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Volumn 64, Issue 3, 1996, Pages 305-322

Geometric heat equation and nonlinear diffusion of shapes and images

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER VISION; FORMAL LOGIC; HIERARCHICAL SYSTEMS; MATHEMATICAL OPERATORS; OBJECT RECOGNITION;

EID: 0030284583     PISSN: 10773142     EISSN: None     Source Type: Journal    
DOI: 10.1006/cviu.1996.0062     Document Type: Article
Times cited : (73)

References (90)
  • 1
    • 0001752835 scopus 로고
    • Axiomatisation et nouveaux operateurs de la morphologie mathematique
    • L. Alvarez, F. Guichard, P. Lions, and J. Morel, Axiomatisation et nouveaux operateurs de la morphologie mathematique, C. R. Acad. Sci. Paris 315, 1992, 265-268.
    • (1992) C. R. Acad. Sci. Paris , vol.315 , pp. 265-268
    • Alvarez, L.1    Guichard, F.2    Lions, P.3    Morel, J.4
  • 2
    • 0000005125 scopus 로고
    • Axiomes et equations fondementales du traitement d'Images (analyse multi-echelle at e.d.p)
    • L. Alvarez, F. Guichard, P.-L. Lions, and J.-M. Morel, Axiomes et equations fondementales du traitement d'images (analyse multi-echelle at e.d.p), C. R. Acad. Sci. Paris 1, 1992, 135-138.
    • (1992) C. R. Acad. Sci. Paris , vol.1 , pp. 135-138
    • Alvarez, L.1    Guichard, F.2    Lions, P.-L.3    Morel, J.-M.4
  • 4
    • 0028413507 scopus 로고
    • Signal and image restoration using shock filters and anisotropic diffusion
    • L. Alvarez and L. Mezzora, Signal and image restoration using shock filters and anisotropic diffusion, SIAM J. Numer. Anal. 31, 1994.
    • (1994) SIAM J. Numer. Anal. , vol.31
    • Alvarez, L.1    Mezzora, L.2
  • 5
    • 0026883886 scopus 로고
    • Image selective smoothing and edge detection by nonlinear diffusion: II
    • June
    • L. Alvarez, P.-L. Lions, and J.-M. Morel, Image selective smoothing and edge detection by nonlinear diffusion: II, SIAM J. Numer. Anal. 29(3), June 1992, 845-866.
    • (1992) SIAM J. Numer. Anal. , vol.29 , Issue.3 , pp. 845-866
    • Alvarez, L.1    Lions, P.-L.2    Morel, J.-M.3
  • 6
    • 84974253506 scopus 로고
    • Formalization and computational aspects of image analysis
    • L. Alvarez and J.-M. Morel, Formalization and computational aspects of image analysis, Acta Numer. 1994, 1-59.
    • (1994) Acta Numer. , pp. 1-59
    • Alvarez, L.1    Morel, J.-M.2
  • 11
    • 0015581337 scopus 로고
    • Biological shape and visual science
    • H. Blum, Biological shape and visual science, J. Theor. Biol. 38, 1973, 205-287.
    • (1973) J. Theor. Biol. , vol.38 , pp. 205-287
    • Blum, H.1
  • 12
    • 0026821645 scopus 로고
    • Image selective smoothing and edge detection by nonlinear diffusion
    • February
    • F. Catté, P.-L. Lions, J.-M. Morel, and T. Coll, Image selective smoothing and edge detection by nonlinear diffusion. SIAM J. Numer. Anal. 29(1), February 1992, 182-193.
    • (1992) SIAM J. Numer. Anal. , vol.29 , Issue.1 , pp. 182-193
    • Catté, F.1    Lions, P.-L.2    Morel, J.-M.3    Coll, T.4
  • 13
    • 0039939096 scopus 로고
    • Remarks on viscosity solutions for evolution equations
    • Y. Chen, Y. Giga, and S. Goto, Remarks on viscosity solutions for evolution equations, Proc. Japan Acad. 67(Ser. A), 1991, 323-328.
    • (1991) Proc. Japan Acad. , vol.67 , Issue.SER. A , pp. 323-328
    • Chen, Y.1    Giga, Y.2    Goto, S.3
  • 14
    • 84972499852 scopus 로고
    • Uniqueness and existence of viscosity solutions of generalized mean curvature flow equations
    • Y. Chen, Y. Giga, and S. Goto, Uniqueness and existence of viscosity solutions of generalized mean curvature flow equations, J. Diff. Geom. 33(3), 1991, 749-786.
