메뉴 건너뛰기




Volumn 124, Issue 1, 1996, Pages 154-196

Affine geometry, curve flows, and invariant numerical approximations

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0030495603     PISSN: 00018708     EISSN: None     Source Type: Journal    
DOI: 10.1006/aima.1996.0081     Document Type: Article
Times cited : (76)

References (32)
  • 1
    • 0346927716 scopus 로고
    • Sophus Lie's 1880 transformation group paper
    • Brookline, MA
    • 1. M. Ackerman and R. Hermann, "Sophus Lie's 1880 Transformation Group Paper," Math. Sci. Press, Brookline, MA, 1975.
    • (1975) Math. Sci. Press
    • Ackerman, M.1    Hermann, R.2
  • 2
    • 9644254503 scopus 로고
    • Sophus Lie's 1884 differential invariant paper
    • Brookline, MA
    • 2. M. Ackerman and R. Hermann, "Sophus Lie's 1884 Differential Invariant Paper," Math. Sci. Press, Brookline, MA, 1976.
    • (1976) Math. Sci. Press
    • Ackerman, M.1    Hermann, R.2
  • 3
    • 0026883886 scopus 로고
    • Image selective smoothing and edge detection by nonlinear diffusion
    • 3. L. Alvarez, P. L. Lions, and J. M. Morel, Image selective smoothing and edge detection by nonlinear diffusion, SIAM J. Numer. Anal. 29 (1992), 845-866.
    • (1992) SIAM J. Numer. Anal. , vol.29 , pp. 845-866
    • Alvarez, L.1    Lions, P.L.2    Morel, J.M.3
  • 7
    • 0001158863 scopus 로고
    • Transformation groups in net spaces
    • 7. V. A. Dorodnitsyn, Transformation groups in net spaces, J. Sov. Math. 55 (1991), 1490-1517.
    • (1991) J. Sov. Math. , vol.55 , pp. 1490-1517
    • Dorodnitsyn, V.A.1
  • 8
    • 0003355320 scopus 로고
    • Symmetry of finite difference equations
    • N. H. Ibragimov, Ed., CRC Press, Boca Raton, FL
    • 8. V. A. Dorodnitsyn, Symmetry of finite difference equations, in "CRC Handbook of Lie Group Analysis of Differential Equations," Vol. 1, (N. H. Ibragimov, Ed.), pp. 349-403, CRC Press, Boca Raton, FL, 1994.
    • (1994) CRC Handbook of Lie Group Analysis of Differential Equations , vol.1 , pp. 349-403
    • Dorodnitsyn, V.A.1
  • 9
    • 84963023423 scopus 로고
    • The heat equation shrinking convex plane curves
    • 9. M. Gage and R. S. Hamilton, The heat equation shrinking convex plane curves, J. Differential Geom. 23 (1986), 69-96.
    • (1986) J. Differential Geom. , vol.23 , pp. 69-96
    • Gage, M.1    Hamilton, R.S.2
  • 10
    • 84972528479 scopus 로고
    • The heat equation shrinks embedded plane curves to round points
    • 10. M. Grayson, The heat equation shrinks embedded plane curves to round points, J. Differential Geom. 26 (1987), 285-314.
    • (1987) J. Differential Geom. , vol.26 , pp. 285-314
    • Grayson, M.1
  • 11
    • 0001469020 scopus 로고
    • The moving frame, differential invariants and rigidity theorems for curves in homogeneous spaces
    • 11. M. L. Green, The moving frame, differential invariants and rigidity theorems for curves in homogeneous spaces, Duke Math. J. 45 (1978), 735-779.
    • (1978) Duke Math. J. , vol.45 , pp. 735-779
    • Green, M.L.1
  • 13
    • 0004707344 scopus 로고
    • On the evolution of curves via a function of curvature
    • 13. B. Kimia, A. Tannenbaum, and S. Zucker, On the evolution of curves via a function of curvature, J. Math. Anal. Appl. 163 (1992), 438-458.
    • (1992) J. Math. Anal. Appl. , vol.163 , pp. 438-458
    • Kimia, B.1    Tannenbaum, A.2    Zucker, S.3
  • 15
    • 0011498825 scopus 로고
    • Theorie der Transformationsgruppen I
