Nonlocal Linear Image Regularization and Supervised Segmentation

By Guy Gilboa, Stanley J. Osher. Multiscale Modeling & simulation, 2007

562 citations recorded by the source corpus.

Subfields: Computer Vision and Pattern Recognition, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/61453a6ae56b00e3c9cf7fb3eb07558d665d5e5c

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In Computer Vision and Pattern Recognition

In Mathematical Physics

Citations in the corpus

Removing Multiplicative Noise by Douglas-Rachford Splitting Methods (2010, methodology): “The idea of nonlocal means goes back to [12] and was incorporated into the variational framework in [35–37 , 67 In the following, we review variational methods for removing multiplicative noise, where we restrict our attention to TV regularizers.”
From Local Kernel to Nonlocal Multiple-Model Image Denoising (2009, background): “Recently, a novel class of the variational methods involving nonlocal penalty terms has been proposed (see Kindermann et al. 2005; Gilboa and Osher 2007a, 2007b; Lou et al. 2008a, 2008b; Elmoataz et al. 2008 and references therein).”
Image Recovery via Nonlocal Operators (2010, methodology): “Inspired by graph theory [26], Gilboa and Osher [11] pro-pose a particular functional g , which turns out to be a linear regularization for denoising and can be applied to supervised segmentation as well; they formalize a systematic and coherent framework [12] for nonlocal operators.”
Nonlocal Discrete Regularization on Weighted Graphs: A Framework for Image and Manifold Processing (2008, background): “This framework can also be considered as a discrete analogue of the nonlocal continuous regularization for the case of images [27], [33].”
Generalizing the Nonlocal-Means to Super-Resolution Reconstruction (2009, background): “Following the rationale and steps taken in [33] and [35], we present such a penalty function, and show how these algorithms emerge from it.”
Nonlocal Image and Movie Denoising (2008, methodology): “This law is used to synthesize similar texture images by an iterative algorithm.”
Image super-resolution: The techniques, applications, and future (2016, background): “regularization [47], NLTV regularization [114], and the original HR image.”
Image Denoising Methods. A New Nonlocal Principle (2010, background): “Several articles on deblurring have followed this variational line [49], [66], [43] (for image segmentation), [9] (in fluorescence microscopy), [99], (again for nonlocal deconvolution), and [55] (for deconvolution and tomographic reconstruction).”
Characterization of Sobolev and BV Spaces (2011, background): “[11] A. Bertozzi, J. Greer, S. Osher, and K. Vixie.”
Identification of the Diffusion Parameter in Nonlocal Steady Diffusion Problems (2013, methodology): “Among those applications we have image analyses [14, 24, 25, 32], machine learning [36], nonlocal Dirichlet forms [6], kinetic equations [8, 31], phase transitions [11, 23], and nonlocal heat conduction [12].”
Analysis and Approximation of Nonlocal Diffusion Problems with Volume Constraints (2012, background): “The operator L and its generalizations arise in many applications such as image analyses [19, 32, 33, 39], machine learning [47], nonlocal Dirichlet forms [5, Sec.”
Image denoising with nonlocal spectral graph wavelets (2010, background): “Many extensions and variations of the original nonlocal means have been been studied [6, 7, 8].”
$\Gamma$-convergence of graph Ginzburg-Landau functionals (2012, background): “3 Asymptotic behavior of nonlocal means The functionals of nonlocal means type —or (anisotropic) nonlocal total variation type— we consider are built on the square grid in which the graphs are fully connected, [21, 34, 35, 20].”
Non-local Regularization of Inverse Problems (2008, methodology): “Denoising using quadratic penalization on image graphs is studied by Guilboa and Osher for image restoration and segmentation [14].”
Localization of nonlocal gradients in various topologies (2015, methodology): “We mention, for instance, some in image processing [4] and [16, 17], the peridynamic model of continuum mechanics [13, 23, 24] and nonlocal diffusion [3, 18].”
Nonlocal Operators with Applications to Image Processing (2008, methodology): “In the more common case where the weights are computed with a Gaussian-like formula, e.g. as in [9],[28],[52],[30], the weights decay fast for distances above a certain threshold (usually related to the noise variance).”