Modeling Textures with Total Variation Minimization and Oscillating Patterns in Image Processing

By Luminita A. Vese, Stanley J. Osher. Journal of Scientific Computing, 2003

781 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computer Vision and Pattern Recognition

View Paper: https://www.semanticscholar.org/paper/0a2ec3895dc72143f998c6129b0789200d1519e7

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In Computational Mechanics

In Computer Vision and Pattern Recognition

Citations in the corpus

A Review of Image Denoising Algorithms, with a New One (2005, methodology): “Because of the different and more ambitious scopes of the Meyer method [2, 36, 26], which makes it parameter- and implementation-dependent, we could not draw it into the discussion.”
Aspects of Total Variation Regularized L[sup 1] Function Approximation (2005, methodology): “For example, following up on Meyer’s ideas Vese and Osher [24],”
Iteratively solving linear inverse problems under general convex constraints (2007, background): “image, as in [9], which was in turn, inspired by [7] and [17].”
Image Decomposition and Restoration Using Total Variation Minimization and the H1 (2003, methodology): “Fig. 8. More comparisons with the model [ 21 ] from (1.4).”
Recent Developments in Total Variation Image Restoration (2004, background): “[18] S. Esedoglu and S. Osher.”
Signal Recovery by Proximal Forward-Backward Splitting (2005, background): “…regularization problems [10, 30, 31, 36], Fourier regularization problems [46, 50], geometry/texture image decomposition problems [5, 6, 7, 57, 71], hard-constrained inconsistent feasibility problems [26], alternating projection signal synthesis problems [38, 60], least square-distance…”
On image denoising methods (2004, methodology): “Because of the difierent and more ambitious scopes of the Meyer method, [2, 38, 29], which makes it parameter and implementation-dependent, we could not draw it into the discussion.”
Deblurring and Denoising of Images by Nonlocal Functionals (2005, methodology): “Several other methods such as texture models ([17, 19, 25]) or methods for diﬀerent noise models [21] are derived from the original ROF model.”
Simultaneous structure and texture image inpainting (2003, methodology): “In this section, we review the image decomposition approach proposed in [30], [31], which is one of the three key ingredients of the simultaneous texture and structure image inpainting algorithm.”
Split Bregman Methods and Frame Based Image Restoration (2009, background): “These two layers have very different characteristics; see [3, 54, 64].”
From Local Kernel to Nonlocal Multiple-Model Image Denoising (2009, methodology): “4.3): (Kindermann et al. 2005; Gilboa and Osher 2007a, 2007b; Lou et al. 2008a, 2008b; Elmoataz et al. 2008; Tschumperlé and Brun 2008a, 2008b) M U L T IP O IN T Section 3 (Local multipoint modeling) Section 5 (Nonlocal multipoint modeling) Overcomplete transform (Öktem et al. 1999, 2001; Egiazarian”
The asymptotic behavior of the composition of two resolvents (2005, background): “We thus recover problems arising in variational inequalities[30], best approximation[12], image processing[4,44], mechanics[34], and optimization[1,31].”
Structure-Texture Image Decomposition—Modeling, Algorithms, and Parameter Selection (2006, background): “This approach has recently been analyzed in Meyer (2001), which is the inspiration source of many works (Vese and Osher, 2003; Osher et al. 2003; Aujol et al., 2005; Aubert and Aujol, 2005; Starck et al., 2003; Aujol and Chambolle, 2005; Bect et al., 2004; Chan and Esedoglu, 2004; Daubechies and Tes”
Forward-Douglas–Rachford splitting and forward-partial inverse method for solving monotone inclusions (2012, background): “ization [18, 44], variational inequalities [31, 46, 47], monotone operator theory [23, 37, 32, 43], partial diﬀerential equations [26, 27, 31, 34, 51], economics [29, 36], signal and image processing [2, 3, 13, 14, 21, 22, 39, 40, 48], evolution inclusions [1, 28, 42], and traﬃc theory [8, 9, 25, 38”
Image Decomposition into a Bounded Variation Component and an Oscillating Component (2005, methodology): “We propose to solve the following variant of Osher and Vese’s functional [ 12 ]:”