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Volumn 41, Issue 11, 2008, Pages 3328-3342

Graph spectral image smoothing using the heat kernel

Author keywords

Anisotropic diffusion; Denoising; Graph Laplacian; Graph spectra; Heat equation; Heat kernel; Image smoothing; Low pass filtering

Indexed keywords

DIFFUSION; GRAPH THEORY; IMAGE ENHANCEMENT; LAPLACE TRANSFORMS; LINEAR EQUATIONS; PARTIAL DIFFERENTIAL EQUATIONS; SEMICONDUCTOR DOPING; SIGNAL PROCESSING; STANDARDS;

EID: 48149111839     PISSN: 00313203     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.patcog.2008.05.007     Document Type: Article
Times cited : (176)

References (59)
  • 3
    • 0020891393 scopus 로고    scopus 로고
    • A. Witkin, Scale-space filtering, in: Proceedings of the International Joint Conference on Artificial Intelligence, 1983, pp. 1019-1021.
    • A. Witkin, Scale-space filtering, in: Proceedings of the International Joint Conference on Artificial Intelligence, 1983, pp. 1019-1021.
  • 4
    • 0021136434 scopus 로고
    • The structure of images
    • Koenderink J. The structure of images. Biol. Cybern. 50 (1984) 363-370
    • (1984) Biol. Cybern. , vol.50 , pp. 363-370
    • Koenderink, J.1
  • 6
    • 0025465145 scopus 로고
    • Scale-space and edge detection using anisotropic diffusion
    • Perona P., and Malik J. Scale-space and edge detection using anisotropic diffusion. IEEE Trans. Pattern Anal. Mach. Intell. 12 7 (1990) 629-639
    • (1990) IEEE Trans. Pattern Anal. Mach. Intell. , vol.12 , Issue.7 , pp. 629-639
    • Perona, P.1    Malik, J.2
  • 7
    • 0026821645 scopus 로고
    • Image selective smoothing and edge detection by nonlinear diffusion
    • Catté F., Lions P., Morel J., and Coll T. Image selective smoothing and edge detection by nonlinear diffusion. SIAM J. Numer. Anal. 29 (1992) 182-193
    • (1992) SIAM J. Numer. Anal. , vol.29 , pp. 182-193
    • Catté, F.1    Lions, P.2    Morel, J.3    Coll, T.4
  • 8
    • 0026883886 scopus 로고
    • Image selective smoothing and edge detection by nonlinear diffusion
    • Alvarez L., Lions P., and Morel J. 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.2    Morel, J.3
  • 10
    • 0030283909 scopus 로고    scopus 로고
    • Behavioral analysis of anisotropic diffusion in image processing
    • You Y., Xu W., Tannenbaum A., and Kaveh M. Behavioral analysis of anisotropic diffusion in image processing. IEEE Trans. Image Process. 5 11 (1996) 1539-1553
    • (1996) IEEE Trans. Image Process. , vol.5 , Issue.11 , pp. 1539-1553
    • You, Y.1    Xu, W.2    Tannenbaum, A.3    Kaveh, M.4
  • 11
    • 0032666007 scopus 로고    scopus 로고
    • Coherence-enhancing diffusion filtering
    • Weickert J. Coherence-enhancing diffusion filtering. Int. J. Comput. Vision 31 (1999) 111-127
    • (1999) Int. J. Comput. Vision , vol.31 , pp. 111-127
    • Weickert, J.1
  • 13
    • 0742321110 scopus 로고    scopus 로고
    • Smart nonlinear diffusion: a probabilistic approach
    • Bao Y., and Krim H. Smart nonlinear diffusion: a probabilistic approach. IEEE Trans. Pattern Anal. Mach. Intell. 26 1 (2004) 63-72
    • (2004) IEEE Trans. Pattern Anal. Mach. Intell. , vol.26 , Issue.1 , pp. 63-72
    • Bao, Y.1    Krim, H.2
  • 14
    • 3242723371 scopus 로고    scopus 로고
    • Image enhancement and denoising by complex diffusion processes
    • Gilboa G., Sochen N., and Zeevi Y. Image enhancement and denoising by complex diffusion processes. IEEE Trans. Pattern Anal. Mach. Intell. 26 8 (2004) 1020-1036
    • (2004) IEEE Trans. Pattern Anal. Mach. Intell. , vol.26 , Issue.8 , pp. 1020-1036
    • Gilboa, G.1    Sochen, N.2    Zeevi, Y.3
  • 15
    • 85177189706 scopus 로고    scopus 로고
    • A. Chambolle, Partial differential equations and image processing, in: Proceedings of the IEEE International Conference on Image Processing, 1994, pp. 16-20.
