3D distance fields: A survey of techniques and applications

IEEE Transactions on Visualization and Computer Graphics

Volumn 12, Issue 4, 2006, Pages 518-599

  Jones, Mark W ^a,d   Bærentzen, J Andreas ^b   Sramek, Milos ^c  

^a SWANSEA UNIVERSITY   (United Kingdom)

^b TECHNICAL UNIVERSITY OF DENMARK   (Denmark)

^c ERICH SCHMID INSTITUTE OF MATERIALS SCIENCE   (Austria)

^d Department of Computer Science ^*  (United Kingdom)

Author keywords

Cut locus; Distance field; Distance transform; Fast marching method; Level set method; Medial axis; Skeletonization; Visualization; Volume; Volume data; Voxel; Voxelization

Indexed keywords

COMPUTATIONAL COMPLEXITY; COMPUTER GRAPHICS; COMPUTER VISION; FOURIER TRANSFORMS; LEVEL CONTROL; VISUALIZATION;

DISTANCE FIELDS; TECHNIQUES;

DISTANCE MEASUREMENT;

ALGORITHM; COMPARATIVE STUDY; COMPUTER ASSISTED DIAGNOSIS; COMPUTER GRAPHICS; COMPUTER INTERFACE; COMPUTER PROGRAM; EVALUATION; IMAGE ENHANCEMENT; INFORMATION RETRIEVAL; MATHEMATICAL COMPUTING; METHODOLOGY; REVIEW; THREE DIMENSIONAL IMAGING;

ALGORITHMS; COMPUTER GRAPHICS; IMAGE ENHANCEMENT; IMAGE INTERPRETATION, COMPUTER-ASSISTED; IMAGING, THREE-DIMENSIONAL; INFORMATION STORAGE AND RETRIEVAL; NUMERICAL ANALYSIS, COMPUTER-ASSISTED; SOFTWARE; USER-COMPUTER INTERFACE;

EID: 33744723487     PISSN: 10772626     EISSN: None     Source Type: Journal    
DOI: 10.1109/TVCG.2006.56     Document Type: Conference Paper

References (143)

