A moment-based nonlocal-means algorithm for image denoising

Image denoising is a crucial step to increase image quality and to improve the performance of all the tasks needed for quantitative imaging analysis. The nonlocal (NL) means filter is a very successful technique for denoising textured images. However, this algorithm is only defined up to translation without considering the orientation and scale for each image patch. In this paper, we introduce the Zernike moments into NL-means filter, which are the magnitudes of a set of orthogonal complex moments of the image. The Zernike moments in small local windows of each pixel in the image are computed to obtain the local structure information for each patch, and then the similarities according to this information are computed instead of pixel intensity. For the rotation invariant of the Zernike moments, we can get much more pixels or patches with higher similarity measure and make the similarity of patches translation-invariant and rotation-invariant. The proposed algorithm is demonstrated on real images corrupted by white Gaussian noise (WGN). The comparative experimental results show that the improved NL-means filter achieves better denoising performance.     

Salt and pepper noise filtering with fuzzy-cellular automata

A new image denoising algorithm is proposed to restore digital images corrupted by impulse noise. It is based on two dimensional cellular automata (CA) with the help of fuzzy logic theory. The algorithm describes a local fuzzy transition rule which gives a membership value to the corrupted pixel neighborhood and assigns next state value as a central pixel value. The proposed method removes the noise effectively even at noise level as high as 90%. Extensive simulations show that the proposed algorithm provides better performance than many of the existing filters in terms of noise suppression and detail preservation. Also, qualitative and quantitative measures of the image produce better results on different images compared with the other algorithms.     

Space-time adaptation for patch-based image sequence restoration

We present a novel space-time patch-based method for image sequence restoration. We propose an adaptive statistical estimation framework based on the local analysis of the bias-variance trade-off. At each pixel, the space-time neighborhood is adapted to improve the performance of the proposed patch-based estimator. The proposed method is unsupervised and requires no motion estimation. Nevertheless, it can also be combined with motion estimation to cope with very large displacements due to camera motion. Experiments show that this method is able to drastically improve the quality of highly corrupted image sequences. Quantitative evaluations on standard artificially noise-corrupted image sequences demonstrate that our method outperforms other recent competitive methods. We also report convincing results on real noisy image sequences     

Denoising of document images based on similarity and connectivity principles

This paper proposes a highly efficient denoising technique in restoring document images that have been corrupted by impulse noise. The proposed algorithm consists of a number of shells and is based on the connectivity principle; whereby, pixels that have connections with at least one other pixel in each of the consecutive shells are deemed noise-free pixels. Simulation results indicate that the new denoising method is not only useful in eliminating the noise efficiently; it also keeps the fine details of the image.     

Multiresolution Adaptive Image Smoothing

A hierarchical image smoothing method is presented which does not require user specified parameters. For every pixel the largest centered window (7 × 7, 5 × 5 or 3 × 3) containing a constant patch is sought. The selection is made by comparing a locally computed homogeneity measure with its robust global estimate. If the window is declared homogeneous, the pixel is assigned the spatial average. Around discontinuities an adaptive least squares smoothing method is applied for 3 × 3 windows. The performance of the algorithm is compared with several other smoothing techniques for additively corrupted images. The smoothing of synthetic aperture radar images is used as an example for multiplicative noise.     

Fast averaging peer group filter for the impulsive noise removal in color images

In the paper, a new approach to the impulsive noise removal in color images is presented. The new filtering design is based on the peer group concept, which determines the membership of a central pixel of the filtering window to its local neighborhood, in terms of the number of close pixels. Two pixels are declared as close if their distance in a given color space does not exceed a predefined threshold value. A pixel is treated as not corrupted by the impulsive noise process, if its peer group consists of at least two close pixels, otherwise this pixel is replaced by a weighted average of uncorrupted samples from the local neighborhood. The peer group size assigned to each pixel is used for the averaging operation, so that pixels which have many peers are taken with higher weight. The new filtering design proved to restore efficiently color images corrupted by even strong impulsive noise, while preserving tiny image details. The beneficial property of the proposed filter is its very low computational complexity, which allows its application in real-time image processing tasks.     