    • A. Chambolle, Partial differential equations and image processing, in: Proceedings of the IEEE International Conference on Image Processing, 1994, pp. 16-20.
  • 16
    • 0030286977 scopus 로고    scopus 로고
    • Anisotropic diffusion of multivalued images with application to color filtering
    • Sapiro G., and Ringach D. Anisotropic diffusion of multivalued images with application to color filtering. IEEE Trans. Image Process. 5 11 (1996) 1582-1586
    • (1996) IEEE Trans. Image Process. , vol.5 , Issue.11 , pp. 1582-1586
    • Sapiro, G.1    Ringach, D.2
  • 18
    • 0032026262 scopus 로고    scopus 로고
    • Color TV: total variation methods for restoration of vector-valued images
    • Blomgren P., and Chan T. Color TV: total variation methods for restoration of vector-valued images. IEEE Trans. Image Process. 7 3 (1998) 304-309
    • (1998) IEEE Trans. Image Process. , vol.7 , Issue.3 , pp. 304-309
    • Blomgren, P.1    Chan, T.2
  • 19
    • 17144426986 scopus 로고    scopus 로고
    • Vector-valued image regularization with PDEs: a common framework for different applications
    • Tschumperle D., and Deriche R. Vector-valued image regularization with PDEs: a common framework for different applications. IEEE Trans. Pattern Anal. Mach. Intell. 27 4 (2005) 506-517
    • (2005) IEEE Trans. Pattern Anal. Mach. Intell. , vol.27 , Issue.4 , pp. 506-517
    • Tschumperle, D.1    Deriche, R.2
  • 20
    • 0003882879 scopus 로고    scopus 로고
    • American Mathematical Society, Providence, RI
    • Chung F.R.K. Spectral Graph Theory (1997), American Mathematical Society, Providence, RI
    • (1997) Spectral Graph Theory
    • Chung, F.R.K.1
  • 21
    • 48149094449 scopus 로고    scopus 로고
    • R. Kondor, J. Lafferty, Diffusion kernels on graphs and other discrete structures, in: Proceedings of the 19th International Conference on Machine Learning, 2002, pp. 315-322.
    • R. Kondor, J. Lafferty, Diffusion kernels on graphs and other discrete structures, in: Proceedings of the 19th International Conference on Machine Learning, 2002, pp. 315-322.