1. H. Aanæs and J.A. Bærentzen, "Pseudo-Normals for Signed Distance Computation," Proc. Conf. Vision, Modeling, and Visualization, pp. 407-413, 2003.
2. M. Akmal Butt and P. Maragos, "Optimum Design of Chamfer Distance Transforms," IEEE Trans. Linage Processing, vol. 7, no. 10, pp. 1477-1484, 1998.
3. D. Adalsteinsson and J.A. Sethian, "The Fast Construction of Extension Velocities in Level-Set Methods," J. Computational Physics, vol. 148, no. 1, pp. 2-22, 1999.
4. J.A. Bæerentzen and H. Aanæs, "Signed Distance Computation Using the Angle Weighted Pseudo-Normal," IEEE Trans. Visualization and Computer Graphics, vol. 11, no. 3, pp. 243-253, May/ June 2005.
5. J.A. Bærentzen, "Volumetric Manipulations with Applications to Sculpting," PhD thesis, IMM, Technical Univ. of Denmark, 2001.
6. J.A. Bærentzen, "On the Implementation of Fast Marching Methods for 3D Lattices," Technical Report IMM-REP-2001-13, DTU.IMM, 2001.
7. J.A. Bærentzen, "Robust Generation of Signed Distance Fields from Triangle Meshes," Proc. Int'l Workshop Volume Graphics, pp. 167-175, June 2005.
8. A.H. Barr, "Superquadrics and Angle-Preserving Transformations, " IEEE Computer Graphics and Applications, vol., 1, no. 1, pp. 11-23, Jan. 1981.
9. M. Botsch, D. Bommes, C. Vogel, and L. Kobbelt, "CPU-Based Tolerance Volumes for Mesh Processing," Proc. Conf. Pacific Graphics '04, pp. 237-243, 2004.
10. J.A. Bærentzen and N.J. Christensen, "Interactive Modelling of Shapes Using the Level-Set Method," Int'l J. Shape Modeling, vol. 8, no. 2, pp. 79-97, Dec. 2002.
11. J.A. Bærentzen and N.J. Christensen, "A Technique for Volumentric CSG Based on Morphology," Proc. Conf. Volume Graphics '01, pp. 71-79, June 2002.
12. I. Bitter, A.E. Kaufman, and M. Sato, "Penalized-Distance Volumetric Skeleton Algorithm," IEEE Trans. Visualization and Computer Graphics, vol. 7, no. 3, pp. 195-206, 2001.
13. Introduction to Implicit Surfaces, J. Bloomonthal, ed., Computer Graphics and Geometric Modeling, Morgan Kaufman, 1997.
14. H. Blum, "A Transformation for Extracting New Descriptors of Shape," Proc. Symp. Models for the Perception of Speech and Visual Form, Nov. 1964.
15. R. Bridson, S. Marino, and R. Fedkiw, "Simulation of Clothing with Folds and Wrinkles," Proc. ACM SIGGRAPH/Eurographics Symp. Computer Animation (SCA), pp. 28-36, 2003.
16. D.E. Breen, S. Mauch, and R.T. Whitaker, "3D Scan Conversion of CSG Models into Distance Volumes," Proc. IEEE Symp. Volume Visualization, pp. 7-14, Oct. 1998.
17. D. Breen, S. Mauch, and R. Whitaker, "3D Scan Conversion of CSG Models into Distance, Closest-Point and Colour Volumes," Volume Graphics, M. Chen, A.E. Kaufman, and R. Yagel, eds., pp. 135-158, London: Springer, 2000.
18. G. Borgefors, "On Digital Distance Transforms in Three Dimensions," Computer Vision and Image Understanding, vol. 64, no. 3, pp. 368-376, 1996.
19. D. Breen, "Constructive Cubes: CSG Evaluation for Display Using Discrete 3D Scalar Data Sets," Proc. EUROGRAPHICS '91, pp. 127-142, 1991.
20. S. Bouix and K. Siddiqi, "Divergence-Based Medial. Surfaces," ECCV '00: Proc. Sixth European Conf. Computer Vision-Part I, pp. 603-618, June 2000.
21. I. Bitter, M. Sato, M. Bender, K.T. McDonnell, A. Kaufmann, and M. Wan, "CEASAR: A Smooth, Accurate and Robust Centerline Extraction Algorithm," Proc. Conf. Visualization '00, pp. 45-52, 2000.
22. D.E. Breen and R.T. Whitaker, "A Level-Set Approach for the Metamorphosis of Solid Models," IEEE Trans. Visualization and Computer Graphics, vol. 7, no. 2, pp. 173-192, 2001.
