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Volumn 26, Issue 2, 2004, Pages 238-251

A Formal Classification of 3D Medial Axis Points and Their Local Geometry

Author keywords

3D medial axis; Curve skeleton; Generalized axis; Local form; Medial topology; Order of contact; Ridges; Shocks; Skeleton

Indexed keywords

3D MEDIAL AXIS; CURVE SKELETON; GENERALIZED AXIS; MEDIAL TOPOLOGY; ORDER OF CONTACT; RIDGES; SHOCKS; SKELETON;

EID: 0742303468     PISSN: 01628828     EISSN: None     Source Type: Journal    
DOI: 10.1109/TPAMI.2004.1262192     Document Type: Article
Times cited : (108)

References (49)
  • 3
    • 0031233471 scopus 로고    scopus 로고
    • Computing and Simplifying 2D and 3D Continuous Skeletons
    • D. Attali and A. Montanvert, "Computing and Simplifying 2D and 3D Continuous Skeletons," Computer Vision and Image Understanding, vol. 67, no. 3, pp. 261-273, 1997.
    • (1997) Computer Vision and Image Understanding , vol.67 , Issue.3 , pp. 261-273
    • Attali, D.1    Montanvert, A.2
  • 6
    • 0006515549 scopus 로고
    • Generalized Cylinder Representation
    • John Wiley and Sons
    • T. Binford, "Generalized Cylinder Representation," Encyclopedia of Artificial Intelligence, John Wiley and Sons, pp. 321-323, 1987.
    • (1987) Encyclopedia of Artificial Intelligence , pp. 321-323
    • Binford, T.1
  • 7
    • 0015581337 scopus 로고
    • Biological Shape and Visual Science
    • H. Blum, "Biological Shape and Visual Science," J. Theoretical Biology, no. 38, pp. 205-287, 1973.
    • (1973) J. Theoretical Biology , Issue.38 , pp. 205-287
    • Blum, H.1
  • 8
    • 0018178205 scopus 로고
    • Shape Description Using Weighted Symmetric Axis Features
    • H. Blum and R. Nagel, "Shape Description Using Weighted Symmetric Axis Features," Pattern Recognition, vol. 10, no. 3, pp. 167-180, 1978.
    • (1978) Pattern Recognition , vol.10 , Issue.3 , pp. 167-180
    • Blum, H.1    Nagel, R.2
  • 9
    • 0041035805 scopus 로고
    • Metamorphoses of Singularities of Minimum Functions, and Bifurcations of Shock Waves of the Burgers Equation with Vanishing Viscosity
    • I.A. Bogaevsky, "Metamorphoses of Singularities of Minimum Functions, and Bifurcations of Shock Waves of the Burgers Equation with Vanishing Viscosity," St. Petersburg (Leningrad) Math. J., vol. 1, no. 4, pp. 807-823, 1990.
    • (1990) St. Petersburg (Leningrad) Math. J. , vol.1 , Issue.4 , pp. 807-823
    • Bogaevsky, I.A.1
  • 10
    • 0033165433 scopus 로고    scopus 로고
    • Computing Skeletons in Three Dimensions
    • July
    • G. Borgefors, I. Nyström, and G. Sanniti di Baja, "Computing Skeletons in Three Dimensions," Pattern Recognition, vol. 32, no. 7, pp. 1225-1236, July 1999.
    • (1999) Pattern Recognition , vol.32 , Issue.7 , pp. 1225-1236
    • Borgefors, G.1    Nyström, I.2    Sanniti di Baja, G.3
  • 13
    • 0030172963 scopus 로고    scopus 로고
    • Ridges, Crests and Sub-Parabolic Lines of Evolving Surfaces
    • J.W. Bruce, P. Giblin, and F. Tari, "Ridges, Crests and Sub-Parabolic Lines of Evolving Surfaces," Int'l J. Computer Vision, vol. 18, no. 3, pp. 195-210, 1996.
    • (1996) Int'l J. Computer Vision , vol.18 , Issue.3 , pp. 195-210
    • Bruce, J.W.1    Giblin, P.2    Tari, F.3
  • 15
    • 0002754556 scopus 로고    scopus 로고
    • Mathematical Theory of Medial Axis
    • H. Choi, S. Choi, and H. Moon, "Mathematical Theory of Medial Axis," Pacific J. Math, vol. 181, no. 1, pp. 57-88, 1997.
    • (1997) Pacific J. Math , vol.181 , Issue.1 , pp. 57-88
    • Choi, H.1    Choi, S.2    Moon, H.3
  • 18
    • 33645441794 scopus 로고    scopus 로고
    • PhD thesis, Division of Eng., Brown Univ., Providence, RI, 02912, Jan.