  • 22
    • 0347799731 scopus 로고    scopus 로고
    • On Krylov subspace approximations to the matrix exponential operator
    • Hochbruck M., and Lubich C. On Krylov subspace approximations to the matrix exponential operator. SIAM J. Numer. Anal. 34 (1997) 1911-1925
    • (1997) SIAM J. Numer. Anal. , vol.34 , pp. 1911-1925
    • Hochbruck, M.1    Lubich, C.2
  • 23
    • 0032010619 scopus 로고    scopus 로고
    • Expokit: a software package for computing matrix exponentials
    • Sidje R. Expokit: a software package for computing matrix exponentials. ACM Trans. Math. Software 24 1 (1998) 130-156
    • (1998) ACM Trans. Math. Software , vol.24 , Issue.1 , pp. 130-156
    • Sidje, R.1
  • 24
    • 0021518209 scopus 로고
    • Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images
    • Geman S., and Geman D. Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images. IEEE Trans. Pattern Anal. Mach. Intell. 6 6 (1984) 721-741
    • (1984) IEEE Trans. Pattern Anal. Mach. Intell. , vol.6 , Issue.6 , pp. 721-741
    • Geman, S.1    Geman, D.2
  • 25
    • 0035278305 scopus 로고    scopus 로고
    • Random walk approach to image enhancement
    • Smolka B., and Wojciechowski K. Random walk approach to image enhancement. Signal Process. 81 (2001) 465-482
    • (2001) Signal Process. , vol.81 , pp. 465-482
    • Smolka, B.1    Wojciechowski, K.2
  • 27
    • 0029179430 scopus 로고    scopus 로고
    • G. Taubin, A signal processing approach to fair surface design, in: Proceedings of SIGGRAPH, 1995, pp. 351-358.
    • G. Taubin, A signal processing approach to fair surface design, in: Proceedings of SIGGRAPH, 1995, pp. 351-358.
  • 28
    • 85015718223 scopus 로고    scopus 로고
    • M. Desbrun, M. Meyer, P. Schroder, A. Barr, Implicit fairing of irregular meshes using diffusion and curvature flow, in: Proceedings of the SIGGRAPH, 1999, pp. 317-324.
    • M. Desbrun, M. Meyer, P. Schroder, A. Barr, Implicit fairing of irregular meshes using diffusion and curvature flow, in: Proceedings of the SIGGRAPH, 1999, pp. 317-324.
  • 30
    • 0042378381 scopus 로고    scopus 로고
    • Laplacian Eigenmaps for dimensionality reduction and data representation
    • Belkin M., and Niyogi P. Laplacian Eigenmaps for dimensionality reduction and data representation. Neural Comput. 15 6 (2003) 1373-1396
    • (2003) Neural Comput. , vol.15 , Issue.6 , pp. 1373-1396
    • Belkin, M.1    Niyogi, P.2
  • 32
    • 78649875091 scopus 로고    scopus 로고
    • F. Zhang, E.R. Hancock, Heat kernel smoothing of scalar and vector image data, in: Proceedings of the IEEE International Conference on Image Processing, 2006, pp. 1549-1552.
    • F. Zhang, E.R. Hancock, Heat kernel smoothing of scalar and vector image data, in: Proceedings of the IEEE International Conference on Image Processing, 2006, pp. 1549-1552.
  • 33
    • 0022808786 scopus 로고
    • A computational approach to edge detection
    • Canny J. A computational approach to edge detection. IEEE Trans. Pattern Anal. Mach. Intell. 8 6 (1986) 679-698
    • (1986) IEEE Trans. Pattern Anal. Mach. Intell. , vol.8 , Issue.6 , pp. 679-698
    • Canny, J.1
  • 34
    • 84968487220 scopus 로고
    • Image processing through reaction combined with nonlinear diffusion
    • Cottet G., and Germain L. Image processing through reaction combined with nonlinear diffusion. Math. Comput. 61 (1993) 659-673
    • (1993) Math. Comput. , vol.61 , pp. 659-673
    • Cottet, G.1    Germain, L.2
  • 35
    • 48149110226 scopus 로고    scopus 로고
    • D. Cvetkovic, M. Doob, H. Sachs, Spectra of Graphs: Theory and Applications, Academic Press, 1997.
    • D. Cvetkovic, M. Doob, H. Sachs, Spectra of Graphs: Theory and Applications, Academic Press, 1997.
  • 36
    • 0029713930 scopus 로고    scopus 로고
    • S. Sarkar, K. Boyer, Quantitative measures of change based on feature organization: eigenvalues and eigenvectors, in: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 1996, p. 478.
    • S. Sarkar, K. Boyer, Quantitative measures of change based on feature organization: eigenvalues and eigenvectors, in: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 1996, p. 478.