23. D.L. Chopp, "Some Improvements of the Fast Marching Method," SIAM J. Scientific Computing, vol. 23, no. 1, pp. 230-244, 2001.
24. Volume Graphics, M. Chen, A.E. Kaufman, and R. Yagel, eds., London: Springer Verlag, 2000.
25. T.H. Cormen, C.E. Leiserson, and R.L. Rivest, Introduction to Algorithms. MIT Press, 1990.
26. O. Cuisenaire and B. Macq, "Applications of the Region Growing Euclidean Distance Transform: Anisotropy and Skeletons," Proc. ICIP '97 VOLI, pp. 200-203, 2000.
27. S. Chen, B. Merriman, S. Osher, and P. Smereka, "A Simple Level Set Method for Solving Stefan Problems," J. Computational Physics, vol. 135, no. 1, pp. 8-29, July 1997.
28. D. Cohen-Or, A. Solomovic, and D. Levin, "Three-Dimensional Distance Field Metamorphosis," ACM Trans. Graphics, vol. 17, no. 2, pp. 116-141, 1998.
29. D. Cohen and Z. Sheffer, "Proximity Clouds-An Acceleration Technique for 3D Grid Traversal," The Visual Computer, vol. 10, no. 11, pp. 27-38, Nov. 1994.
30. M. Chen and J.V. Tucker, "Constructive Volume Geometry," Computer Graphics Forum, vol. 19, no. 4, pp. 281-293, 2000.
31. O. Cuisenaire, "Distance Transformation: Fast Algorithms and Applications to Medical Image Processing," PhD thesis, Univ. Catholique de Louvain, Oct. 1999.
32. P.-E. Danielsson, "Euclidean Distance Mapping," Computer Graphics and Image Processing, vol. 14, pp. 227-248, 1980.
33. J. Danskin and P. Hanrahan, "Fast Algorithms for Volume Ray Tracing," Proc. Workshop Volume Visualization, pp. 91-98, 1992.
34. F. Dachille and A. Kaufman, "Incremental Triangle Voxelization," Proc. Graphics Interface '00, pp. 205-212, 2000.
35. K. Erleben and H. Dohlman, personal communication, 2005.
36. K. Erleben, "Stable, Robust, and Versatile Multibody Dynamics Animation," PhD thesis, Dept. of Computer Science, Univ. of Copenhagen, 2004.
37. I. Fujishiro and E. Aoki, "Volume Graphics Modeling of Ice Thawing," Proc. Conf. Volume Graphics '01, pp. 69-80, 2001.
38. J.D. Foley and A. Van Dam, Fundamentals of Interactive Computer Graphics. Addison-Wesley, 1982.
39. P.-F. Fung and P.-A. Heng, "Efficient Volume Rendering by Isoregion Leaping Acceleration," Proc. Sixth Int'l Conf. Central. Europe Computer Graphics and Visualization '98, pp. 495-501, 1998.
40. J. Freund and K. Sloan, "Accelerated Volume Rendering Using Homogenous Region Encoding," Proc. IEEE Conf. Visualization '97, pp. 191-196, Nov. 1997.
41. E. Guendelman, R. Bridson, and R.P. Fedkiw, "Nonconvex Rigid Bodies with Stacking," ACM Trans. Graphics, vol. 22, no. 3, pp. 871-878, 2003.
42. J. Gomes and O.D. Faugeras, "Reconciling Distance Functions and Level Sets," Scale-Space Theories in Computer Vision, pp. 70-81, 1999.
43. S.F.F. Gibson, "Using Distance Maps for Accurate Surface Representation in Sampled Volumes," Proc. IEEE Symp. Volume Visualization, pp. 23-30, Oct. 1998.
44. J. Gielis, "A Generic Geometric Transformation that Unifies a Wide Range of Natural and Abstract Shapes," Am, J. Botany, vol. 90, pp. 333-338, 2003.
45. S.F. Frisken Gibson, R.N. Perry, A.P. Rockwood, and T.R. Jones, "Adaptively Sampled Distance Fields: A General Representation of Shape for Computer Graphics," Proc. SIGGRAPH '00, pp. 249-254, 2000.
46. N. Gagvani and D. Silver, "Parameter-Controlled Volume Thinning," Proc. CVGIP: Graph. Models Image Process., vol. 61, no. 3, pp. 149-164, 1999.
47. N. Gagvani and D. Silver, "Animating Volumetric Models," Graph. Models, vol. 63, no. 6, pp. 443-458/2001.
48. A. Guéziec, "Meshsweeper: Dynamic Point-to-Polygonal Mesh Distance and Applications," IEEE Trans. Visualization and Computer Graphics, vol. 7, no. 1, pp. 47-60, Jan.-Mar. 2001.
