Nonlocal Similarity Image Filtering

Lou, Yifei; Favaro, Paolo; Soatto, Stefano; Bertozzi, Andrea L.

doi:10.1007/978-3-642-04146-4_9

Cited by 34 publications

(26 citation statements)

References 30 publications

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“…Extension of the original approach including scale and rotation invariance for the data patches used to deÞne the weights are proposed in Lou et al [73] and Zimmer et al [120].…”

Section: Weights Deþned By Neighborhoodwise Differences: Nl-means Algmentioning

confidence: 99%

“…Recently, a novel class of the variational methods involving nonlocal penalty terms has been proposed (see Kindermann et al [64], Gilboa and Osher [40], [39], Lou et al [73], [74], Elmoataz et al [28] and references therein). If the Euler-Lagrange equations are used for these methods they have a form of difference-integral equations.…”

Section: Variational Formulationsmentioning

confidence: 99%

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From Local Kernel to Nonlocal Multiple-Model Image Denoising

et al. 2009

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We review the evolution of the nonparametric regression modeling in imaging from the local Nadaraya-Watson kernel estimate to the nonlocal means and further to transform-domain Þltering based on nonlocal block-matching. The considered methods are classiÞed mainly according to two main features: local/nonlocal and pointwise/multipoint. Here nonlocal is an alternative to local, and multipoint is an alternative to pointwise. These alternatives, though obvious simpliÞcations, allow to impose a fruitful and transparent classiÞcation of the basic ideas in the advanced techniques. Within this framework, we introduce a novel single-and multiplemodel transform domain nonlocal approach. The Block Matching and 3-D Filtering (BM3D) algorithm, which is currently one of the best performing denoising algorithms, is treated as a special case of the latter approach.

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“…Extension of the original approach including scale and rotation invariance for the data patches used to deÞne the weights are proposed in Lou et al [73] and Zimmer et al [120].…”

Section: Weights Deþned By Neighborhoodwise Differences: Nl-means Algmentioning

confidence: 99%

Section: Variational Formulationsmentioning

confidence: 99%

From Local Kernel to Nonlocal Multiple-Model Image Denoising

et al. 2009

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“…The difference lies in the way the patch similarity is evaluated. Due to the structural resemblance of the filters (53) and (54) to isotropic and anisotropic penalisation [83] we call (54) anisotropic NL-means. As a third example, let both → 0 and → 0.…”

Section: Gnds Filter Familymentioning

confidence: 99%

“…In particular, it can be seen as a bilateral filter [75] with a patch-based photometric similarity measure. Several variational formulations of the NL-means filter have been proposed [47,38,5,13,52] together with acceleration techniques [55,8,26,28,13,60] and invariant patch similarity measures [79,48,91,53]. This method has inspired the appearance of numerous so-called patch-based approaches for image smoothing, deblurring, segmentation, inpainting, super-resolution, and texture synthesis, among others.…”

Section: Introductionmentioning

confidence: 99%

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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“…In the context of nonlocal means, it makes sense also to involve pixels in the averaging process which belong to a neighbourhood that differs from the reference patch only by rotation or mirroring. Some models that consider invariances have been presented for example by Alexander et al [1], Kleinschmidt et al [27] and Lou et al [29]. Alexander et al have proposed a general model for the affine self-similarity of images, whereas the classical NL means algorithm only considers self-similarity in the translational sense.…”

Section: Introductionmentioning

confidence: 99%

Rotationally invariant similarity measures for nonlocal image denoising

Grewenig

Zimmer

Weickert

2011

Journal of Visual Communication and Image Representation

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Many natural or texture images contain structures that appear several times in the image. One of the denoising filters that successfully take advantage of such repetitive regions is the nonlocal means filter. It is simple and yields very good denoising results. Unfortunately, the block matching within the standard nonlocal means filter is not able to handle rotation or mirroring. Rotated or mirrored instances are not detected as variations of the corresponding original structures. In this paper, we analyse two natural approaches for a rotationally invariant similarity measure that will be used as an alternative to, respectively a modification of the well-known block matching algorithm in nonlocal means denoising. The first approach is based on similarity distances computed with the help of moment invariants whereas the second one estimates the rotation angle, rotates the block via interpolation and then uses a standard block matching. In contrast to the standard method, the presented algorithms can find similar regions or patches in an image even if they appear in several rotated or mirrored instances. With this modification, the nonlocal means filter is able to find more suitable regions for its weighted average.

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Nonlocal Similarity Image Filtering

Cited by 34 publications

References 30 publications

From Local Kernel to Nonlocal Multiple-Model Image Denoising

From Local Kernel to Nonlocal Multiple-Model Image Denoising

Generalised Nonlocal Image Smoothing

Rotationally invariant similarity measures for nonlocal image denoising

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