Fundamental relationship between bilateral filtering, adaptive smoothing, and the nonlinear diffusion equation

Barash, Danny

doi:10.1109/tpami.2002.1008390

Cited by 452 publications

(282 citation statements)

References 13 publications

(19 reference statements)

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“…Although the original idea of bilateral filtering was non-iterative, Barash [30] showed that an iterative application of bilateral filtering may be required in images with high levels of noise. Using the robust median estimate [37] for noise standard deviation σ n in the smoothed image, we can determine if further smoothing is required.…”

Section: Iterative Multilateral Filteringmentioning

confidence: 99%

“…The main idea is that only perceptually analogous colors are averaged together to avoid unexpected color combination in images. Barash [30] unified anisotropic diffusion and non-linear bilateral filtering as another effective edge preserving filtering technique. However, one of the main limitations of bilateral filtering is that the range filter coefficients rely heavily on actual pixel intensity values, as it does not take into account any regional characteristics, which may in turn have been influenced by noise therefore potentially resulting in smoothed textured regions.…”

Section: Introductionmentioning

confidence: 99%

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A multiresolution framework for local similarity based image denoising

Rajpoot

Butt²

2012

Pattern Recognition

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In this paper, we present a generic framework for denoising of images corrupted with additive white Gaussian noise based on the idea of regional similarity. The proposed framework employs a similarity function using the distance between pixels in a multidimensional feature space, whereby multiple feature maps describing various local regional characteristics can be utilized, giving higher weight to pixels having similar regional characteristics. An extension of the proposed framework into a multiresolution setting using wavelets and scale space is presented. It is shown that the resulting multiresolution multilateral (MRM) filtering algorithm not only eliminates the coarse-grain noise but can also faithfully reconstruct anisotropic features, particularly in the presence of high levels of noise.

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Section: Iterative Multilateral Filteringmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A multiresolution framework for local similarity based image denoising

Rajpoot

Butt²

2012

Pattern Recognition

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“…As a primary low-level image processing procedure, noise removal has been extensively studied and many denoising schemes have been proposed, from the earlier smoothing filters and frequency domain denoising methods [25] to the lately developed wavelet [1][2][3][4][5][6][7][8][9][10], curvelet [11] and ridgelet [12] based methods, sparse representation [13] and K-SVD [14] methods, shape-adaptive transform [15], bilateral filtering [16,17], non-local mean based methods [18,19] and non-local collaborative filtering [20]. With the rapid development of modern digital imaging devices and their increasingly wide applications in our daily life, there are increasing requirements of new denoising algorithms for higher image quality.…”

Section: Introductionmentioning

confidence: 99%

“…The idea of NLM can be traced back to [23], where the similar image pixels are averaged according to their intensity distance. Similar ideas were used in the bilateral filtering methods [16,17], where both the spatial and intensity similarities are exploited for pixel averaging. In [18], the NLM denoising framework was well established.…”

Section: Introductionmentioning

confidence: 99%

Two-stage image denoising by principal component analysis with local pixel grouping

Zhang

Dong

Shi

2010

Pattern Recognition

572

396

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a b s t r a c tThis paper presents an efficient image denoising scheme by using principal component analysis (PCA) with local pixel grouping (LPG). For a better preservation of image local structures, a pixel and its nearest neighbors are modeled as a vector variable, whose training samples are selected from the local window by using block matching based LPG. Such an LPG procedure guarantees that only the sample blocks with similar contents are used in the local statistics calculation for PCA transform estimation, so that the image local features can be well preserved after coefficient shrinkage in the PCA domain to remove the noise. The LPG-PCA denoising procedure is iterated one more time to further improve the denoising performance, and the noise level is adaptively adjusted in the second stage. Experimental results on benchmark test images demonstrate that the LPG-PCA method achieves very competitive denoising performance, especially in image fine structure preservation, compared with state-of-the-art denoising algorithms.

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“…The bilateral filter, which can be shown to be an Euclidean approximation of the Beltrami kernel, was studied in different contexts (see [2,4,10,22,23,27]), and in [18] signal processing acceleration methods were proposed for efficient evaluation of this filter. Recently, a related filter, the nonlocal means filter, was proposed in [6] and shown to be useful in denoising of gray-scale and color images.…”

Section: Introductionmentioning

confidence: 99%

On Semi-implicit Splitting Schemes for the Beltrami Color Flow

Dascal

Rosman

Tai

et al. 2009

Lecture Notes in Computer Science

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The Beltrami flow is an efficient nonlinear filter, that was shown to be effective for color image processing. The corresponding anisotropic diffusion operator strongly couples the spectral components. Usually, this flow is implemented by explicit schemes, that are stable only for very small time steps and therefore require many iterations. In this paper we introduce a semi-implicit Crank-Nicolson scheme based on locally one-dimensional (LOD)/additive operator splitting (AOS) for implementing the anisotropic Beltrami operator. The mixed spatial derivatives are treated explicitly, while the non-mixed derivatives are approximated in an implicit manner. In case of constant coefficients, the LOD splitting scheme is proven to be unconditionally stable. Numerical experiments indicate that the proposed scheme is also stable in more general settings. Stability, accuracy, and efficiency of the splitting schemes are tested in applications such as the Beltrami-based scale-space, Beltrami denoising and Beltrami deblurring. In order to further accelerate the convergence of the numerical scheme, the reduced rank extrapolation (RRE) vector extrapolation technique is employed.

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Fundamental relationship between bilateral filtering, adaptive smoothing, and the nonlinear diffusion equation

Cited by 452 publications

References 13 publications

A multiresolution framework for local similarity based image denoising

A multiresolution framework for local similarity based image denoising

Two-stage image denoising by principal component analysis with local pixel grouping

On Semi-implicit Splitting Schemes for the Beltrami Color Flow

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