49. R. Gonzalez and R. Woods, Digital Image Processing. Addison-Wesley, 1993.
50. F. Hartmann, "On the Curvature of Curves and Surfaces Defined by Normalforms," Computer Aided Geometric Design, vol. 16, no. 5, pp. 355-376, 1999.
51. G. Hirota, S. Fisher, and A. State, "An Improved Finite Element Contact Model for Anatomical Simulations," The Visual Computer, vol. 19, no. 5, pp. 291-309, 2003.
52. K.H. Höhne and W.A. Hanson, "Interactive 3D Segmentation of MRI and CT Volumes Using Morphological Operations," J. Computer Assisted Tomography, vol. 16, no. 2, pp. 285-294, 1992.
53. J. Huang, Y. Li, R. Crawfis, S.-C. Lu, and S.-Y. Liou, "A Complete Distance Field Representation," Visualization, 2001, VIS '01 Proc., pp. 247-254, 2001.
54. C.M. Hoffmann, Geometric and Solid Modeling. Morgan Kaufmann, 1989.
55. J. Helmsen, F. Puckett, P. Colella, and M. Dorr, "Two New Methods for Simulating Photolithography Development in 3D," SPIE 2726, pp. 253-261/1996.
56. I. Holländer and M. Sramek, "An Interactive Tool for Manipulation and Presentation of 3D Tomographie Data," Proc. CAR '93 Computer Assisted Radiology, pp. 278-383, 1993.
57. T. Ju, F. Losasso, S. Schaefer, and J. Warren, "Dual Contouring of Hermite Data," Proc. 29th Ann. Conf. Computer Graphics and Interactive Techniques, pp. 339-346, 2002.
58. M.W. Jones, "The Production of Volume Data from Triangular Meshes Using Voxelisation," Computer Graphics Forum, vol. 15, no. 5, pp. 311-318, 1996.
59. M.W. Jones, "Facial Reconstruction Using Volumetric Data," Proc. Vision Modeling and Visualization Conf. '01 (VMV-01), pp. 135-150, Nov. 2001.
60. M.W. Jones, "Melting Objects," The J. WSCG, vol. 11, no. 2, pp. 247-254, 2003.
61. M.W. Jones, "Distance Field Compression," The J. WSCG, vol. 12, no. 2, pp. 199-204, 2004.
62. A. Kaufman, "Efficient Algorithms for 3D Scan-Conversion of Parametric Curves, Surfaces, and Volumes," Computer Graphics (SIGGRAPH '87 Proc.), vol. 21, no. 4, pp. 171-179, July 1987.
63. L.P. Kobbelt, M. Botsch, U. Schwanecke, and H.-P. Seidel, "Feature Sensitive Surface Extraction from Volume Data," SIGGRAPH '01: Proc. 28th Ann. Conf. Computer Graphics and Interactive Techniques, pp. 57-66, 2001.
64. A. Kaufman, D. Cohen, and R. Yagel, "Volume Graphics," Computer, vol. 26, no. 7, pp. 51-64, July 1993.
65. S. Kim, "An O(N) Level Set Method for Eikonal Equations," SIAM J. Scientific Computing, vol. 22, no. 6, pp. 2178-2193, 2000.
66. C.-Y. Kao, S. Osher, and J. Qian, "Lax-Friedrichs Sweeping Scheme for Static Hamilton-Jacobi Equations," J. Computational Physics, vol. 196, no. 1, pp. 367-391, May 2004.
67. k Hypersurfaces," J. Differential Equations, vol. 40, no. 1, pp. 116-20, 1981.
68. R. Kimmel and J.A. Sethian, "Computing Geodesic Paths on Manifolds," Proc. Nat'l. Academy of Sciences, vol. 95, no. 15, pp. 8431-8435, 1998.
69. H. Löffelmann and E. Gröller, "Parameterizing Superquadrics," Proc. Winter School of Computer Graphics '95, pp. 162-172, Feb. 1995.
70. S. Mauch, "A Fast Algorithm for Computing the Closest Point and Distance Transform," Technical Report caltechASCI/2000.077, Applied and Computational Math., Calif. Inst. of Technology, 2000.
71. S. Mauch, "Efficient Algorithms for Solving Static Hamilton-Jacobi. Equations," PhD thesis, Calif. Inst. of Technology, Pasadena, Calif., 2003.
72. O. Monga, S. Benayoun, and O.D. Faugeras, "From Partial Derivatives of 3D Density Images to Ridge Lines," Proc. SPIE-The Int'l. Soc. for Optical. Eng., vol. 1808, pp. 118-26, 1992.
