Optics, mechanics, and Hamilton-Jacobi skeletons

Advances in Imaging and Electron Physics

Volumn 135, Issue , 2005, Pages 1-39

  Bouix, Sylvain ^a   Siddiqi, Kaleem ^b  

^a BRIGHAM AND WOMEN S HOSPITAL   (United States)

^b MCGILL UNIVERSITY   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; GEOMETRICAL OPTICS; MECHANICS; MEDICAL COMPUTING;

CLASSICAL MECHANICS; HAMILTON-JACOBI SKELETONS; MEDICAL SETS;

MEDICAL IMAGING;

EID: 25144441868     PISSN: 10765670     EISSN: None     Source Type: Book Series    
DOI: 10.1016/S1076-5670(04)35001-9     Document Type: Review

References (56)

1. Amenta N., Choi S., and Kolluri R. The power crust, unions of balls, and the medial axis transform Computational Geometry: Theory and Applications 19 2 2001 127 153
2. Arcelli C., and di Baja G.S. Ridge points in Euclidean distance maps Pattern Recognition Letters 13 4 1992 237 243
3. Arcelli C., and Sanniti di Baja G. A width-independent fast thinning algorithm IEEE Transactions on Pattern Analysis and Machine Intelligence 7 4 1985 463 474
4. Armstrong M.A. Basic Topology 1997 Springer-Verlag New York
5. Arnold V.I. Mathematical Methods of Classical Mechanics 1989 Springer-Verlag New York
6. Arnold V.I. The Theory of Singularities and Its Applications 1991 Cambridge University Press Cambridge, MA
7. Attali D., and Montanvert A. Computing and simplifying 2D and 3D continuous skeletons Computer Vision and Image Understanding 67 3 1997 261 273
8. Bertrand G. A parallel thinning algorithm for medial surfaces Pattern Recognition Letters 16 1995 979 986
9. Blum H. A transformation for extracting new descriptors of shape 1967 MIT Press Cambridge, MA
10. Blum H. Biological shape and visual science Journal of Theoretical Biology 38 1973 205 287
11. Borgefors G. Distance transformations in arbitrary dimensions Computer Vision, Graphics, and Image Processing 27 1984 321 345
12. Borgefors G., Nystrom I., and Baja G.S.D. Computing skeletons in three dimensions Pattern Recognition 32 1999 1225 1236
13. Brandt J.W., and Algazi V.R. Continuous skeleton computation by Voronoi diagram Computer Vision, Graphics, and Image Processing 55 3 1992 329 338
14. Damon J. Global geometry of regions and boundaries via skeletal and medial integrals, submitted 2005
15. Dimitrov P. Flux invariants for shape 2003 School of Computer Science, McGill University M.Sc. thesis
16. Dimitrov P., Damon J.N., and Siddiqi K. Flux invariants for shape Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition Vol. 1 2003 Madison WI 835 841
17. Dimitrov P., Phillips C., and Siddiqi K. Robust and efficient skeletal graphs Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition 2003 Hilton Head SC 417 423
18. Giblin P.J., and Kimia B.B. Transitions of the 3D medial axis under a one-parameter family of deformations Proceedings of the European Conference on Computer Vision Vol. 2351 2002 Dublin Springer 718 734 Lecture Notes in Computer Science.
19. Giblin P.J., and Kimia B.B. On the local form and transitions of symmetry sets, medial axes, and shocks International Journal of Computer Vision 54 1 2003 143 157
20. Giblin P.J., and Kimia B.B. A formal classification of 3D medial axis points and their local geometry IEEE Transactions on Pattern Analysis and Machine Intelligence 26 2 2004 238 251
21. Goldak J.A., Yu X., Knight A., and Dong L. Constructing discrete medial axis of 3-D objects International Journal of Computational Geometry and Applications 1 3 1991 327 339
22. Gomes J., and Faugeras O. Reconciling distance functions and level sets Tech. Rep. TR3666, INRIA 1 1999 1 15
23. Kimmel R., Shaked D., and Kiryati N. Skeletonization via distance maps and level sets Computer Vision and Image Understanding 62 3 1995 382 391
24. Kong T.Y., and Rosenfeld A. Digital topology: Introduction and survey Computer Vision, Graphics, and Image Processing 48 3 1989 357 393
25. Lee T.-C., and Kashyap R.L. Building skeleton models via 3-D medial surface/axis thinning algorithm Graphical Models and Image Processing 56 6 1994 462 478
26. Leymarie F., and Levine M.D. Simulating the grassfire transform using an active contour model IEEE Transactions on Pattern Analysis and Machine Intelligence 14 1 1992 56 75
27. Lieutier A. Medial axis homotopy Tech. rep., LMC-IMAG and Dassault Systemes 2002
28. Luneburg R.Y. Mathematical Theory of Optics 1964 University of California Press Berkeley, CA