    • F. Fol-Leymarie, "3D Shape Representation via Shock Flows," PhD thesis, Division of Eng., Brown Univ., Providence, RI, 02912, Jan. 2003.
    • (2003) 3D Shape Representation via Shock Flows
    • Fol-Leymarie, F.1
  • 20
    • 0742329426 scopus 로고    scopus 로고
    • Symmetry Sets and Medial Axes in Two and Three Dimensions
    • R. Cipolla and R. Martin, eds., Springer-Verlag
    • P. Giblin, "Symmetry Sets and Medial Axes in Two and Three Dimensions," The Math. of Surfaces IX, R. Cipolla and R. Martin, eds., Springer-Verlag, pp. 306-321, 2000.
    • (2000) The Math. of Surfaces IX , pp. 306-321
    • Giblin, P.1
  • 21
    • 0004577105 scopus 로고    scopus 로고
    • On the Local Form and Transitions of Symmetry Sets, and Medial Axes, and Shocks in 2D
    • Technical Report LEMS-170, LEMS, Brown Univ., Apr. to appear
    • P.J. Giblin and B.B. Kimia, "On the Local Form and Transitions of Symmetry Sets, and Medial Axes, and Shocks in 2D," Technical Report LEMS-170, LEMS, Brown Univ., Apr. 1998. Int'l J. Computer Vision, to appear.
    • (1998) Int'l J. Computer Vision
    • Giblin, P.J.1    Kimia, B.B.2
  • 22
    • 0032627287 scopus 로고    scopus 로고
    • On the Intrinsic Reconstruction of Shape from Its Symmetries
    • June. IEEE Trans. Pattern Analysis and Machine Intelligence, to appear
    • P.J. Giblin and B.B. Kimia, "On the Intrinsic Reconstruction of Shape from Its Symmetries," Proc. IEEE Computer Soc. Conf. Computer Vision and Pattern Recognition, pp. 79-84, June 1999. IEEE Trans. Pattern Analysis and Machine Intelligence, to appear.
    • (1999) Proc. IEEE Computer Soc. Conf. Computer Vision and Pattern Recognition , pp. 79-84
    • Giblin, P.J.1    Kimia, B.B.2
  • 23
    • 0033285178 scopus 로고    scopus 로고
    • On the Local Form and Transitions of Symmetry Sets, and Medial Axes, and Shocks in 2D
    • P.J. Giblin and B.B. Kimia, "On the Local Form and Transitions of Symmetry Sets, and Medial Axes, and Shocks in 2D," Proc. Int'l Conf. Computer Vision, pp. 385-391, 1999.
    • (1999) Proc. Int'l Conf. Computer Vision , pp. 385-391
    • Giblin, P.J.1    Kimia, B.B.2
  • 24
    • 84948964136 scopus 로고    scopus 로고
    • Transitions of the 3D Medial Axis under a One-Parameter Family of Deformations
    • May
    • P.J. Giblin and B.B. Kimia, "Transitions of the 3D Medial Axis under a One-Parameter Family of Deformations," Proc. Seventh European Conf. Computer Vision, pp. 718-724, May 2002.
    • (2002) Proc. Seventh European Conf. Computer Vision , pp. 718-724
    • Giblin, P.J.1    Kimia, B.B.2
  • 28
    • 0036919723 scopus 로고    scopus 로고
    • A Skeleton-Based Approach for Detection of Perceptually Salient Features on Polygonal Surfaces
    • M. Hisada, A. Belyaev, and T. Kunii, "A Skeleton-Based Approach for Detection of Perceptually Salient Features on Polygonal Surfaces," Computer Graphics Forum, vol. 21, no. 4, pp. 1-12, 2002.
    • (2002) Computer Graphics Forum , vol.21 , Issue.4 , pp. 1-12
    • Hisada, M.1    Belyaev, A.2    Kunii, T.3
  • 31
    • 0002432238 scopus 로고
    • Shape Manifolds, Procrustean Metrics and Complex Protective Spaces
    • D.G. Kendall, "Shape Manifolds, Procrustean Metrics and Complex Protective Spaces," Bull. London Math. Soc., 16, pp. 81-121, 1984.
    • (1984) Bull. London Math. Soc. , vol.16 , pp. 81-121
    • Kendall, D.G.1
  • 32
    • 0029344326 scopus 로고
    • Shapes, Shocks, and Deformations, I: The Components of Shape and the Reaction-Diffusion Space
    • B.B. Kimia, A.R. Tannenbaum, and S.W. Zucker, "Shapes, Shocks, and Deformations, I: The Components of Shape and the Reaction-Diffusion Space, " Int'l J. Computer Vision, vol. 15, no. 3, pp. 189-224, 1995.
