, T. Darom, D. Saupe, and N. Kiryati, "Approximating Geodesics on Point Set Surfaces," Proc. IEEE/Eurographics Symp. PointBased Graphics, pp. 8593, 2006.
[22] J.A. Sethian, "A Fast Marching Level Set Method for Monotonically Advancing Fronts," Proc. Nat'l Academy of Sciences of USA, vol. 93, pp. 15911595, 1996.
[23] F. Qin, Y. Luo, K. Olsen, W. Cai, and G. Schuster, "FiniteDierence Solution of the Eikonal Equation along Expanding Wavefronts," Geophysics, vol. 57, no. 3, pp. 478487, 1992.
[24] J. Tsitsiklis, "Efficient Algorithms for Globally Optimal Trajectories," IEEE Trans. Automatic Control, vol. 40, no. 9, pp. 1528 1538, Sept. 1995.
[25] F. Mémoli and G. Sapiro, "Fast Computation of Weighted Distance Functions and Geodesics on Implicit HyperSurfaces: 730," J. Computational Physics, vol. 173, no. 2, p. 764, 2001.
[26] F. Memoli and G. Sapiro, "Distance Functions and Geodesics on Points Cloud," Proc. IEEE Workshop Variational Geometric and Level Set Methods in Computer Vision, 2003.
[27] A. Spira and R. Kimmel, "An Efficient Solution to the Eikonal Equation on Parametric Manifolds," Interfaces and Free Boundaries, vol. 6, pp. 315327, 2003.
[28] O. Weber, Y.S. Devir, A.M. Bronstein, M.M. Bronstein, and R. Kimmel, "Parallel Algorithms for Approximation of Distance Maps on Parametric Surfaces," ACM Trans. Graphics, vol. 27, no. 4, pp. 116, 2008.
[29] P.E. Danielsson, "Euclidean Distance Mapping," Computer Graphics and Image Processing, vol. 14, no. 3, pp. 227248, 1980.
[30] M. Boue and P. Dupuis, "Markov Chain Approximations for Deterministic Control Problems with Affine Dynamics and Quadratic Cost in the Control," Proc. IEEE 36th Conf. Decision and Control, vol. 4, pp. 3424 3429, Dec. 1997.
[31] J. Qian, Y.T. Zhang, and H.K. Zhao, "A Fast Sweeping Method for Static Convex HamiltonJacobi Equations," J. Scientific Computing, vol. 31, nos. 1/2, pp. 237271, 2007.
[32] C.Y. Kao, S. Osher, and J. Qian, "LegendreTransformBased Fast Sweeping Methods for Static HamiltonJacobi Equations on Triangulated Meshes," J. Computational Physics, vol. 227, no. 24, pp. 10 20910 225, 2008.
[33] L. Polymenakos, D. Bertsekas, and J. Tsitsiklis, "Implementation of Efficient Algorithms for Globally Optimal Trajectories," IEEE Trans. Automatic Control, vol. 43, no. 2, pp. 278283, Feb. 1998.
[34] F. Bornemann and C. Rasch, "FiniteElement Discretization of Static HamiltonJacobi Equations Based on a Local Variational Principle," Computing and Visualization in Science, vol. 9, pp. 5769, 2006.
[35] W.K. Jeong, P.T. Fletcher, R. Tao, and R. Whitaker, "Interactive Visualization of Volumetric White Matter Connectivity in DTMRI Using a ParallelHardware HamiltonJacobi Solver," IEEE Trans. Visualization and Computer Graphics, vol. 13, no. 6, pp. 14801487, Nov. 2007.
[36] J.K. Seong, W.K. Jeong, and E. Cohen, "Anisotropic Geodesic Distance Computation for Parametric Surfaces," Proc. IEEE Int'l Conf. Shape Modeling and Applications, pp. 179186, June 2008.
[37] J.A. Sethian and A. Vladimirsky, "Fast Methods for the Eikonal and Related Hamilton?? Jacobi Equations on Unstructured Meshes," Proc. Nat'l Academy of Sciences of the USA, vol. 97, no. 11, pp. 56995703, 2000.
[38] E. Konukoglu, M. Sermesant, O. Clatz, J.M. Peyrat, H. Delingette, and N. Ayache, "A Recursive Anisotropic Fast Marching Approach to Reaction Diffusion Equation: Application to Tumor Growth Modeling," Proc. 20th Int'l Conf. Information Processing in Medical Imaging (IPMI '07), pp. 687699, 2007.
[39] H. Wang, C. Scheidegger, and C. Silva, "Optimal Bandwidth Selection for Mls Surfaces," Proc. IEEE Int'l Conf. Shape Modeling and Applications, pp. 111120, June 2008.
[40] K. Watanabe and A. Belyaev, "Detection of Salient Curvature Features on Polygonal Surfaces," Computer Graphics Forum, vol. 20, pp. 385392, 2001.
[41] D. DeCarlo, A. Finkelstein, S. Rusinkiewicz, and A. Santella, "Suggestive Contours for Conveying Shape," ACM Trans. Graphics, vol. 22, no. 3, pp. 848855, 2003.
[42] N. Amenta, S. Choi, T.K. Dey, and N. Leekha, "A Simple Algorithm for Homeomorphic Surface Reconstruction," Proc. 16th Ann. Symp. Computational Geometry (SCG '00), pp. 213222, 2000.
[43] CGAL, "Computational Geometry Algorithms Library," http:/www.cgal.org, 2009.
[44] K. Siddiqi, S. Bouix, A. Tannenbaum, and S.W. Zucker, "HamiltonJacobi Skeletons," Int'l J. Computer Vision, vol. 48, no. 3, pp. 215231, 2002.
[45] Y. Shi, P. Thompson, I. Dinov, and A. Toga, "Hamilton? Jacobi Skeleton on Cortical Surfaces," IEEE Trans. Medical Imaging, vol. 27, no. 5, pp. 664673, May 2008.
[46] Y. Ohtake, A. Belyaev, and H.P. Seidel, "RidgeValley Lines on Meshes via Implicit Surface Fitting," ACM Trans. Graphics, vol. 23, no. 3, pp. 609612, 2004.