一种改进的自适应中值滤波方法

提出了一种改进的自适应中值滤波算法,以有效地去除图像中的脉冲噪声,并保留图像细节。在进行噪声点检测时,引入了最小集合距离测度,有效地避免了将高频细节信号误判为噪声。采用最小无污染点集合的中值恢复噪声点,消除了其邻域噪声点的影响。通过与RAMF、NASMF等方法的比较实验表明,新算法噪声检测的正确率高、降噪与保留细节效果好, 尤其对含噪声密度高的图像的处理效果优势更为明显。     

双边非局部均值滤波图像去噪算法

为提高图像去噪的视觉效果,本文根据自然图像通常包含较多的重复性结构这一现象,以及双边滤波器的在图像去噪中所具有的优点,提出了一种新的基于双边滤波与非局部均值（ NLM）的图像去噪算法。利用NLM思想对当前的像素灰度值进行估计。过程中,不仅考虑到了当前像素的灰度值对预测结果的影响,而且考虑到了当前像素的位置与周围像素位置之间的关系,构建了非局部邻域内的位置系数来对预测结果进行约束,最后考虑到非局部邻域内同质像素的相似性,设计了双边NLM滤波器。实验结果表明：本文算法比双边滤波算法运行时间快了0.114 s、峰值信噪比（ PSNR）提高了0.9、图像相似度（ MSSIM）提高了0.181,图像保真度（ VIF）提高了0.2147。本文提出的方法能够更好地保留图片信息的完整性,提高了图像的亮度和图像纹理的清晰度。     

Adaptive image-smoothing using a coplanar matrix and its application to document image binarization

Abstract. For document images corrupted by various kinds of noise, direct binarization images may be severely blurred and degraded. A common treatment for this problem is to pre-smooth input images using noise-suppressing filters. This article proposes an image-smoothing method used for prefiltering the document image binarization. Conceptually, we propose that the influence range of each pixel affecting its neighbors should depend on local image statistics. Technically, we suggest using coplanar matrices to capture the structural and textural distribution of similar pixels at each site. This property adapts the smoothing process to the contrast, orientation, and spatial size of local image structures. Experimental results demonstrate the effectiveness of the proposed method, which compares favorably with existing methods in reducing noise and preserving image features. In addition, due to the adaptive nature of the similar pixel definition, the proposed filter output is more robust regarding different noise levels than existing methods. Received: October 31, 2001 / October 09, 2002 Correspondence to:L. Fan (e-mail: fanlixin@ieee.org)     

一种基于极值和方向的滤波算法

提出了一种有效的椒盐噪声图像滤波算法。该算法首先对含有噪声的图像取3×3邻域,判断某点是否为邻域极值将全部像素点分为可疑噪声与信号点集合;其次对每一个可疑噪声点在其3×3邻域内构造八个方向的梯度算子模板,通过比较8个方向梯度的大小,进一步确定其是否为噪声点;最后对噪声点进行邻域的中值滤波。实验结果表明该算法在滤除噪声的同时,很好地保存了图像的原始信息且有较好的信噪比。     

Optimal-selection-based suppressed fuzzy c-means clustering algorithm with self-tuning non local spatial information for image segmentation

Suppressed fuzzy c-means clustering algorithm (S-FCM) is one of the most effective fuzzy clustering algorithms. Even if S-FCM has some advantages, some problems exist. First, it is unreasonable to compulsively modify the membership degree values for all the data points in each iteration step of S-FCM. Furthermore, duo to only utilizing the spatial information derived from the pixel’s neighborhood window to guide the process of image segmentation, S-FCM cannot obtain satisfactory segmentation results on images heavily corrupted by noise. This paper proposes an optimal-selection-based suppressed fuzzy c-means clustering algorithm with self-tuning non local spatial information for image segmentation to solve the above drawbacks of S-FCM. Firstly, an optimal-selection-based suppressed strategy is presented to modify the membership degree values for data points. In detail, during each iteration step, all the data points are ranked based on their biggest membership degree values, and then the membership degree values of the top r ranked data points are modified while the membership degree values of the other data points are not changed. In this paper, the parameter r is determined by the golden section method. Secondly, a novel gray level histogram is constructed by using the self-tuning non local spatial information for each pixel, and then fuzzy c-means clustering algorithm with the optimal-selection-based suppressed strategy is executed on this histogram. The self-tuning non local spatial information of a pixel is derived from the pixels with a similar neighborhood configuration to the given pixel and can preserve more information of the image than the spatial information derived from the pixel’s neighborhood window. This method is applied to Berkeley and other real images heavily contaminated by noise. The image segmentation experiments demonstrate the superiority of the proposed method over other fuzzy algorithms.     