    • 15. S. Lie, Theorie der Transformationsgruppen I, Math. Ann. 16 (1880), 441-528; also "Gesammelte Abhandlungen," Vol. 6, pp. 1-94, Teubner, Leipzig, 1927; see [1] for an English translation.
    • (1880) Math. Ann. , vol.16 , pp. 441-528
    • Lie, S.1
  • 16
    • 0011498825 scopus 로고
    • Teubner, Leipzig; see [1] for an English translation
    • 15. S. Lie, Theorie der Transformationsgruppen I, Math. Ann. 16 (1880), 441-528; also "Gesammelte Abhandlungen," Vol. 6, pp. 1-94, Teubner, Leipzig, 1927; see [1] for an English translation.
    • (1927) Gesammelte Abhandlungen , vol.6 , pp. 1-94
  • 17
    • 0000929703 scopus 로고
    • Über differentialinvarianten
    • 16. S. Lie, Über Differentialinvarianten, Math. Ann. 24 (1884), 537-578; also "Gesammelte Abhandlungen," Vol. 6, pp. 95-138, Teubner, Leipzig, 1927; see [2] for an English translation.
    • (1884) Math. Ann. , vol.24 , pp. 537-578
    • Lie, S.1
  • 18
    • 0000929703 scopus 로고
    • Teubner, Leipzig; see [2] for an English translation
    • 16. S. Lie, Über Differentialinvarianten, Math. Ann. 24 (1884), 537-578; also "Gesammelte Abhandlungen," Vol. 6, pp. 95-138, Teubner, Leipzig, 1927; see [2] for an English translation.
    • (1927) Gesammelte Abhandlungen , vol.6 , pp. 95-138
  • 21
    • 0002537667 scopus 로고
    • Differential invariant signatures and flows in computer vision: A symmetry group approach
    • B. M. Ter Haar Romeny, Ed., Kluwer, Dordrecht
    • 19. P. J. Olver, G. Sapiro, and A. Tannenbaum, Differential invariant signatures and flows in computer vision: a symmetry group approach, in "Geometry-Driven Diffusion in Computer Vision" (B. M. Ter Haar Romeny, Ed.), pp. 205-306, Kluwer, Dordrecht, 1994.
    • (1994) Geometry-Driven Diffusion in Computer Vision , pp. 205-306
    • Olver, P.J.1    Sapiro, G.2    Tannenbaum, A.3
  • 22
    • 44749084234 scopus 로고
    • Front propagation with curvature dependent speed: Algorithms based on Hamilton-Jacobi formulations
    • 20. S. Osher and J. Sethian, Front propagation 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
  • 23
    • 0025465145 scopus 로고
    • Scale-space and edge detection using anisotropic diffusion
    • 21. P. Perona and J. Malik, Scale-space and edge detection using anisotropic diffusion, IEEE PAMI 12 (1990), 629-639.
    • (1990) IEEE PAMI , vol.12 , pp. 629-639
    • Perona, P.1    Malik, J.2
  • 26
    • 0001807945 scopus 로고
    • On affine plane curve evolution
    • 24. G. Sapiro and A. Tannenbaum, On affine plane curve evolution, J. Funct. Anal. 119 (1994), 79-120.
    • (1994) J. Funct. Anal. , vol.119 , pp. 79-120
    • Sapiro, G.1    Tannenbaum, A.2
  • 28
    • 0001041397 scopus 로고
    • On invariant curve evolution and image analysis
    • 26. G. Sapiro and A. Tannenbaum, On invariant curve evolution and image analysis, Indiana J. Math. 42 (1993), 985-1009.
    • (1993) Indiana J. Math. , vol.42 , pp. 985-1009
    • Sapiro, G.1    Tannenbaum, A.2
  • 31
    • 0027608818 scopus 로고
    • Geometric invariants and object recognition
    • 29. I. Weiss, Geometric invariants and object recognition, Int. J. Comput. Vision 10 (1993), 207-231.
    • (1993) Int. J. Comput. Vision , vol.10 , pp. 207-231
    • Weiss, I.1
  • 32
    • 0004109271 scopus 로고
    • Princeton Univ. Press, Princeton, NJ
    • 30. H. Weyl, "Classical Groups," Princeton Univ. Press, Princeton, NJ, 1946.
    • (1946) Classical Groups
    • Weyl, H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.