  • 37
    • 0032057853 scopus 로고    scopus 로고
    • A spectral algorithm for seriation and the consecutive ones problem
    • Atkins J., Bowman E., and Hendrickson B. A spectral algorithm for seriation and the consecutive ones problem. SIAM J. Comput. 28 1 (1998) 297-310
    • (1998) SIAM J. Comput. , vol.28 , Issue.1 , pp. 297-310
    • Atkins, J.1    Bowman, E.2    Hendrickson, B.3
  • 38
    • 48149107256 scopus 로고    scopus 로고
    • Y. Azary, A. Fiaty, A. Karlinz, F. McSherryz, J. Saia, Spectral analysis of data, in: Proceedings of the ACM Symposium on Theory of Computing, 2001, pp. 619-626.
    • Y. Azary, A. Fiaty, A. Karlinz, F. McSherryz, J. Saia, Spectral analysis of data, in: Proceedings of the ACM Symposium on Theory of Computing, 2001, pp. 619-626.
  • 39
    • 33751045209 scopus 로고
    • Estimates for the classical parametrix for the Laplacian
    • Zucker S. Estimates for the classical parametrix for the Laplacian. Manuscr. Math. 24 (1978) 1432-1785
    • (1978) Manuscr. Math. , vol.24 , pp. 1432-1785
    • Zucker, S.1
  • 40
    • 26944489604 scopus 로고    scopus 로고
    • M. Hein, J. Audibert, U. von Luxburg, From graphs to manifoldsłweak and strong pointwise consistency of graph Laplacians, in: Proceedings of the 18th Conference on Learning Theory, 2005, pp. 470-485.
    • M. Hein, J. Audibert, U. von Luxburg, From graphs to manifoldsłweak and strong pointwise consistency of graph Laplacians, in: Proceedings of the 18th Conference on Learning Theory, 2005, pp. 470-485.
  • 41
    • 33745133745 scopus 로고    scopus 로고
    • L. Grady, Multilabel random walker image segmentation using prior models, in: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 2005, pp. 763-770.
    • L. Grady, Multilabel random walker image segmentation using prior models, in: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 2005, pp. 763-770.
  • 42
    • 0034215984 scopus 로고    scopus 로고
    • Discrete Green's functions
    • Chung F., and Yau S.-T. Discrete Green's functions. J. Combin. Theory 91 (2000) 191-214
    • (2000) J. Combin. Theory , vol.91 , pp. 191-214
    • Chung, F.1    Yau, S.-T.2
  • 44
    • 48149091677 scopus 로고    scopus 로고
    • S. Lafon, Diffusion maps and geometric harmonics, Ph.D. Dissertation, Yale University, 2004.
    • S. Lafon, Diffusion maps and geometric harmonics, Ph.D. Dissertation, Yale University, 2004.
  • 46
    • 33645653318 scopus 로고    scopus 로고
    • A review of image denoising algorithms, with a new one
    • Buades A., Coll B., and Morel J. A review of image denoising algorithms, with a new one. Multiscale Model. Simul. 4 2 (2005) 490-530
    • (2005) Multiscale Model. Simul. , vol.4 , Issue.2 , pp. 490-530
    • Buades, A.1    Coll, B.2    Morel, J.3
  • 47
    • 85138841131 scopus 로고    scopus 로고
    • A. Efros, T. Leung, Texture synthesis by non parametric sampling, in: Proceedings of the IEEE International Conference on Computer Vision, 1999, pp. 1033-1038.
    • A. Efros, T. Leung, Texture synthesis by non parametric sampling, in: Proceedings of the IEEE International Conference on Computer Vision, 1999, pp. 1033-1038.