基于加权检测的脉冲噪声新滤波器

在分析噪声检测与噪声滤波原理的基础上,提出了用于恢复被脉冲噪声污染的图像的去噪算法。该算法基于方向差异性将检测窗口分解为四个子窗口,并取子窗口的中间像素与相邻像素的灰度值之差的加权平均值与预先定义的阈值进行比较,较准确地区分噪声点和信号点;然后根据方向相关依赖性,采用一种边缘保持滤波方法来重构被噪声污染像素的灰度值。实验结果证明,该算法在提高图像信噪比的同时,可以更好地保持图像的细节信息。     

On the Use of Level Curves in Image Analysis

A digitized image is viewed as a surface over the xy-plane. The level curves of this surface provide information about edge directions and feature locations. This paper presents algorithms for the extraction of tangent directions and curvatures of these level curves. The tangent direction is determined by a least-squares minimization over the surface normals (calculated for each 2 × 2 pixel neighborhood) in an averaging window. The curvature calculation, unlike most previous work on this topic, does not require a parameterized curve, but works instead directly on the tangents across adjacent level curves. The curvature is found by fitting concentric circles to the tangent directions via least-squares minimization. The stability of these algorithms with respect to noise is studied via controlled tests on computer generated data corrupted by simulated noise. Examples on real images are given which show application of these algorithms for directional enhancement, and feature point detection.     

一种改进的非局部均值去噪算法*

针对非局部均值去噪算法在图像块相似度计算方面存在的不足,提出计入图像旋转对相似度贡献的、效果更好的图像块匹配算法.为了获得与给定像素点邻域相似的图像子块,首先对给定像素点周边的相关邻域子块按灰度值大小排序,计算其与同样按灰度值大小排序的给定像素点邻域子块之间的距离,据此筛选出灰度分布相似的图像子块作为候选集,更进一步在候选集中选出结构上更为相似的图像子块.同时为了克服噪声影响,在计算子块相似度之前对输入图像进行预滤波处理.实验表明,与原始的非局部均值去噪算法相比,文中算法在峰值信噪比、平均结构相似性及主观视觉效果等方面均具有一定优势,特别是在噪声较大时,文中算法的去噪效果更好.     

基于图像统计信息的去椒盐噪声算法

本文主要介绍一种基于图像统计信息的去噪算法,主要利用图像中心像素邻域的均值和方差来消除图像中椒盐噪声的影响。首先,介绍了这种算法的基本原理;然后,分别应用中值滤波算法、自适应中值滤波算法以及本文的算法对有椒盐噪声污染的图像进行滤波,并对实验结果进行比较和分析;最后,文章对这种算法的复杂度进行了计算分析,并将其和中值滤波算法以及自适应中值滤波算法的复杂度作比较,并对这种算法的合理性进行了分析与总结。     

滤除椒盐噪声的开关核回归拟合算法

针对椒盐噪声的去噪和细节保护问题,提出一种基于核回归拟合的开关去噪算法。首先,通过高效脉冲检测器对图像中的椒盐噪声像素点进行精确检测;其次,将所检测到的噪声像素点当作缺失数据,应用核回归方法对以噪声像素点为中心的邻域内的非噪声像素点进行拟合,得到符合图像局部结构特征的核回归拟合曲面;最后,以噪声像素点的空间坐标对核回归拟合曲面进行重采样,获得噪声像素点恢复后的灰度值,从而实现椒盐噪声的滤除。与经典的中值滤波器（SMF）、自适应中值滤波器（AMF）、改进型的方向加权中值滤波器（MDWMF）、快速开关中均值滤波器（FSMMF）、图像修补（Ⅱ）等算法进行不同噪声密度的实验对比,所提算法的去噪结果图像的主观视觉质量均为最优;在低密度、中等密度以及高密度噪声场景下,所提算法对不同测试图像去噪结果的峰值信噪比（PSNR）分别平均提高了6.02dB、6.33dB和5.58dB,且平均绝对误差（MAE）分别平均降低了0.90、5.84和25.29。实验结果表明,所提算法不仅能够有效去除各种密度的椒盐噪声,同时具备良好的图像细节保护性能。     

