메뉴 건너뛰기




Volumn 111, Issue 3, 2008, Pages 351-373

On geometric variational models for inpainting surface holes

Author keywords

Absolute minimizing Lipschitz extension; Inpainting; Interpolation; Laplacian; Mean curvature; Scalar and vector fields; Surface holes; Variational formulations

Indexed keywords

AIRCRAFT ENGINES; DIFFERENCE EQUATIONS; DIFFERENTIAL EQUATIONS; DIFFERENTIATION (CALCULUS); EQUATIONS OF MOTION; EULER EQUATIONS; IMAGE SEGMENTATION; LAPLACE EQUATION;

EID: 50249180722     PISSN: 10773142     EISSN: 1090235X     Source Type: Journal    
DOI: 10.1016/j.cviu.2008.01.002     Document Type: Article
Times cited : (30)

References (55)
  • 1
    • 0003282839 scopus 로고    scopus 로고
    • Functions of bounded variation and free discontinuity problems
    • Ambrosio L., Fusco N., and Pallara D. Functions of bounded variation and free discontinuity problems. Oxf. Math. Monogr. (2000)
    • (2000) Oxf. Math. Monogr.
    • Ambrosio, L.1    Fusco, N.2    Pallara, D.3
  • 2
    • 84892197297 scopus 로고    scopus 로고
    • A direct variational approach to a problem arising in image reconstruction
    • Ambrosio L., and Masnou S. A direct variational approach to a problem arising in image reconstruction. Interfaces Free Boundaries 5 (2003) 63-81
    • (2003) Interfaces Free Boundaries , vol.5 , pp. 63-81
    • Ambrosio, L.1    Masnou, S.2
  • 3
    • 0031629515 scopus 로고    scopus 로고
    • N. Amenta, M. Bern, M. Kamvysselis, A new Voronoi-based surface reconstruction algorithm, Proc. SIGGRAPH 1998, ACM (1998) 415-421.
    • N. Amenta, M. Bern, M. Kamvysselis, A new Voronoi-based surface reconstruction algorithm, Proc. SIGGRAPH 1998, ACM (1998) 415-421.
  • 5
    • 50249118876 scopus 로고    scopus 로고
    • Amira, Amira Visualization and Modeling System, Available from: .
    • Amira, Amira Visualization and Modeling System, Available from: .
  • 6
    • 0001457134 scopus 로고
    • Extension of functions satisfying Lipschitz conditions
    • Aronsson G. Extension of functions satisfying Lipschitz conditions. Ark. Math. 6 (1967) 551-561
    • (1967) Ark. Math. , vol.6 , pp. 551-561
    • Aronsson, G.1
  • 8
    • 0029201534 scopus 로고    scopus 로고
    • C.L. Bajaj, F. Bernardini, G. Xu, Automatic reconstruction of surfaces and scalar fields from 3D scans, Proc. ACM SIGGRAPH 1995, ACM (1995) 109-118.
    • C.L. Bajaj, F. Bernardini, G. Xu, Automatic reconstruction of surfaces and scalar fields from 3D scans, Proc. ACM SIGGRAPH 1995, ACM (1995) 109-118.
  • 10
    • 2542432962 scopus 로고    scopus 로고
    • Dissoclusion by joint interpolation of vector fields and gray levels
    • Ballester C., Caselles V., and Verdera J. Dissoclusion by joint interpolation of vector fields and gray levels. Multiscale Model. Simul. 2 (2003) 80-123
    • (2003) Multiscale Model. Simul. , vol.2 , pp. 80-123
    • Ballester, C.1    Caselles, V.2    Verdera, J.3
  • 11
    • 50249136943 scopus 로고    scopus 로고
    • p = f and related extremal problems, Rendiconti Sem. Mat. Fascicolo Speciale Nonlinear PDEs, Univ. di Torino (1989) 15-68.
    • p = f and related extremal problems, Rendiconti Sem. Mat. Fascicolo Speciale Nonlinear PDEs, Univ. di Torino (1989) 15-68.
  • 13
    • 0035690734 scopus 로고    scopus 로고
    • M. Bertalmio, A.L. Bertozzi, G. Sapiro, Navier-Stokes, fluid dynamics, and image and video inpainting, Proc. IEEE Computer Vision and Pattern Recognition (CVPR), Hawaii, (2001) 355-362.
    • M. Bertalmio, A.L. Bertozzi, G. Sapiro, Navier-Stokes, fluid dynamics, and image and video inpainting, Proc. IEEE Computer Vision and Pattern Recognition (CVPR), Hawaii, (2001) 355-362.
  • 14
    • 0034446966 scopus 로고    scopus 로고