    • (1991) J. Diff. Geom. , vol.33 , Issue.3 , pp. 749-786
    • Chen, Y.1    Giga, Y.2    Goto, S.3
  • 15
    • 84968507121 scopus 로고
    • Some properties of viscosity solutions of Hamilton-Jacobi equations
    • M. Crandall, L. Evans, and P. Lions, Some properties of viscosity solutions of Hamilton-Jacobi equations, Trans. Am. Math. Soc. 282, 1984, 487-502.
    • (1984) Trans. Am. Math. Soc. , vol.282 , pp. 487-502
    • Crandall, M.1    Evans, L.2    Lions, P.3
  • 16
    • 84967708673 scopus 로고
    • User's guide to viscosity solutions of second order partial differential equations
    • M. G. Crandall, H. Ishii, and P.-L. Lions, User's guide to viscosity solutions of second order partial differential equations, Bull. Am. Math. Soc. 27(1), 1992, 1-67.
    • (1992) Bull. Am. Math. Soc. , vol.27 , Issue.1 , pp. 1-67
    • Crandall, M.G.1    Ishii, H.2    Lions, P.-L.3
  • 17
    • 84967758647 scopus 로고
    • Viscosity solutions of Hamilton-Jacobi equations
    • M. G. Crandall and P.-L. Lions, Viscosity solutions of Hamilton-Jacobi equations, Trans. Am. Math. Soc. 277, 1983, 1-42.
    • (1983) Trans. Am. Math. Soc. , vol.277 , pp. 1-42
    • Crandall, M.G.1    Lions, P.-L.2
  • 20
    • 0003310610 scopus 로고
    • The curve shortening flow
    • (A. Chorin and A. Majda Eds.), Springer-Verlag, New York
    • C. Epstein and M. Gage, The Curve Shortening Flow, in Wave Motion: Theory, Modelling and Computation, (A. Chorin and A. Majda Eds.), Springer-Verlag, New York, 1987.
    • (1987) Wave Motion: Theory, Modelling and Computation
    • Epstein, C.1    Gage, M.2
  • 21
    • 84972518016 scopus 로고
    • Motion of level sets by mean curvature I
    • May
    • L. C. Evans and J. Spruck. Motion of level sets by mean curvature I, J. Diff. Geom. 33(3), May 1991, 635-681.
    • (1991) J. Diff. Geom. , vol.33 , Issue.3 , pp. 635-681
    • Evans, L.C.1    Spruck, J.2
  • 22
    • 84961297506 scopus 로고
    • Motion of level sets by mean curvature II
    • L. C. Evans and J. Spruck, Motion of level sets by mean curvature II, Trans. Am. Math. Soc. 330, 1992, 321-332.
    • (1992) Trans. Am. Math. Soc. , vol.330 , pp. 321-332
    • Evans, L.C.1    Spruck, J.2
  • 23
    • 0000007598 scopus 로고
    • Motion of level sets by mean curvature III
    • L. C. Evans and J. Spruck, Motion of level sets by mean curvature III, J. Geom. Analysis 2, 1992, 121-150.
    • (1992) J. Geom. Analysis , vol.2 , pp. 121-150
    • Evans, L.C.1    Spruck, J.2
  • 26
    • 84972571195 scopus 로고
    • An isoperimetric inequality with applications to curve shortening
    • M. Gage, An isoperimetric inequality with applications to curve shortening, Duke Math. J. 50, 1983, 1225-1229.
    • (1983) Duke Math. J. , vol.50 , pp. 1225-1229
    • Gage, M.1
  • 27
    • 0000500198 scopus 로고
    • Curve shortening makes convex curves circular
    • M. Gage, Curve shortening makes convex curves circular, Invent. Math. 76, 1984, 357-364.
    • (1984) Invent. Math. , vol.76 , pp. 357-364
    • Gage, M.1
  • 28
    • 0002764090 scopus 로고
    • On an area-preserving evolution equation for plane curves
    • M. Gage, On an area-preserving evolution equation for plane curves, Contemp. Math. 51, 1986, 51-62.
    • (1986) Contemp. Math. , vol.51 , pp. 51-62
    • Gage, M.1
  • 29
    • 84963023423 scopus 로고
    • The heat equation shrinking convex plane curves
    • M. Gage and R. S. Hamilton, the heat equation shrinking convex plane curves, J. Diff. Geom. 23, 1986, 69-96.