局部特定空间关系统计特征的RVIN噪声检测器

目的 随机脉冲噪声（random-valued impulse noise，RVIN）检测器将局部图像统计值（local image statistics，LIS）作为图块中心像素点是否为噪声的判断依据，但LIS的描述能力较弱，在不同程度上制约了RVIN检测器的检测正确率，影响了后续开关型降噪模块的修复效果。为此，提出了一种基于局部特定空间关系统计特征的RVIN噪声检测器。方法 以局部中心像素点的8个邻域像素对数差值排序值（rank-ordered logarithmic difference，ROLD）并结合1个最小方向对数差值（minimum orientation logarithmic difference，MOLD）共9个反映局部特定空间关系的LIS统计值构成描述中心像素点是否为RVIN的噪声感知特征矢量，并通过在大量样本图块数据上提取的RVIN噪声感知特征矢量及其对应的噪声标签作为训练对（training pairs），训练获得一个基于多层感知网络（multi-layer perception，MLP）的RVIN噪声检测器。结果 对比实验从检测正确率和实际应用效果2个方面检验所提出的RVIN检测器的有效性，分别在10幅常用图像和50幅BSD （Berkeley segmentation data）纹理图像上进行测试，并与经典的脉冲噪声降噪算法中包含的噪声检测器以及MLPNNC （MLP neural network classifier）噪声检测器相比较，以漏检数、误检数和错检总数作为评价噪声检测正确率的指标。在常用图像集上本文所提RVIN检测器的漏检数和误检数较为平衡，在错检总数上排名处于所有对比算法中的前2名，为后续的降噪模块打下了很好的基础。在BSD纹理图像集上，将本文提出的RVIN检测器和GIRAF （generic iteratively reweighted annihilating filter）算法组合构成一种RVIN噪声降噪算法（proposed-GIRAF），proposed-GIRAF算法在50幅BSD图像上的峰值信噪比（peak signal-to-noise ratio，PSNR）均值在各个噪声比例下均取得了最优结果，与排名第2的对比算法相比，提升了0.471.96 dB。实验数据表明，所提出的RVIN噪声检测器的检测正确率优于现有的检测器，与修复算法联用后即可获得一种降噪效果更佳的开关型RVIN降噪算法。结论 本文提出的RVIN噪声检测器在各个噪声比例下具有鲁棒的预测准确性，配合GIRAF算法使用后，与经典的RVIN降噪算法相比，降噪效果最佳，具有很强的实用性。     

改进椒盐去噪方法在井下图像中的应用

为了提高井下图像采集的质量,针对目前改进中值滤波算法的优缺点,提出了一种新的去除井下图像椒盐噪声的算法。该算法首先判断出图像中的噪声点和非噪声点,然后根据窗口内噪声点的密度大小自适应地确定滤波窗口的大小,并按照一定的规律赋予窗口内像素点不同的权重,最后采用加权中值方法处理图像中的噪声点。计算机模拟实验证明该方法不仅能有效地去除不同密度的椒盐噪声,而且能很好地保持图像的细节,滤波效果比已提出的中值滤波算法更好。     

米字型各向异性扩散模型的图像去噪算法

针对原始的各向异性扩散模型在对带噪图像去噪时,只利用了邻域内东、南、西、北4个方向上的参考信息,使得去噪效果不够明显的问题,提出了米字型各向异性扩散模型的图像去噪算法。该算法在利用了原始算法中待修复点周围4个方向上参考信息的基础上,还引入了该点邻域内对角线方向上的新信息,给出了采用周围8个方向上的信息进行对图像去噪的新模型,同时证明了该模型的合理性。用新提出的算法与原算法以及一种改进的同类算法对4幅带噪图像进行去噪。实验结果表明,新提出算法去噪效果的峰值信噪比(PSNR)相比原算法和改进同类算法平均提高1.90dB和1.43dB,平均结构相似度(MSSIM)分别平均提高0.175和0.1,说明该算法更适合于图像去噪。     

Adaptive-neighborhood histogram equalization for image enhancement

By modifying the histogram of an image, a dramatic improvement in the perceptibility of details can often be achieved. However, the two commonly used methods of full-frame histogram equalization and local-area histogram equalization often fail to produce adequate enhancement when the image contains relatively small but variable-sized regions in which there are objects or features of interest with low visual contrast. A new method of adaptive-neighborhood histogram equalization that is effective in enhancing these types of images is proposed in this paper. In this method, an adaptive neighborhood is developed for each pixel in the image. The adaptive neighborhood is a compound region made up of a foreground that contains 8-connected pixels close in gray level to that of the seed pixel, and a background of neighboring pixels molded around the foreground. The histogram of this adaptive neighborhood is equalized to provide the transformation that is applied to the seed pixel. Major advantages of this method are the avoidance of block edge artifacts that are encountered in local-area histogram equalization, and improved perceptibility of image detail. Examples of images transformed using the three methods of histogram modification are presented along with a discussion of the merits of the adaptive-neighborhood method.