Graph spectral image smoothing using the heat kernel

Weickert, 1998

Sapiro, 2001

A. Witkin, Scale-space filtering, in: Proceedings of the International Joint Conference on Artificial Intelligence, 1983, pp. 1019–1021.

Koenderink, 1984, The structure of images, Biol. Cybern., 50, 363, 10.1007/BF00336961

Babaud, 1986, Uniqueness of the Gaussian kernel for scale-space filtering, IEEE Trans. Pattern Anal. Mach. Intell., 8, 26, 10.1109/TPAMI.1986.4767749

Perona, 1990, Scale-space and edge detection using anisotropic diffusion, IEEE Trans. Pattern Anal. Mach. Intell., 12, 629, 10.1109/34.56205

Catté, 1992, Image selective smoothing and edge detection by nonlinear diffusion, SIAM J. Numer. Anal., 29, 182, 10.1137/0729012

Alvarez, 1992, Image selective smoothing and edge detection by nonlinear diffusion, SIAM J. Numer. Anal., 29, 845, 10.1137/0729052

Saint-Marc, 1991, Adaptive smoothing: a general tool for early vision, IEEE Trans. Pattern Anal. Mach. Intell., 13, 514, 10.1109/34.87339

You, 1996, Behavioral analysis of anisotropic diffusion in image processing, IEEE Trans. Image Process., 5, 1539, 10.1109/83.541424

Weickert, 1999, Coherence-enhancing diffusion filtering, Int. J. Comput. Vision, 31, 111, 10.1023/A:1008009714131

Black, 1998, Robust anisotropic diffusion, IEEE Trans. Image Process., 7, 421, 10.1109/83.661192

Bao, 2004, Smart nonlinear diffusion: a probabilistic approach, IEEE Trans. Pattern Anal. Mach. Intell., 26, 63, 10.1109/TPAMI.2004.1261079

Gilboa, 2004, Image enhancement and denoising by complex diffusion processes, IEEE Trans. Pattern Anal. Mach. Intell., 26, 1020, 10.1109/TPAMI.2004.47

A. Chambolle, Partial differential equations and image processing, in: Proceedings of the IEEE International Conference on Image Processing, 1994, pp. 16–20.

Sapiro, 1996, Anisotropic diffusion of multivalued images with application to color filtering, IEEE Trans. Image Process., 5, 1582, 10.1109/83.541429

Sochen, 1998, A general framework for low level vision, IEEE Trans. Image Process., 7, 310, 10.1109/83.661181

Blomgren, 1998, Color TV: total variation methods for restoration of vector-valued images, IEEE Trans. Image Process., 7, 304, 10.1109/83.661180

Tschumperle, 2005, Vector-valued image regularization with PDEs: a common framework for different applications, IEEE Trans. Pattern Anal. Mach. Intell., 27, 506, 10.1109/TPAMI.2005.87

Chung, 1997

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.

Hochbruck, 1997, On Krylov subspace approximations to the matrix exponential operator, SIAM J. Numer. Anal., 34, 1911, 10.1137/S0036142995280572

Sidje, 1998, Expokit: a software package for computing matrix exponentials, ACM Trans. Math. Software, 24, 130, 10.1145/285861.285868

Geman, 1984, Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images, IEEE Trans. Pattern Anal. Mach. Intell., 6, 721, 10.1109/TPAMI.1984.4767596

Smolka, 2001, Random walk approach to image enhancement, Signal Process., 81, 465, 10.1016/S0165-1684(00)00226-7

Coifman, 2006, Diffusion wavelets, Appl. Comput. Harmon. Anal., 21, 53, 10.1016/j.acha.2006.04.004

G. Taubin, A signal processing approach to fair surface design, in: Proceedings of SIGGRAPH, 1995, pp. 351–358.

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.

Shi, 2000, Normalized cuts and image segmentation, IEEE Trans. Pattern Anal. Mach. Intell., 22, 888, 10.1109/34.868688

Belkin, 2003, Laplacian Eigenmaps for dimensionality reduction and data representation, Neural Comput., 15, 1373, 10.1162/089976603321780317

Zhang, 2005, Image scale-space from the heat Kernel, vol. 3773, 181

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.

Canny, 1986, A computational approach to edge detection, IEEE Trans. Pattern Anal. Mach. Intell., 8, 679, 10.1109/TPAMI.1986.4767851

Cottet, 1993, Image processing through reaction combined with nonlinear diffusion, Math. Comput., 61, 659, 10.1090/S0025-5718-1993-1195422-2

D. Cvetkovic, M. Doob, H. Sachs, Spectra of Graphs: Theory and Applications, Academic Press, 1997.

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.

Atkins, 1998, A spectral algorithm for seriation and the consecutive ones problem, SIAM J. Comput., 28, 297, 10.1137/S0097539795285771

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.

Zucker, 1978, Estimates for the classical parametrix for the Laplacian, Manuscr. Math., 24, 1432, 10.1007/BF01168560

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.

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.

Chung, 2000, Discrete Green's functions, J. Combin. Theory, 91, 191, 10.1006/jcta.2000.3094

Chavel, 1984

S. Lafon, Diffusion maps and geometric harmonics, Ph.D. Dissertation, Yale University, 2004.

Di Zenzo, 1986, A note on the gradient of a multi-image, Comput. Vision Graphics Image Process., 33, 116, 10.1016/0734-189X(86)90223-9

Buades, 2005, A review of image denoising algorithms, with a new one, Multiscale Model. Simul., 4, 490, 10.1137/040616024

A. Efros, T. Leung, Texture synthesis by non parametric sampling, in: Proceedings of the IEEE International Conference on Computer Vision, 1999, pp. 1033–1038.

Golub, 1996

Moler, 2003, Nineteen Dubious ways to compute the exponential of a matrix, twenty-five years later, SIAM Rev., 45, 3, 10.1137/S00361445024180

Saad, 1992, Analysis of some Krylov subspace approximations to the matrix exponential operator, SIAM J. Numer. Anal., 29, 209, 10.1137/0729014

Saad, 1989, Krylov subspace methods on supercomputers, SIAM J. Sci. Stat. Comput., 10, 1200, 10.1137/0910073

A. Grigor’yan, Analysis on manifolds and heat kernel, in: Personal Lecture Notes, 2005.

Rosenberg, 1997

Y. Weiss, Segmentation using eigenvectors: a unifying view, in: Proceedings of the IEEE International Conference on Computer Vision, 1999, pp. 975–982.

Rudin, 1992, Nonlinear total variation based noise removal algorithms, Physica D, 60, 259, 10.1016/0167-2789(92)90242-F

Portilla, 2003, Image denoising using scale mixtures of Gaussians in the wavelet domain, IEEE Trans. Image Process., 12, 1338, 10.1109/TIP.2003.818640

Awate, 2006, Unsupervised, information-theoretic, adaptive image filtering for image restoration, IEEE Trans. Pattern Anal. Mach. Intell., 28, 364, 10.1109/TPAMI.2006.64

Tschumperle, 2006, Fast anisotropic smoothing of multi-valued images using curvature-preserving PDE's, Int. J. Comput. Vision, 68, 65, 10.1007/s11263-006-5631-z

Mrazek, 2003, Selection of optimal stopping time for nonlinear diffusion filtering, Int. J. Comput. Vision, 52, 189, 10.1023/A:1022908225256