    • (1986) J. Diff. Geom. , vol.23 , pp. 69-96
    • Gage, M.1    Hamilton, R.S.2
  • 30
    • 0002534068 scopus 로고
    • Motion of hypersurfaces and geometric equations
    • Y. Giga and S. Goto, Motion of hypersurfaces and geometric equations, J. Math. Soc. Jpn. 44(1), 1992, 99-111.
    • (1992) J. Math. Soc. Jpn. , vol.44 , Issue.1 , pp. 99-111
    • Giga, Y.1    Goto, S.2
  • 31
    • 84972528479 scopus 로고
    • The heat equation shrinks embedded plane curves to round points
    • M. A. Grayson, The heat equation shrinks embedded plane curves to round points, J. Diff. Geom. 26, 1987, 285-314.
    • (1987) J. Diff. Geom. , vol.26 , pp. 285-314
    • Grayson, M.A.1
  • 32
    • 40749159424 scopus 로고
    • High resolution schemes for hyperbolic conservation laws
    • A. Harten, High resolution schemes for hyperbolic conservation laws, J. Comput. Phys. 49, 1983, 357-393.
    • (1983) J. Comput. Phys. , vol.49 , pp. 357-393
    • Harten, A.1
  • 36
    • 84990575194 scopus 로고
    • On uniqueness and existence of viscosity solutions of fully nonlinear second-order elliptic pde's
    • H. Ishii, On uniqueness and existence of viscosity solutions of fully nonlinear second-order elliptic pde's, Commun. Pure Appl. Math. 42, 1989, 15-45.
    • (1989) Commun. Pure Appl. Math. , vol.42 , pp. 15-45
    • Ishii, H.1
  • 37
    • 33646945027 scopus 로고
    • The maximum principle for viscosity solutions of fully nonlinear second-order partial differential equations
    • R. Jensen, The maximum principle for viscosity solutions of fully nonlinear second-order partial differential equations, Arch. Rational Mech. Anal. 101, 1988, 1-27.
    • (1988) Arch. Rational Mech. Anal. , vol.101 , pp. 1-27
    • Jensen, R.1
  • 38
    • 0005463014 scopus 로고
    • Ph.D. dissertation, McGill Centre for Intelligent Machines, McGill University, Montreal, Canada
    • B. B. Kimia, Conservation laws and a theory of shape, Ph.D. dissertation, McGill Centre for Intelligent Machines, McGill University, Montreal, Canada, 1990.
    • (1990) Conservation Laws and a Theory of Shape
    • Kimia, B.B.1
  • 44
    • 0004707344 scopus 로고
    • On the evolution of curves via a function of curvature, I: The classical case
    • Jan.
    • B. B. Kimia, A. R. Tannenbaum, and S. W. Zucker, On the evolution of curves via a function of curvature, I: The classical case. JMAA 163(2), Jan. 1992.
    • (1992) JMAA , vol.163 , Issue.2
    • Kimia, B.B.1    Tannenbaum, A.R.2    Zucker, S.W.3
  • 47
    • 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. J. Comput. Vision 15(3), 1995, 189-224.
    • (1995) Int. J. Comput. Vision , vol.15 , Issue.3 , pp. 189-224
    • Kimia, B.B.1    Tannenbaum, A.R.2    Zucker, S.W.3
  • 48
    • 0021136434 scopus 로고
    • The structure of images
    • J. J. Koenderink, The structure of images, Biol. Cybernetics 50, 1984, 363-370.
    • (1984) Biol. Cybernetics , vol.50 , pp. 363-370
    • Koenderink, J.J.1
  • 49
    • 0018079745 scopus 로고
    • Visual detection of spatial contrast: Influence of location in the visual field, target extent and illuminance level
    • J. J. Koenderink and A. J. van Dorn, Visual detection of spatial contrast: Influence of location in the visual field, target extent and illuminance level, Biol. Cybernetics 30, 1978, 157-167.
    • (1978) Biol. Cybernetics , vol.30 , pp. 157-167
    • Koenderink, J.J.1    Van Dorn, A.J.2
  • 51
    • 0003261490 scopus 로고
    • Hyperbolic systems of conservation laws and the mathematical theory of shock waves
    • Philadelphia
    • P. D. Lax, Hyperbolic Systems of Conservation Laws and the Mathematical Theory of Shock Waves, SIAM Regional Conference series in Applied Mathematics, Philadelphia, 1973.