  • 49
    • 0037354371 scopus 로고    scopus 로고
    • Nineteen Dubious ways to compute the exponential of a matrix, twenty-five years later
    • Moler C., and Van Loan C. Nineteen Dubious ways to compute the exponential of a matrix, twenty-five years later. SIAM Rev. 45 1 (2003) 3-49
    • (2003) SIAM Rev. , vol.45 , Issue.1 , pp. 3-49
    • Moler, C.1    Van Loan, C.2
  • 50
    • 0026818185 scopus 로고
    • Analysis of some Krylov subspace approximations to the matrix exponential operator
    • Saad Y. Analysis of some Krylov subspace approximations to the matrix exponential operator. SIAM J. Numer. Anal. 29 (1992) 209-228
    • (1992) SIAM J. Numer. Anal. , vol.29 , pp. 209-228
    • Saad, Y.1
  • 51
    • 0001609443 scopus 로고
    • Krylov subspace methods on supercomputers
    • Saad Y. Krylov subspace methods on supercomputers. SIAM J. Sci. Stat. Comput. 10 (1989) 1200-1232
    • (1989) SIAM J. Sci. Stat. Comput. , vol.10 , pp. 1200-1232
    • Saad, Y.1
  • 52
    • 48149106239 scopus 로고    scopus 로고
    • A. Grigor'yan, Analysis on manifolds and heat kernel, in: Personal Lecture Notes, 2005.
    • A. Grigor'yan, Analysis on manifolds and heat kernel, in: Personal Lecture Notes, 2005.
  • 54
    • 85139272337 scopus 로고    scopus 로고
    • Y. Weiss, Segmentation using eigenvectors: a unifying view, in: Proceedings of the IEEE International Conference on Computer Vision, 1999, pp. 975-982.
    • Y. Weiss, Segmentation using eigenvectors: a unifying view, in: Proceedings of the IEEE International Conference on Computer Vision, 1999, pp. 975-982.
  • 55
    • 44049111982 scopus 로고
    • Nonlinear total variation based noise removal algorithms
    • Rudin L., Osher S., and Fatemi E. Nonlinear total variation based noise removal algorithms. Physica D 60 (1992) 259-268
    • (1992) Physica D , vol.60 , pp. 259-268
    • Rudin, L.1    Osher, S.2    Fatemi, E.3
  • 56
    • 0242636409 scopus 로고    scopus 로고
    • Image denoising using scale mixtures of Gaussians in the wavelet domain
    • Portilla J., Strela V., Wainwright M., and Simoncelli E. Image denoising using scale mixtures of Gaussians in the wavelet domain. IEEE Trans. Image Process. 12 11 (2003) 1338-1351
    • (2003) IEEE Trans. Image Process. , vol.12 , Issue.11 , pp. 1338-1351
    • Portilla, J.1    Strela, V.2    Wainwright, M.3    Simoncelli, E.4
  • 57
    • 31544453901 scopus 로고    scopus 로고
    • Unsupervised, information-theoretic, adaptive image filtering for image restoration
    • Awate S., and Whitaker R. Unsupervised, information-theoretic, adaptive image filtering for image restoration. IEEE Trans. Pattern Anal. Mach. Intell. 28 3 (2006) 364-376
    • (2006) IEEE Trans. Pattern Anal. Mach. Intell. , vol.28 , Issue.3 , pp. 364-376
    • Awate, S.1    Whitaker, R.2
  • 58
    • 33646581986 scopus 로고    scopus 로고
    • Fast anisotropic smoothing of multi-valued images using curvature-preserving PDE's
    • Tschumperle D. Fast anisotropic smoothing of multi-valued images using curvature-preserving PDE's. Int. J. Comput. Vision 68 1 (2006) 65-82
    • (2006) Int. J. Comput. Vision , vol.68 , Issue.1 , pp. 65-82
    • Tschumperle, D.1
  • 59
    • 0038681971 scopus 로고    scopus 로고
    • Selection of optimal stopping time for nonlinear diffusion filtering
    • Mrazek P., and Navara M. Selection of optimal stopping time for nonlinear diffusion filtering. Int. J. Comput. Vision 52 (2003) 189-203
    • (2003) Int. J. Comput. Vision , vol.52 , pp. 189-203
    • Mrazek, P.1    Navara, M.2


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