29. Malandain G., Bertrand G., and Ayache N. Topological segmentation of discrete surfaces International Journal of Computer Vision 10 2 1993 183 197
30. Malandain G., and Fernandez-Vidal S. Euclidean skeletons Image and Vision Computing 16 1998 317 327
31. Manzanera A., Bernard T.M., Preteux F., and Longuet B. Medial faces from a concise 3D thinning algorithm Proceedings of the IEEE International Conference on Computer Vision 1999 Kerkyra Greece 337 343
32. Mather J.N. Distance from a submanifold in euclidean space Proceedings of Symposia in Pure Mathematics 40 2 1983 199 216
33. Matheron G. Examples of topological properties of skeletons J. Serra Image Analysis and Mathematical Morphology Vol. 2 1988 Academic Press 217 238
34. Millman D. The central function of the boundary of a domain and its differential properties Journal of Geometry 14 1980 182 202
35. Näf M., Kübler O., Kikinis R., Shenton M.E., and Szekely G. Characterization and recognition of 3D organ shape in medical image analysis using skeletonization IEEE Workshop on Mathematical Methods in Biomedical Image Analysis 1996 139 150
36. Ogniewicz R.L. Discrete Voronoi Skeletons 1993 Hartung-Gorre Verlag Konstanz, Germany
37. Osher S., and Sethian J. Fronts propagating with curvature dependent speed: Algorithms based on Hamilton-Jacobi formaulation Journal of Computational Physics 79 1988 12 49
38. Pudney C. Distance-ordered homotopic thinning: A skeletonization algorithm for 3D digital images Computer Vision and Image Understanding 72 3 1998 404 413
39. Rouy E., and Tourin A. A viscosity solutions approach to shape-from-shading SIAM Journal of Numerical Analysis 29 3 1992 867 884
40. Savadjiev P., Ferrie F.P., and Siddiqi K. Surface recovery from 3D point data using a combined parametric and geometric flow approach International Workshop on Energy Minimization Methods in Computer Vision and Pattern Recognition Vol. LNCS 2683 2003 Springer-Verlag Lisbon,Portugal 325 340
41. Schmitt M. Some examples of algorithms analysis in computational geometry by means of mathematical morphology techniques J. Boissonnat J. Laumond Geometry and Robotics Vol. LNCS 391 1989 Springer-Verlag New York 225 246
42. Serra J. Image Analysis and Mathematical Morphology 1982 Academic Press New York
43. Sethian J.A. A fast marching level set method for monotonically advancing fronts Proceedings of the National Academy of Sciences USA 93 1996 1591 1595
44. Shankar R. Principles of Quantum Mechanics 1994 Plenum Press New York
45. Sheehy D.J., Armstrong C.G., and Robinson D.J. Shape description by medial surface construction IEEE Transactions on Visualization and Computer Graphics 2 1 1996 62 72
46. Sherbrooke E.C., Patrikalakis N., and Brisson E. An algorithm for the medial axis transform of 3D polyhedral solids IEEE Transactions on Visualization and Computer Graphics 2 1 1996 44 61
47. Siddiqi K., Bouix S., Tannenbaum A., and Zucker S.W. The Hamilton-Jacobi skeleton Proceedings of the IEEE International Conference on Computer Vision 1999 Kerkyra Greece 828 834
48. Siddiqi K., Bouix S., Tannenbaum A., and Zucker S.W. Hamilton-Jacobi skeletons International Journal of Computer Vision 48 3 2002 215 231
49. Siddiqi K., and Pizer S.M. Medial Representations: Mathematics, Algorithms and Applications 2005 Kluwer, Boston
50. Stavroudis O.N. The Optics of Rays, Wavefronts and Caustics 1972 Academic Press New York
51. Sussman M., Smereka P., and Osher S. A level set approach for computing solutions to incompressible two-phase flow Journal of Computational Physics 114 1994 146 154
52. Tek H., and Kimia B.B. Symmetry maps of free-form curve segments via wave propagation Proceedings of the IEEE International Conference on Computer Vision 1999 Kerkyra Greece 362 369
53. Wolter F.-E. Cut locus and medial axis in global shape interrogation and representation Tech. Rep. 92-2 1992 MIT, Department of Ocean Engineering, Design Laboratory Cambridge, MA
54. Xia Y. Skeletonization via the realization of the fire front's propagation and extinction in digital binary shapes IEEE Transactions on Pattern Analysis and Machine Intelligence 11 10 1989 1076 1086
55. Yomdin Y. On the local structure of a generic central set Compositio Mathematica 43 2 1981 225 238
56. Zhao H.K., Osher S., and Fedkiw R. Fast surface reconstruction using the level set method IEEE Workshop on Variational and Level Set Methods 2001 Vancouver BC 104 111