    • (1973) SIAM Regional Conference Series in Applied Mathematics
    • Lax, P.D.1
  • 54
    • 5644259251 scopus 로고
    • Linear scale space I: Basic theory
    • (B. M. ter Haar Romeny, Ed.), Kluwer, Academic, Dordrecht/Norwell, MA
    • T. Lindeberg and B. M. ter Haar Romeny, Linear scale space I: Basic theory, in Geometry-Driven Diffusion in Computer Vision, (B. M. ter Haar Romeny, Ed.), pp. 1-38, Kluwer, Academic, Dordrecht/Norwell, MA, 1994.
    • (1994) Geometry-driven Diffusion in Computer Vision , pp. 1-38
    • Lindeberg, T.1    Ter Har Romeny, B.M.2
  • 55
    • 0006852174 scopus 로고
    • Linear scale space II: Early visual operations
    • (B. M. ter Haar Romeny, Ed.), Kluwer, Academic, Dordrecht/Norwell, MA
    • T. Lindeberg and B. M. ter Haar Romeny, Linear scale space II: Early visual operations, in Geometry-Driven Diffusion in Computer Vision (B. M. ter Haar Romeny, Ed.), pp. 39-72, Kluwer, Academic, Dordrecht/Norwell, MA, 1994.
    • (1994) Geometry-driven Diffusion in Computer Vision , pp. 39-72
    • Lindeberg, T.1    Ter Haar Romeny, B.M.2
  • 59
    • 0004198869 scopus 로고
    • Cambridge Univ. Press, Cambridge, UK
    • Y. Meyer, Wavelets and Operators, Cambridge Univ. Press, Cambridge, UK, 1989.
    • (1989) Wavelets and Operators
    • Meyer, Y.1
  • 61
    • 0026903040 scopus 로고
    • A theory of multiscale, curvature-based shape representation for planar curves
    • August
    • F. Mokhtarian and A. Mackworth, A theory of multiscale, curvature-based shape representation for planar curves, IEEE Trans. Pattern Anal. Machine Intell. 14(8), August 1992, 789-805.
    • (1992) IEEE Trans. Pattern Anal. Machine Intell. , vol.14 , Issue.8 , pp. 789-805
    • Mokhtarian, F.1    Mackworth, A.2
  • 63
    • 84989921626 scopus 로고
    • Biased anisotropic diffusion - A unified regularization and diffusion approach to edge detection
    • (O. Faugeras, Ed.), Springer Verlag, Berlin
    • N. Nordström, Biased anisotropic diffusion - A unified regularization and diffusion approach to edge detection, In Proceedings of the First European Conference on Computer Vision (O. Faugeras, Ed.), pp. 18-27, Springer Verlag, Berlin, 1990.
    • (1990) Proceedings of the First European Conference on Computer Vision , pp. 18-27
    • Nordström, N.1
  • 64
    • 0027561309 scopus 로고
    • Local reproducible smoothing without shrinkage
    • March
    • J. Oliensis, Local reproducible smoothing without shrinkage, IEEE Trans. Pattern Anal. Machine Intell. 15(3), March 1993, 307-312.
    • (1993) IEEE Trans. Pattern Anal. Machine Intell. , vol.15 , Issue.3 , pp. 307-312
    • Oliensis, J.1
  • 65
    • 0021513288 scopus 로고
    • High resolution schemes and the entropy condition
    • S. Osher and S. Chakravarthy, High resolution schemes and the entropy condition, SIAM J. Numer. Anal. 21, 1984, 955-984.
    • (1984) SIAM J. Numer. Anal. , vol.21 , pp. 955-984
    • Osher, S.1    Chakravarthy, S.2
  • 66
    • 0025474774 scopus 로고
    • Feature-oriented image enhancement using shock filters
    • Aug.
    • S. Osher and L. I. Rudin, Feature-oriented image enhancement using shock filters, SIAM J. Numer. Anal. 27(4), Aug. 1990, 919-940.
    • (1990) SIAM J. Numer. Anal. , vol.27 , Issue.4 , pp. 919-940
    • Osher, S.1    Rudin, L.I.2
  • 67
    • 44749084234 scopus 로고
    • Fronts propagating with curvature dependent speed: Algorithms based on Hamilton-Jacobi formulations
    • S. Osher and J. Sethian, Fronts propagating with curvature dependent speed: Algorithms based on Hamilton-Jacobi formulations, J. Comput. Phys. 79, 1988, 12-49.