73. K. Museth, D.E. Breen, R.T. Whitaker, and A.M. Barr, "Level Set Surface Editing Operators," SIGGRAPH '02: Proc. 29th Ann. Conf. Computer Graphics and Interactive Techniques, pp. 330-338, 2002.
74. D. Meagher, "Geometric Modeling Using Octree Encoding," Computer Graphics and Image Processing, vol. 19, no. 2, pp. 26-147, June 1982.
75. G. Malandain and S. Fernández-Vidal, "Euclidean Skeletons," Image and Vision Computing, vol. 16, no. 5, pp. 317-327, 1998.
76. CM. Miller and M.W. Jones, "Texturing and Hypertexturing of Volumetric Objects," Proc. Int'l Workshop Volume Graphics '05, pp. 117-125, 2005.
77. U. Montanari, "A Method for Obtaining Skeletons Using a Quasi-Euclidean Distance," J. ACM, vol. 15, no. 4, pp. 600-624, 1968.
78. J.C. Mullikin, "The Vector Distance Transform in Two and Three Dimensions," CVGIP: Graphical Models and Image Processing, vol. 54, no. 6, pp. 526-535, 1992.
79. M.B. Nielsen and K. Museth, "Dynamic Tubular Grid: An Efficient Data Structure and Algorithms for High Resolution Level. Sets," J. Scientific Computing, 2006.
80. P. Novotny, "CSG Operations with Voxelized Solids," master's thesis, Comenius Univ., Faculty of Math., Physics and Informatics, Bratislava, Slovakia, May 2003.
81. P. Novotny, M. Sramek, and L.I. Dimitrov, "CSG Operations with Voxelizad Solids," Proc. CGI Conf. '04, pp. 370-373, 2004.
82. F.S. Nooruddin and G. Turk, "Simplification and Repair of Polygonal Models Using Volumetric Techniques," IEEE Trans. Visualization and Computer Graphics, vol. 9, no. 2, pp. 191-205, Apr.-June 2003.
83. P. Novotny and M. Sramek, "Representation of Objects with Sharp Details in Truncated Distance Fields," Proc. Conf. Volume Graphics '05, pp. 109-116, 2005.
84. S.J. Osher and R.P. Fedkiw, Level Set Methods and Dynamic Implicit Surfaces, first ed., Springer Verlag, Nov. 2002.
85. Geometric Level Set Methods in Imaging, Vision, and Graphics, S. Osher and N. Paragios, eds., Springer, 2003.
86. S. Osher and J.A. Sethian, "Fronts Propagating with Curvature-Dependent Speed: Algorithms Based on Hamilton-Jacobi Formulations," J. Computational Physics, vol. 79, no. 1, pp. 12-49, Nov. 1988.
87. P.-O. Persson, "Mesh Generation for Implicit Geometries," PhD thesis, Mass. Inst. of Technology, Feb. 2005.
88. R.N. Perry and S.F. Frisken, "Kizamu: A System for Sculpting Digital Characters," Proc. SIGGRAPH, pp. 47-56, 2001.
89. K. Perlin and E. Hoffert, "Hypertexture," Computer Graphics (Proc. SIGGRAPH '89), vol. 23, no. 3, pp. 253-262, July/Aug. 1989.
90. D. Peng, B. Merriman, S. Osher, H. Zhao, and M. Kang, "A PDE-Based Fast Local Level Set Method," J. Computational Physics, vol. 155, no. 2, Nov. 1999.
91. R. Peikert and C. Sigg, "Optimized Bounding Polyhedra for CPU-Based Distance Transform," Dagstuhl Seminar 023231 on Scientific Visualization: Extracting Information and Knowledge from Scientific Data Sets, 2003.
92. B.A. Payne and A.W. Toga, "Distance Field Manipulation of Surface Models," Computer Graphics and Applications, vol. 12, no. 1, 1992.
93. H. Qu, N. Zhang, R. Shao, A. Kaufman, and K. Mueller, "Feature Preserving Distance Fields," VV '04: Proc. 2004 IEEE Symp. Volume Visualization and Graphics (VV '04), pp. 39-46, 2004.
94. I. Ragnemalm, "The Euclidean Distance Transform in Arbitrary Dimensions," Pattern Recogn. Lett., vol. 14, no. 11, pp. 883-888, 1993.
95. N. Molino, R. Bridson, J. Teran, and R. Fedkiw, "Adaptive Physics Based Tetrahedral Mesh Generation Using Level Sets," Eng. with Computers, vol. 21, pp. 2-18, 2005.
96. F. Rhodes, "Discrete Euclidean Metrics," Pattern Recognition Letters, vol. 13, no. 9, pp. 623-628, 1992.