    • M. Bertalmi{dotless}́o, G. Sapiro, V. Caselles, and C. Ballester, Image inpainting, Proc. SIGGRAPH 2000, ACM, (2000) 417-424.
    • M. Bertalmi{dotless}́o, G. Sapiro, V. Caselles, and C. Ballester, Image inpainting, Proc. SIGGRAPH 2000, ACM, (2000) 417-424.
  • 16
    • 0035157649 scopus 로고    scopus 로고
    • J.C. Carr, R.K. Beatson, J.B. Cherrie, T.J. Mitchell, W.R. Fright, B.C. McCallum, and T.R. Evans, Reconstruction and representation of 3D objects with radial basis functions, Proc. SIGGRAPH 2001, ACM, (2001) 67-76.
    • J.C. Carr, R.K. Beatson, J.B. Cherrie, T.J. Mitchell, W.R. Fright, B.C. McCallum, and T.R. Evans, Reconstruction and representation of 3D objects with radial basis functions, Proc. SIGGRAPH 2001, ACM, (2001) 67-76.
  • 18
    • 0036301838 scopus 로고    scopus 로고
    • Local inpainting models and TV inpainting
    • Chan T., and Shen J. Local inpainting models and TV inpainting. SIAM J. Appl. Math. 62 (2001) 1019-1043
    • (2001) SIAM J. Appl. Math. , vol.62 , pp. 1019-1043
    • Chan, T.1    Shen, J.2
  • 19
    • 0029306824 scopus 로고
    • Description of complex objects from multiple range images using an inflating balloon model
    • Chen Y., and Medioni G. Description of complex objects from multiple range images using an inflating balloon model. Comput. Vis. Image Und. 61 (1995) 325-334
    • (1995) Comput. Vis. Image Und. , vol.61 , pp. 325-334
    • Chen, Y.1    Medioni, G.2
  • 20
    • 50249174847 scopus 로고    scopus 로고
    • U. Clarenz, M. Rumpf, and A. Telea, Finite elements on point based surfaces, Computers and Graphics, to appear, 2005.
    • U. Clarenz, M. Rumpf, and A. Telea, Finite elements on point based surfaces, Computers and Graphics, to appear, 2005.
  • 21
    • 2342475802 scopus 로고    scopus 로고
    • A finite element method for surface restoration with smooth boundary conditions
    • Clarenz U., Diewald U., Dziuk G., Rumpf M., and Rusu R. A finite element method for surface restoration with smooth boundary conditions. Comput. Aided Geom. D. 21 (2004) 427-445
    • (2004) Comput. Aided Geom. D. , vol.21 , pp. 427-445
    • Clarenz, U.1    Diewald, U.2    Dziuk, G.3    Rumpf, M.4    Rusu, R.5
  • 22
    • 84967708673 scopus 로고
    • User's guide to viscosity solutions of second order partial differential equations
    • Crandall M.G., Ishii H., and Lions P.L. User's guide to viscosity solutions of second order partial differential equations. Bull. Amer. Math. Soc. 27 (1992) 1-67
    • (1992) Bull. Amer. Math. Soc. , vol.27 , pp. 1-67
    • Crandall, M.G.1    Ishii, H.2    Lions, P.L.3
  • 23
    • 84928895300 scopus 로고    scopus 로고
    • B. Curless and M. Levoy, A volumetric method for building complex models from range images, Proc. SIGGRAPH 1996, ACM, 5 (1996) 303-312.
    • B. Curless and M. Levoy, A volumetric method for building complex models from range images, Proc. SIGGRAPH 1996, ACM, 5 (1996) 303-312.
  • 24
    • 84964422576 scopus 로고    scopus 로고
    • J. Davis, S. Marschner, M. Garr, and M. Levoy, Filling holes in complex surfaces using volumetric diffusion, First International Symposium on 3D Data Processing, Visualization, and Transmission (3DPVT'02), Padua, Italy, (2002).
    • J. Davis, S. Marschner, M. Garr, and M. Levoy, Filling holes in complex surfaces using volumetric diffusion, First International Symposium on 3D Data Processing, Visualization, and Transmission (3DPVT'02), Padua, Italy, (2002).
  • 25
    • 84942256899 scopus 로고    scopus 로고
    • J.S. De Bonet, Multiresolution sampling procedure for analysis and synthesis of texture images, Proc. SIGGRAPH 1997, ACM, (1997) 361-368.
    • J.S. De Bonet, Multiresolution sampling procedure for analysis and synthesis of texture images, Proc. SIGGRAPH 1997, ACM, (1997) 361-368.
  • 26
