Decomposition of images by the anisotropic Rudin‐Osher‐Fatemi model

Esedoḡlu, Selim; Osher, Stanley

doi:10.1002/cpa.20045

Cited by 184 publications

(146 citation statements)

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“…[NP99,BNP01a,BNP01b,EO04,OBGXY05] and references therein. See also [FM91,C04] for anisotropic problems related to the Willmore functional and [CS09,WX11] for elliptic anisotropic systems inspired by fluidodynamics.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Gradient Bounds and Rigidity Results for Singular, Degenerate, Anisotropic Partial Differential Equations

Cozzi

Farina

Valdinoci

2014

Commun. Math. Phys.

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Abstract:We consider the Wulff-type energy functionalwhere B is positive, monotone and convex, and H is positive homogeneous of degree 1. The critical points of this functional satisfy a possibly singular or degenerate, quasilinear equation in an anisotropic medium.We prove that the gradient of the solution is bounded at any point by the potential F (u) and we deduce several rigidity and symmetry properties.

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Section: Introduction and Main Resultsmentioning

confidence: 99%

Gradient Bounds and Rigidity Results for Singular, Degenerate, Anisotropic Partial Differential Equations

Cozzi

Farina

Valdinoci

2014

Commun. Math. Phys.

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“…Beck and Teboulle [7] derived a similar projection algorithm (equivalent to the one in [6]) and showed how to accelerate it by using information from different iterations. Also of relevance is the work of Esedoglu and Osher [8] where they described a general TV and studied its properties. We note that the directional TV described in this letter does fit into the context described in [8].…”

Section: Previous Workmentioning

confidence: 99%

“…Also of relevance is the work of Esedoglu and Osher [8] where they described a general TV and studied its properties. We note that the directional TV described in this letter does fit into the context described in [8]. However, [8] to the one in this letter.…”

Section: Previous Workmentioning

confidence: 99%

Directional Total Variation

Bayram

Kamasak

2012

IEEE Signal Process. Lett.

100

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Abstract-This paper introduces a "directional total variation" (TV) where the gradients are weighted depending on their direction. This directional TV has increased (and tunable) sensitivity to variations at a selected direction. In order to demonstrate the utility of the directional TV, we consider an image denoising formulation. This formulation requires the realization of the 'proximal map' of the directional TV. Therefore, it is relevant for more general inverse problem settings as well. We derive an algorithm that solves the problem and use the algorithm to study the effects of the parameters of the directional TV.

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“…Assume first that u ≥ 0, and insert the layer cake representation (8) in the formula (18) to get the inequality,…”

Section: Anisotropic Smoothness Termsmentioning

confidence: 99%

“…Note that this framework includes the metrics considered in [11]. Related is the anisotropic ROF-model considered in [8], but they do not use the corresponding coarea formula.…”

Section: Remark (A)mentioning

confidence: 99%