Discrete Regularization on Weighted Graphs for Image and Mesh Filtering

Bougleux, Sébastien; Elmoataz, Abderrahim; Melkemi, Mahmoud

doi:10.1007/978-3-540-72823-8_12

Cited by 48 publications

(48 citation statements)

References 21 publications

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“…We recognize in (1.7) the combinatorial primal-dual formulation [14] of the discrete weighted TV model as defined in [15,14,10]: The weighted TV problem appeared previously as a primal-dual formulation in the continuous setting. In a functional framework, given a planar domain Ω, and denoting by u and u two arbitrary points of Ω, the weighted TV model [14] is given by…”

Section: Particular Cases Of Interestmentioning

confidence: 99%

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Dual Constrained TV-based Regularization on Graphs

Grady¹,

Najman²,

Pesquet³

et al. 2013

SIAM J. Imaging Sci.

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Abstract. Algorithms based on Total Variation (TV) minimization are prevalent in image processing. They play a key role in a variety of applications such as image denoising, compressive sensing and inverse problems in general. In this work, we extend the TV dual framework that includes Chambolle's and Gilboa-Osher's projection algorithms for TV minimization. We use a flexible graph data representation that allows us to generalize the constraint on the projection variable. We show how this new formulation of the TV problem may be solved by means of fast parallel proximal algorithms. On denoising and deblurring examples, the proposed approach is shown not only to perform better than recent TV-based approaches, but also to perform well on arbitrary graphs instead of regular grids. The proposed method consequently applies to a variety of other inverse problems including image fusion and mesh filtering.

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Section: Particular Cases Of Interestmentioning

confidence: 99%

“…Improvements in the quality of the recovery were later obtained by introducing a weighted model [30,15,10,14]. In this model, a discrete TV energy is optimized on edge-weighted graphs.…”

Section: Particular Cases Of Interestmentioning

confidence: 99%

Dual Constrained TV-based Regularization on Graphs

Grady¹,

Najman²,

Pesquet³

et al. 2013

SIAM J. Imaging Sci.

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“…The discretisations involve pixel differences that are weighted by a patch-based similarity between pixels as in [15]. Bougleux et al [9,33,10] designed a discrete graph regularisation framework that can be seen as a digital extension of the continuous framework [38] employing a -Dirichlet regulariser. The same discrete framework has been applied in image segmentation tasks [73].…”

Section: Nds and Graph Regularisationmentioning

confidence: 99%

“…Other definitions of the weighted gradient norm are possible using alternative weighted difference operators (see [41] and references therein). This regulariser has been used in [90,9,33,10] for regularisation on arbitrary graphs. In particular, the following energy functionals have been proposed in [10]:…”

Section: Nds and Graph Regularisationmentioning

confidence: 99%

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Generalised Nonlocal Image Smoothing

Pizarro

Pavel²,

Didas

et al. 2010

Int J Comput Vis

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We propose a discrete variational approach for image smoothing consisting of nonlocal data and smoothness contraints that penalise general dissimilarity measures defined on image patches. One of such dissimilarity measures is the weighted 2 distance between patches. In such a case we derive an iterative neighbourhood filter that induces a new similarity measure in the photometric domain. It can be regarded as an extended patch similarity measure that evaluates not only the patch similarity of two chosen pixels, but also the similarity of their corresponding neighbours. This leads to a more robust smoothing process since the pixels selected for averaging are more coherent with the local image structure. The suggested approach includes two recently proposed filters as special cases: The NLmeans filter of Buades et al. and the NDS filter of Mrázek et al. In fact, the approach introduced here can be considered as a generalisation of the latter filter. We evaluate our method for the task of denoising greyscale and colour images degraded by Gaussian and impulse noise, demonstrating that it compares very well to other more sophisticated patch-based approaches.

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Supervised learning and graph signal processing strategies for beam tracking in highly directional mobile communications

Ortega

Guerreiro

Hui

et al. 2019

Trans Emerging Tel Tech

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The use of efficient beam tracking mechanisms becomes necessary in highly directional communication of the fifth‐generation systems. In this context, this paper analyzes the tracking problem and proposes a framework that exploits the samples in the user equipment (UE) dataset (historical UE dataset) to efficiently estimate and predict the channel state at the base station. The framework is composed of two steps. First, a supervised learning algorithm, namely, K‐nearest neighbors (K‐NN), is evaluated as a mean of (i) finding the most similar historical samples to some beam measurements reported by the UE and (ii) predicting the corresponding channel state. As a second step, a sampling and reconstruction strategy based on graph signal processing (GSP) called K‐nearest neighbors with reconstruction (K‐NN‐R) is introduced in order to reduce the beam search space during the beam measurement stage, which allows a more efficient usage of the feedback channel. Simulation results illustrate the performance of the proposal in terms of normalized mean square error in comparison with three traditional/baseline prediction techniques. The K‐NN technique provides a better performance than the baseline approaches for any length of the observed temporal window and with full beam sweep. Meanwhile, the K‐NN‐R framework outperforms the baseline approaches with only half of the beam pairs and throughout a significantly low length of observed temporal window.

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Discrete Regularization on Weighted Graphs for Image and Mesh Filtering

Cited by 48 publications

References 21 publications

Dual Constrained TV-based Regularization on Graphs

Dual Constrained TV-based Regularization on Graphs

Generalised Nonlocal Image Smoothing

Supervised learning and graph signal processing strategies for beam tracking in highly directional mobile communications

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