97. A. Rosenfeld and J.L. Pfaltz, "Sequential Operations in Digital Picture Processing," J. ACM, vol. 13, no. 4, pp. 471-494, 1966.
98. G. Russo and P. Smereka, "A Remark on Computing Distance Functions," J. Computational Physics, vol. 163, no. 1, pp. 51-67, 2000.
99. E. Rouy and A. Tourin, "A Viscosity Solutions Approach to Shape-From-Shading," SIAM J. Numer. Anal, vol. 29, no. 3, pp. 867-884, 1992.
100. M. Segal and K. Akeley, The 100 Graphics System: A Specification (Version 2.0). SGI, 2004.
101. H. Samet, The Design and Analysis of Spatial Data Structures. Addison-Wesley, 1990.
102. S. Svensson and G. Borgefors, "Digital Distance Transforms in 3D Images Using Information from Neighbourhoods up to 5 × 5 × 5," Computer Vision and Image Understanding, vol. 88, pp. 24-53, 2002.
103. K. Siddiqi, S. Bouix, A. Tannenbaum, and S.W. Zucker, "The Hamilton-Jacobi Skeleton," ICCV '99: Proc. Int'l Conf. Computer Vision, vol. 2, p. 828, 1999.
104. J. Serra, Image Analysis and Mathematical Morphology. Academic Press, 1982.
105. J. A. Sethian, "A Fast Marching Level Set Method for Monotonically Advancing Fronts," Proc. Nat'l Academy of Sciences US-Paper Ed., vol. 93, no. 4, pp. 1591-1595, 1996.
106. J.A. Sethian, "Fast Marching Methods," SIAM Rev., vol. 41, no. 2, pp. 199-235, 1999.
107. J.A. Sethian, Level Set Methods and Fast Marching Methods, Cambridge Monographs on Applied and Computational Math., second ed., Cambridge Univ. Press, 1999.
108. M. Sussman, E. Fatemi, P. Smereka, and S. Osher, "An Improved Level Set Method for Incompressible Two-Phase Flows," Computers and Fluids, vol. 27, nos. 5-6, pp. 663-680, 1998.
109. R. Satherley and M.W. Jones, "Hybrid Distance Field Computation," Proc. Conf. Volume Graphics, pp. 195-209, 2001.
110. R. Satherley and M.W. Jones, "Vector-City Vector Distance Transform," Computer Vision and Image Understanding, vol. 82, no. 3, pp. 238-254, 2001.
111. R. Satherley and M.W. Jones, "Hypertexturing Complex Volume Objects," The. Visual Computer, vol. 18, no. 4, pp. 226-235, 2002.
112. S.K. Semwal and H. Kvarnstrom, "Directed Safe Zones and the Dual. Extent Algorithms for Efficient Grid Traversal during Ray Tracing," Graphics Interface, W. Davis, M. Mantei, and V. Klassen, eds., pp. 76-87, May 1997.
113. M. Sramek and A. Kaufman, "Alias-Free Voxclization of Geometric Objects," IEEE Trans. Visualization and Computer Graphics, vol. 5, no. 3, pp. 251-266, 1999.
114. M. Sramek and A. Kaufman, "Fast Ray-Tracing of Rectilinear Volume Data Using Distance Transforms," IEEE Trans. Visualization and Computer Graphics, vol., 6, no. 3, pp. 236-252, 2000.
115. M. Sramek and A. Kaufman, "vxt: A C++ Class Library for Object Voxelization," Volume Graphics, M'. Chen, A.E. Kaufman, and R. Yagel, eds., pp. 119-134, London: Springer Verlag, 2000.
116. W.J. Schroeder, W.E. Lorensen, and S. Linthicum, "Implicit Modeling of Swept Surfaces and Volumes," Proc. IEEE Conf. Visualization, pp. 40-45, Oct. 1994.
117. J.A. Sethian and A. Mihai Popovici, "3D Traveltime Computation Using the Fast Marching Method," Geophysics, vol. 64, no. 2, pp. 516-523, 1999.
118. A. Sud, M.A. Otaduy, and D. Manocha, "Difi: Fast 3D Distance Field Computation Using Graphics Hardware," Computer Graphics Forum, vol. 23, no. 3, 2004.
119. C. Sigg, R. Peikert, and M. Gross, "Signed Distance Transform. Using Graphics Hardware," Proc. IEEE Conf. Visualization '03, pp. 83-90, 2003.
120. M. Sharghi and I.W. Ricketts, "A Novel Method for Accelerating the Visualisation Process Used in Virtual Colonoscopy," Proc. Fifth Int'l. Conf. Information Visualization, pp. 167-172, Aug. 2001.
