The Total Variation Flow in RN

By Giovanni Bellettini, V. Caselles, Matteo Novaga. 2002

289 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Computer Vision and Pattern Recognition, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/462d2d262adb4a8c78a372ad573334107495dfcb

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Citations in the corpus

LOCAL SOLVABILITY OF A CONSTRAINED GRADIENT SYSTEM OF TOTAL VARIATION (2003, background): “, [6, 8] and also [13, 17, 19]), for a recent L1-theory, see [1, 2, 3, 7].”
Uniqueness of the Cheeger set of a convex body (2007, result): “This has been proved in [Giusti 1978; Bellettini et al. 2002; Kawohl and Lachand-Robert 2006; Alter et al. 2005b; Kawohl and Novaga 2006], though it was stated in terms of calibrability in the second and fourth of these references.”
The anisotropic total variation flow (2005, background): “Pf (Qµ ,B ˜ f (0; R) \ F) . Working as in [ 16 ] we obtain that div( ˜”
Equivalent definitions of BV space and of total variation on metric measure spaces (2014, methodology): “Specifically, in our case we shall use the gradient flow in L(2)(X,m) of the functional f 7→ |Df |∗(X), also called total variation flow in image processing [9].”
A characterization of convex calibrable sets in RN with respect to anisotropic norms (2008, methodology): “The characterization of the calibrability of a convex set in R(2), with respect to the euclidean perimeter was proved by Giusti in [4] and was rederived in [2] where calibrable sets were used to construct explicit solutions of the denoising problem in image processing.”
Total Variation Flow and Sign Fast Diffusion in one dimension (2011, result): “The asymptotic behaviour of the TVF is still an open problem in many aspects, even if partial results have appeared in [4, 3, 5, 7, 8, 9, 17].”
Edge-preserving and scale-dependent properties of total variation regularization (2003, background): “In [7], Bellettini et al discuss conservation of shape and scale parameters controlling evolution within the TV-flow context.”
Local smoothing effects, positivity, and Harnack inequalities for the fast p-Laplacian equation (2009, background): “the 1-Laplacian, whenever Ω is a set of finite perimeter P (Ω), satisfying certain condition on the curvature of the boundary, we refer to [1, 4] for further details.”
Variable Exponent, Linear Growth Functionals in Image Restoration (2006, background): “More related work on linear growth functionals and their flows can be found in [2, 3, 4, 5, 6, 7, 11, 13, 32].”
Crystalline Mean Curvature Flow of Convex Sets (2006, background): “As in [13] we may prove that u is a solution of (4.”
Aspects of Total Variation Regularized L[sup 1] Function Approximation (2005, result): “The results of [4] generalize the results of [18], but also show that the class of binary images that have this weaker property (i.”
DIRICHLET PROBLEMS FOR THE 1-LAPLACE OPERATOR, INCLUDING THE EIGENVALUE PROBLEM (2007, background): “13) can be found in the papers [6] and [7] of Belletini, Caselles and Novaga.”
CHARACTERIZATION OF CHEEGER SETS FOR CONVEX SUBSETS OF THE PLANE (2006, background): “Theorem 4 in [4] can be interpreted as a variant of our Theorem 2, but its proof uses different and more technical methods.”