    • (1995) Int'l J. Computer Vision , vol.15 , Issue.3 , pp. 189-224
    • Kimia, B.B.1    Tannenbaum, A.R.2    Zucker, S.W.3
  • 34
    • 84957585735 scopus 로고    scopus 로고
    • The Shock Scaffold for Representing 3D Shapes
    • C. Arcelli, L. Cordelia, and G.S. di Baja, eds., May
    • F. Leymarie and B.B. Kimia, "The Shock Scaffold for Representing 3D Shapes," Proc. Int'l Workshop on Visual Form, C. Arcelli, L. Cordelia, and G.S. di Baja, eds., pp. 216-228, May 2001.
    • (2001) Proc. Int'l Workshop on Visual Form , pp. 216-228
    • Leymarie, F.1    Kimia, B.B.2
  • 36
    • 0033284591 scopus 로고    scopus 로고
    • Approximate Tree Matching and Shape Similarity
    • T. Liu and D. Geiger, "Approximate Tree Matching and Shape Similarity," Proc. Int'l Conf. Computer Vision, pp. 456-462, 1999.
    • (1999) Proc. Int'l Conf. Computer Vision , pp. 456-462
    • Liu, T.1    Geiger, D.2
  • 37
    • 0030284743 scopus 로고    scopus 로고
    • A Fully Parallel 3D Thinning Algorithm and Its Applications
    • C. Ma and M. Sonka, "A Fully Parallel 3D Thinning Algorithm and Its Applications," Computer Vision and Image Understanding, vol. 64, no. 3, pp. 420-433, 1996.
    • (1996) Computer Vision and Image Understanding , vol.64 , Issue.3 , pp. 420-433
    • Ma, C.1    Sonka, M.2
  • 39
    • 0026886521 scopus 로고
    • Dynamic Deformation of Solid Primitives with Constraints
    • D. Metaxas and D. Terzopoulos, "Dynamic Deformation of Solid Primitives with Constraints," Computer Graphics, vol. 26, no. 2, pp. 309-312, 1992.
    • (1992) Computer Graphics , vol.26 , Issue.2 , pp. 309-312
    • Metaxas, D.1    Terzopoulos, D.2
  • 41
    • 0742311715 scopus 로고    scopus 로고
    • Spatial Tessellations: Concepts and Applications of Voronoi Diagrams
    • New York, New York: Wiley, second ed.
    • A. Okabe, B. Boots, K. Sugihara, and S.N. Chiu, "Spatial Tessellations: Concepts and Applications of Voronoi Diagrams," Probability and Statistics, New York, New York: Wiley, second ed., 2000.
    • (2000) Probability and Statistics
    • Okabe, A.1    Boots, B.2    Sugihara, K.3    Chiu, S.N.4
  • 46
    • 0026254852 scopus 로고
    • Estimation of Planar Curves, Surfaces, and Nonplanar Space Curves Defined by Implicit Equations with Applications to Edge and Range Image Segmentation
    • Nov.
    • G. Taubin, "Estimation of Planar Curves, Surfaces, and Nonplanar Space Curves Defined by Implicit Equations with Applications to Edge and Range Image Segmentation," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 13, no. 11, pp. 1115-1138, Nov. 1991.
    • (1991) IEEE Trans. Pattern Analysis and Machine Intelligence , vol.13 , Issue.11 , pp. 1115-1138
    • Taubin, G.1
  • 47
    • 0035329224 scopus 로고    scopus 로고
    • Boundary Smoothing via Symmetry Transforms
    • May
    • H. Tek and B.B. Kimia, "Boundary Smoothing via Symmetry Transforms," J. Math. Imaging and Vision, vol. 14, no. 3, pp. 211-223, May 2001.
    • (2001) J. Math. Imaging and Vision , vol.14 , Issue.3 , pp. 211-223
    • Tek, H.1    Kimia, B.B.2
  • 49
    • 0030104217 scopus 로고    scopus 로고
    • Three-Dimensional Descriptions Based on the Analysis of the Invariant and Quasi-Invariant Properties of some Curved-Axis Generalized Cylinders
    • Mar.
    • M. Zerroug and R. Nevatia, "Three-Dimensional Descriptions Based on the Analysis of the Invariant and Quasi-Invariant Properties of some Curved-Axis Generalized Cylinders," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 18, no. 3, pp. 237-253, Mar. 1996.
    • (1996) IEEE Trans. Pattern Analysis and Machine Intelligence , vol.18 , Issue.3 , pp. 237-253
    • Zerroug, M.1    Nevatia, R.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.