121. S. Turek and S.-R. Hysing, "The Eikonal Equation: Numerical. Efficiency vs. Algorithmic Complexity on Quadrilateral Grids," Proc. ALGORITMY 2005, pp. 22-31, Mar. 2005.
122. M. Sussman, P. Smereka, and S. Osher, "A Level. Set Approach for Computing Solutions to Incompressible Two-Phase Flow," J. Computational Physics, vol. 114, no. 1, pp. 146-159, Sept. 1994.
123. J. Strain, "Fast Tree-Based Redistancing for Level Set Computations," J. Computational Physics, vol. 1.52, no. 2, pp. 664-686, 1999.
124. Y.R. Tsai, "Rapid and Accurate Computation of the Distance Function Using Grids," J. Computational Physics, vol. 178, pp. 175-195, 2002.
125. J.N. Tsitsiklis, "Efficient Algorithms for Globally Optimal Trajectories," IEEE Trans. Automatic Control, vol. 40, no. 9, pp. 1528-1538, Sept. 1995.
126. G. Thürmer and C.A. Wüthrich, "Computing Vertex Normals from Polygonal Facets," J. Graphics Tools, vol. 3, no. 1, pp. 43-46, 1998.
127. L. Velho, J. Gomes, and L.H. Figueiredo, Implicit Objects in Computer Graphics. New York: Springer Verlag, 2002.
128. A. Vilanova i Bartrolì, A. König, and E. Gröller, "Cylindrical Approximation of Tubular Organs for Virtual Endoscopy," Proc. Computer Graphics and Imaging Conf. '00, pp. 283-289, 2000.
129. B.J.H. Verwer, P.W. Verbeek, and S.T. Dekker, "An Efficient Uniform Cost Algorithm Applied to Distance Transforms," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 11, no. 4, pp. 425-429, 1989.
130. M. Wan, F. Dachille, and A. Kaufman, "Distance-Field Based Skeletons for Virtual Navigation," VIS '01: Proc. Conf. Visualization '01, pp. 239-246, 2001.
131. R.T. Whitaker, "A Level-Set Approach to 3D Reconstruction from Range Data," Int'l J. Computer Vision, vol. 29, no. 3, pp. 203-231, 1998.
132. S.W. Wang and A. Kaufman, "Volume-Sampled 3D Modelling," Computer Graphics and Applications, vol. 14, no. 5, pp. 26-32, Sept. 1994.
133. J. Wu and L. Kobbelt, "Piecewise Linear Approximation of Signed Distance Fields," Proc. Vision, Modeling, and Visualization Conf., pp. 513-520, 2003.
134. M. Wan, A. Kaufman, and S. Bryson, "High Performance Presence-Accelerated Ray Casting," Proc. IEEE Conf. Visualization '99, pp. 379-386, Oct. 1999.
135. F.E. Wolter, "Cut Locus and Medial Axis in Global Shape Interrogation and Representation," technical report, MIT, 1993.
136. M. Wan, A. Sadiq, and A. Kaufmann, "Fast and Reliable Space Leaping for Interactive Volume Rendering," Proc. IEEE Conf. Visualization '02, pp. 195-202, 2002.
137. L. Yatziv, A. Bartesaghi, and G. Sapiro, "O(n) Implementation of the Fast Marching Algorithm," IMA Preprint Series No. 2021, Feb. 2005.
138. R. Yagel and A. Kaufman, "Template-Based Volume Viewing," Proc. Eurographics '92, pp. 153-167, June 1992.
139. H.-K. Zhao, T. Chan, B. Merriman, and S. Osher, "A Variaiional Level Set Approach to Multiphase Motion," J. Computational Physics, vol. 127, no. 1, pp. 179-195, Aug. 1996.
140. H.K. Zhao, "Fast Sweeping Method for Eikonal Equations," Math. of Computation, vol. 74, pp. 603-627, 2004.
141. K.J. Zuiderveld, A.H.J. Koning, and M.A. Viergever, "Acceleration of Ray-Casting Using 3D Distance Transforms," Proc. Conf. Visualization in Biomedical Computing '92, pp. 324-335, 1992.
142. K.J. Zuiderveld, A.H.J. Koning, and M.A. Viergever, "Techniques for Speeding up High-Quality Perspective Maximum Intensity Projection," Pattern Recognition Letters, vol. 15, pp. 507-517, 1994.
143. Y. Zhou and A.W. Toga, "Efficient Skeletonization of Volumetric Objects," IEEE Trans. Visualization and Computer Graphics, vol. 5, no. 3, pp. 196-209, July/Sept. 1999.