    • (1988) J. Comput. Phys. , vol.79 , pp. 12-49
    • Osher, S.1    Sethian, J.2
  • 68
    • 0025465145 scopus 로고
    • Scale-space and edge detection using anisotropic diffusion
    • July
    • P. Perona and J. Malik, Scale-space and edge detection using anisotropic diffusion, IEEE Trans. Pattern Anal. Machine Intell. 12(7), July 1990, 629-639.
    • (1990) IEEE Trans. Pattern Anal. Machine Intell. , vol.12 , Issue.7 , pp. 629-639
    • Perona, P.1    Malik, J.2
  • 71
    • 0015064542 scopus 로고
    • Edge and curve detection for visual scene analysis
    • A. Rosenfeld and M. Thurston, Edge and curve detection for visual scene analysis, IEEE Trans. Comput. C-20, 1971, 562-569.
    • (1971) IEEE Trans. Comput. , vol.C-20 , pp. 562-569
    • Rosenfeld, A.1    Thurston, M.2
  • 74
    • 0042534238 scopus 로고
    • Area and length preserving geometric invariant scale-spaces
    • (J.-O. Eklundh, Ed.), Springer Verlag, Stockholm
    • G. Sapiro and A. Tannenbaum, Area and length preserving geometric invariant scale-spaces, in Proceedings, Third European Conference on Computer Vision (J.-O. Eklundh, Ed.), pp. 449-458, Springer Verlag, Stockholm, 1994.
    • (1994) Proceedings, Third European Conference on Computer Vision , pp. 449-458
    • Sapiro, G.1    Tannenbaum, A.2
  • 75
  • 76
    • 0004231628 scopus 로고
    • Ph.D. dissertation, University of California, Berkeley, Berkeley, CA
    • J. Sethian, An analysis of flame propagation, Ph.D. dissertation, University of California, Berkeley, Berkeley, CA, 1985.
    • (1985) An Analysis of Flame Propagation
    • Sethian, J.1
  • 78
    • 0001335838 scopus 로고
    • A review of recent numerical algorithms for hypersurfaces moving with curvature dependent speed
    • J. Sethian, A review of recent numerical algorithms for hypersurfaces moving with curvature dependent speed, J. Diff. Goem. (33), 1989, 131-161.
    • (1989) J. Diff. Goem. , Issue.33 , pp. 131-161
    • Sethian, J.1
  • 80
    • 34250118137 scopus 로고
    • Curvature and the evolution of fronts
    • J. A. Sethian, Curvature and the evolution of fronts, Commun. Math. Physics 101, 1985, 487-499.
    • (1985) Commun. Math. Physics , vol.101 , pp. 487-499
    • Sethian, J.A.1
  • 83
    • 0022756380 scopus 로고
    • Regularization of inverse visual problems involving discontinuities
    • July
    • D. Terzopoulos, Regularization of inverse visual problems involving discontinuities, IEEE Trans. Pattern Anal. Machine Intell. 8, July 1986, 413-424.
    • (1986) IEEE Trans. Pattern Anal. Machine Intell. , vol.8 , pp. 413-424
    • Terzopoulos, D.1
  • 84
    • 0345372139 scopus 로고
    • Geometry-limited diffusion in the characterization of geometric patches in images
    • Jan.
    • R. T. Whitaker, Geometry-limited diffusion in the characterization of geometric patches in images, Comput. Vision Graphics Image Process. 57, Jan. 1993, 111-120.
    • (1993) Comput. Vision Graphics Image Process. , vol.57 , pp. 111-120
    • Whitaker, R.T.1
  • 86
    • 0039810196 scopus 로고
    • Some recent developments in differential geometry
    • B. White, Some recent developments in differential geometry, Math. Intelligenecer 11(4), 1989, 11-47.
    • (1989) Math. Intelligenecer , vol.11 , Issue.4 , pp. 11-47
    • White, B.1
  • 90
    • 0022625147 scopus 로고
    • Receptive fields and the representation of visual information
    • S. W. Zucker and R. Hummel, Receptive fields and the representation of visual information. Human Neurobiol. 5, 1986, 121-128.
    • (1986) Human Neurobiol. , vol.5 , pp. 121-128
    • Zucker, S.W.1    Hummel, R.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.