    • 33646388390 scopus 로고    scopus 로고
    • Error analysis of a finite element method for the Willmore flow of graphs
    • Deckelnick K., and Dziuk G. Error analysis of a finite element method for the Willmore flow of graphs. Interfaces and free boundaries 8 (2006) 21-46
    • (2006) Interfaces and free boundaries , vol.8 , pp. 21-46
    • Deckelnick, K.1    Dziuk, G.2
  • 28
    • 2542539269 scopus 로고    scopus 로고
    • A level set formulation of Willmore flow
    • Droske M., and Rumpf M. A level set formulation of Willmore flow. Interfaces and Free Boundaries 6 3 (2004) 361-378
    • (2004) Interfaces and Free Boundaries , vol.6 , Issue.3 , pp. 361-378
    • Droske, M.1    Rumpf, M.2
  • 30
    • 85138843843 scopus 로고    scopus 로고
    • A.A. Efros and T.K. Leung, Texture synthesis by non-parametric sampling, IEEE International Conference on Computer Vision, Corfu, Greece, (1999) 1033-1038.
    • A.A. Efros and T.K. Leung, Texture synthesis by non-parametric sampling, IEEE International Conference on Computer Vision, Corfu, Greece, (1999) 1033-1038.
  • 32
    • 0029182262 scopus 로고    scopus 로고
    • D. Heeger and J. Bergen, Pyramid based texture analysis/synthesis, Proc. SIGGRAPH 1995, ACM, (1995) 229-238.
    • D. Heeger and J. Bergen, Pyramid based texture analysis/synthesis, Proc. SIGGRAPH 1995, ACM, (1995) 229-238.
  • 33
    • 0026888013 scopus 로고    scopus 로고
    • H. Hoppe, T. DeRose, T. Duchamp, J. McDonald, and W. Stuetzle, Surface reconstruction from unorganized points, Proc. SIGGRAPH 1992, ACM, (1992) 71-78.
    • H. Hoppe, T. DeRose, T. Duchamp, J. McDonald, and W. Stuetzle, Surface reconstruction from unorganized points, Proc. SIGGRAPH 1992, ACM, (1992) 71-78.
  • 34
    • 0033457563 scopus 로고    scopus 로고
    • An active set strategy based on the augmented Lagrangian formulation for image restoration
    • Ito K., and Kunisch K. An active set strategy based on the augmented Lagrangian formulation for image restoration. M2AN Math. Model. Numer. Anal. 33 (1999) 1-21
    • (1999) M2AN Math. Model. Numer. Anal. , vol.33 , pp. 1-21
    • Ito, K.1    Kunisch, K.2
  • 35
    • 21144476154 scopus 로고
    • Uniqueness of Lipschitz extensions: Minimizing the sup norm of the gradient
    • Jensen R. Uniqueness of Lipschitz extensions: Minimizing the sup norm of the gradient. Arch. Rat. Mech. Anal. 123 (1993) 51-74
    • (1993) Arch. Rat. Mech. Anal. , vol.123 , pp. 51-74
    • Jensen, R.1
  • 37
    • 50249179510 scopus 로고    scopus 로고
    • M. Levoy, K. Pulli, B. Curless, S. Rusinkiewicz, D. Koller, L. Pereira, M. Ginzton, S. Anderson, J. Davis, J. Ginsberg, J. Shade, and D. Fulk, The Digital Michelangelo Project: 3D scanning of large statues, Proc. SIGGRAPH 2000, ACM, (2000) 269-276.
    • M. Levoy, K. Pulli, B. Curless, S. Rusinkiewicz, D. Koller, L. Pereira, M. Ginzton, S. Anderson, J. Davis, J. Ginsberg, J. Shade, and D. Fulk, The Digital Michelangelo Project: 3D scanning of large statues, Proc. SIGGRAPH 2000, ACM, (2000) 269-276.
  • 38
    • 16244380214 scopus 로고    scopus 로고
    • Filling the signed distance field by fitting local quadrics, second international symp. on 3D data processing
    • Masuda T. Filling the signed distance field by fitting local quadrics, second international symp. on 3D data processing. Visualization and Transmission (3DPVT'04) (2004) 1003-1010
    • (2004) Visualization and Transmission (3DPVT'04) , pp. 1003-1010
    • Masuda, T.1
  • 40
    • 50249151737 scopus 로고    scopus 로고
    • B. Merriman, J.K. Bence, and S.J. Osher, Diffusion generated motion by mean curvature, In AMS Selected Lectures in Math. The Comput. Crystal Grower's workshop. Edited by J. Taylor. AMS Providence (1993), 73-83.
