The staircasing effect in neighborhood filters and its solution

Buades, Antoni; Coll, Bartomeu; Morel, Jean‐Michel

doi:10.1109/tip.2006.871137

Cited by 196 publications

(122 citation statements)

References 19 publications

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“…Nonlinear filters such as median filter and anisotropic diffusion filter (ADF) are known to be effective in reducing noise while preserving sharp edges. However, they also tend to introduce artifacts such as flat zones and boundaries inside smooth regions (26,27). In our preliminary studies (data not shown), the application of ADF successfully reduced many false "holes" without compromising spatial resolution as previously demonstrated in Jones et al (18).…”

Section: Discussionsupporting

confidence: 71%

Improved myelin water quantification using spatially regularized non‐negative least squares algorithm

Hwang

2009

Magnetic Resonance Imaging

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Purpose: To improve the myelin water quantification in the brain in the presence of measurement noise and to increase the visibility of small focal lesions in myelin-waterfraction (MWF) maps. Materials and Methods:A spatially regularized non-negative least squares (srNNLS) algorithm was developed for robust myelin water quantification in the brain. The regularization for the conventional NNLS algorithm was expanded into the spatial domain in addition to the spectral domain. Synthetic data simulations were performed to study the effectiveness of this new algorithm. Experimental free-induction-decay measurements were obtained using a multi-gradient-echo pulse sequence and MWF maps were estimated using the srNNLS algorithm. The results were compared with other conventional methods.Results: A substantial decrease in MWF variability was observed in both simulations and experimental data when the srNNLS algorithm was applied. As a result, false lesions in the MWF maps disappeared and the visibility of small focal lesions improved greatly. On average, the contrast-tonoise ratio for focal lesions was improved by a factor of 2. Conclusion:The MWF variability due to the measurement noise can be substantially reduced and the detection of small focal lesions can be improved by using the srNNLS algorithm.Key Words: myelin content; myelin water fraction; multiple sclerosis; non-negative least squares; regularization; multiexponential analysis. QUANTITATIVE MEASUREMENTS of myelin content can substantially improve our understanding of the pathological progress of several white matter (WM) diseases, such as multiple sclerosis (MS) (1-4). A technique that provides specific and sensitive information about the myelin content was developed based on an analysis of T 2 relaxation times (5,6). It has been reported that the T 2 spectrum of WM and several myelinated tissue samples consists of multiple components (7-13) and that the short component with T 2 between 10 ms and 50 ms corresponds to the water pool within the myelin sheath (2-6). Myelin content can therefore be quantitated using the fraction of this short T 2 component. To implement this method, T 2 decay signals are acquired using a 32-echo single-slice Carr-Purcell-Meiboom-Gill (CPMG) sequence with composite 90x-180y-90x refocusing pulses and big crusher gradients around the refocusing pulses (5,6,14,15). A non-negative least squares (NNLS) algorithm can then be used to estimate the T 2 spectrum from the acquired decay signal, and the myelin water fraction (MWF) can be calculated from the ratio of the short T 2 component (10 ms Ͻ T 2 Ͻ 50 ms) to the total (16). A strong correlation was found between the MWF measured using this technique and the myelin distribution using histopathology in fixed brains (4,17). This technique has been used to quantitatively measure the MWF in brains of subjects with MS (3-6,17).T 2 spectrum regularization has been applied to the NNLS algorithm to improve the reliability of fitting in the presence of noise. The regularized non-negative least squ...

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Section: Discussionsupporting

confidence: 71%

Improved myelin water quantification using spatially regularized non‐negative least squares algorithm

Hwang

2009

Magnetic Resonance Imaging

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“…It is proved by Buades, Coll, and Morel [11], [12] for the estimate (25) where the window w h is truncated Gaussian. This equivalence has a place provided that the width of the truncated Gaussian window and its standard deviation h are small and have the same order of magnitude.…”

Section: Nonlocal Pointwise Higher-order Modelsmentioning

confidence: 93%

“…the so-called "staircasing" or "shock" effects. In order to repair and avoid these undesirable effects, the nonlocal polynomial models of the Þrst and higher orders have been proposed by Buades, Coll, and Morel [11], [12]. Similar higher-order nonlocal algorithm has been reported in Chatterjee and Milanfar [16], where the polynomial approximations up to second order are used.…”

Section: Nonlocal Pointwise Higher-order Modelsmentioning

confidence: 99%

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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“…This filter is defined as: [14] have established the link existing between bilateral filtering and PM equation. They have proven that for small neighborhoods, bilateral filtering using a box function as spatial weight, asymptotically behaves as the Perona-Malik model.…”

Section: B Bilateral Filter and Anisotropic Diffusionmentioning

confidence: 99%

Fast Image Diffusion for Feature Detection and Description

Liu¹,

Wu²,

Liu³

2016

IJCTE

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Abstract-In this paper, we introduce a new multiscale 2D feature detection and description method based on optimal O(1) bilateral filter feature (OBFF). Existing methods detect and describe features by analyzing the scale space generated by linear and nonlinear diffusion kernel function, like Gaussian scale space and anisotropic diffusion scale space. By using the anisotropic diffusion scale space, KAZE features achieve significant progress on the 2D feature detection by using the anisotropic diffusion scale space. It makes the blurring locally adaptive and retains better feature localization accuracy and distinctiveness than the SIFT method. Our method OBFF also generates the nonlinear scale space of image to detect the local feature. The optimal bilateral filter is advantage in object boundary preserving and antinoise ability and dramatically speed up feature detection in nonlinear scale space. We use the benchmark datasets to compare our method with state-of-the-art approaches.Index Terms-Bilateral filter, nonlinear scale space, feature detection, SIFT, binary descriptor.

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The staircasing effect in neighborhood filters and its solution

Cited by 196 publications

References 19 publications

Improved myelin water quantification using spatially regularized non‐negative least squares algorithm

Improved myelin water quantification using spatially regularized non‐negative least squares algorithm

From Local Kernel to Nonlocal Multiple-Model Image Denoising

Fast Image Diffusion for Feature Detection and Description

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