    • B. Merriman, J.K. Bence, and S.J. Osher, Diffusion generated motion by mean curvature, In AMS Selected Lectures in Math. The Comput. Crystal Grower's workshop. Edited by J. Taylor. AMS Providence (1993), 73-83.
  • 42
    • 21644465169 scopus 로고    scopus 로고
    • A convergent difference scheme for the infinity Laplacian: construction of absolutely minimizing Lipschitz extensions
    • Oberman A.M. A convergent difference scheme for the infinity Laplacian: construction of absolutely minimizing Lipschitz extensions. Math. Comp. 74 (2005) 1217-1230
    • (2005) Math. Comp. , vol.74 , pp. 1217-1230
    • Oberman, A.M.1
  • 44
    • 3042841518 scopus 로고    scopus 로고
    • Level set methods and dynamic implicit surfaces
    • Springer-Verlag, New York
    • Osher S., and Fedkiw R. Level set methods and dynamic implicit surfaces. Appl. Math. Sci. 153 (2003), Springer-Verlag, New York
    • (2003) Appl. Math. Sci. , vol.153
    • Osher, S.1    Fedkiw, R.2
  • 45
    • 44749084234 scopus 로고
    • Fronts propagating with curvature dependent speed: Algorithms based on Hamilton-Jacobi formulation
    • Osher S., and Sethian J.A. Fronts propagating with curvature dependent speed: Algorithms based on Hamilton-Jacobi formulation. J. Comput. Phys. 79 (1988) 12-49
    • (1988) J. Comput. Phys. , vol.79 , pp. 12-49
    • Osher, S.1    Sethian, J.A.2
  • 46
    • 0037854586 scopus 로고    scopus 로고
    • Structure and texture filling-in of missing image blocks in wireless transmission and compression applications
    • Rane S., Sapiro G., and Bertalmio M. Structure and texture filling-in of missing image blocks in wireless transmission and compression applications. IEEE Trans. Image Processing 12 (2003) 269-303
    • (2003) IEEE Trans. Image Processing , vol.12 , pp. 269-303
    • Rane, S.1    Sapiro, G.2    Bertalmio, M.3
  • 47
    • 84867849647 scopus 로고    scopus 로고
    • Taking consensus of signed distance field for complementing unobservable surface
    • Sagawa R., and Ikeuchi K. Taking consensus of signed distance field for complementing unobservable surface. Proceedings 3DIM (2003) 410-417
    • (2003) Proceedings 3DIM , pp. 410-417
    • Sagawa, R.1    Ikeuchi, K.2
  • 49
    • 84977776020 scopus 로고    scopus 로고
    • G. Turk and M. Levoy, Zippered polygon meshes from range images, Proc. SIGGRAPH 1994 ACM, (1994) 311-318.
    • G. Turk and M. Levoy, Zippered polygon meshes from range images, Proc. SIGGRAPH 1994 ACM, (1994) 311-318.
  • 50
  • 51
    • 0344703718 scopus 로고    scopus 로고
    • J. Verdera, V. Caselles, M. Bertalmi{dotless}́o, and G. Sapiro, Inpainting surface holes, IEEE International Conference on Image Processing, ICIP 2003, Barcelona, Spain, (2003) 903-906.
    • J. Verdera, V. Caselles, M. Bertalmi{dotless}́o, and G. Sapiro, Inpainting surface holes, IEEE International Conference on Image Processing, ICIP 2003, Barcelona, Spain, (2003) 903-906.
  • 53
    • 0032155928 scopus 로고    scopus 로고
    • A level-set approach to 3D reconstruction from range data
    • Whitaker R. A level-set approach to 3D reconstruction from range data. Int. J. Comput. Vision 29 (1998) 203-231
    • (1998) Int. J. Comput. Vision , vol.29 , pp. 203-231
    • Whitaker, R.1
  • 54
  • 55
    • 84967164960 scopus 로고    scopus 로고
    • H.K. Zhao, S. Osher, and R. Fedkiw, Fast surface reconstruction using the level set method, Proc. First IEEE Workshop on Variational and Level Set Methods, in conjunction with Proc. IEEE ICCV (2001) 194-202.
    • H.K. Zhao, S. Osher, and R. Fedkiw, Fast surface reconstruction using the level set method, Proc. First IEEE Workshop on Variational and Level Set Methods, in conjunction with Proc. IEEE ICCV (2001) 194-202.


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.