3-D discrete shearlet transform and video processing

In this paper, we introduce a digital implementation of the 3-D shearlet transform and illustrate its application to problems of video denoising and enhancement. The shearlet representation is a multiscale pyramid of well-localized waveforms defined at various locations and orientations, which was introduced to overcome the limitations of traditional multiscale systems in dealing with multidimensional data. While the shearlet approach shares the general philosophy of curvelets and surfacelets, it is based on a very different mathematical framework, which is derived from the theory of affine systems and uses shearing matrices rather than rotations. This allows a natural transition from the continuous setting to the digital setting and a more flexible mathematical structure. The 3-D digital shearlet transform algorithm presented in this paper consists in a cascade of a multiscale decomposition and a directional filtering stage. The filters employed in this decomposition are implemented as finite-length filters, and this ensures that the transform is local and numerically efficient. To illustrate its performance, the 3-D discrete shearlet transform is applied to problems of video denoising and enhancement, and compared against other state-of-the-art multiscale techniques, including curvelets and surfacelets.     

Gray and color image contrast enhancement by the curvelet transform

We present a new method for contrast enhancement based on the curvelet transform. The curvelet transform represents edges better than wavelets, and is therefore well-suited for multiscale edge enhancement. We compare this approach with enhancement based on the wavelet transform, and the multiscale retinex. In a range of examples, we use edge detection and segmentation, among other processing applications, to provide for quantitative comparative evaluation. Our findings are that curvelet based enhancement out-performs other enhancement methods on noisy images, but on noiseless or near noiseless images curvelet based enhancement is not remarkably better than wavelet based enhancement.     

Shearlet-Based Deconvolution

In this paper, a new type of deconvolution algorithm is proposed that is based on estimating the image from a shearlet decomposition. Shearlets provide a multidirectional and multiscale decomposition that has been mathematically shown to represent distributed discontinuities such as edges better than traditional wavelets. Constructions such as curvelets and contourlets share similar properties, yet their implementations are significantly different from that of shearlets. Taking advantage of unique properties of a new M-channel implementation of the shearlet transform, we develop an algorithm that allows for the approximation inversion operator to be controlled on a multiscale and multidirectional basis. A key improvement over closely related approaches such as ForWaRD is the automatic determination of the threshold values for the noise shrinkage for each scale and direction without explicit knowledge of the noise variance using a generalized cross validation (GCV). Various tests show that this method can perform significantly better than many competitive deconvolution algorithms.      

Shearlet-Based Total Variation Diffusion for Denoising

We propose a shearlet formulation of the total variation (TV) method for denoising images. Shearlets have been mathematically proven to represent distributed discontinuities such as edges better than traditional wavelets and are a suitable tool for edge characterization. Common approaches in combining wavelet-like representations such as curvelets with TV or diffusion methods aim at reducing Gibbs-type artifacts after obtaining a nearly optimal estimate. We show that it is possible to obtain much better estimates from a shearlet representation by constraining the residual coefficients using a projected adaptive total variation scheme in the shearlet domain. We also analyze the performance of a shearlet-based diffusion method. Numerical examples demonstrate that these schemes are highly effective at denoising complex images and outperform a related method based on the use of the curvelet transform. Furthermore, the shearlet-TV scheme requires far fewer iterations than similar competitors.     

Contrast enhancement in retinal image via multi-scale geometrical analysis

Recently,there has been a growing awareness to theobservation that wavelets may not be the best choiceforrepresenting natural i mages .This observation is due tothe fact that wavelets are blindtothe smoothness alongthe edges commonly found in i mages .In …     

No-reference image quality assessment using statistical characterization in the shearlet domain

Image and video quality measurements are crucial for many applications, such as acquisition, compression, transmission, enhancement, and reproduction. Nowadays, no-reference (NR) image quality assessment (IQA) methods have drawn extensive attention because it does not rely on any information of original images. However, most of the conventional NR-IQA methods are designed only for one or a set of predefined specific image distortion types, which are unlikely to generalize for evaluating image/video distorted with other types of distortions. In order to estimate a wide range of image distortions, in this paper, we present an efficient general-purpose NR-IQA algorithm which is based on a new multiscale directional transform (shearlet transform) with a strong ability to localize distributed discontinuities. This is mainly based on distorted natural image that leads to significant variation in the spread discontinuities in all directions. Thus, the statistical property of the distorted image is significantly different from that of natural images in fine scale shearlet coefficients, which are referred to as ‘distorted parts’. However, some ‘natural parts’ are reserved in coarse scale shearlet coefficients. The algorithm relies on utilizing the natural parts to predict the natural behavior of distorted parts. The predicted parts act as ‘reference’ and the difference between the reference and distorted parts is used as an indicator to predict the image quality. In order to achieve this goal, we modify the general sparse autoencoder to serve as a predictor to get the predicted parts from natural parts. By translating the NR-IQA problem into classification problem, the predicted parts and distorted parts are utilized to form features and the differences between them are identified by softmax classifier. The resulting algorithm, which we name SHeArlet based No-reference Image quality Assessment (SHANIA), is tested on several database (LIVE, Multiply Distorted LIVE and TID2008) and shown to be suitable for many common distortions, consistent with subjective assessment and comparable to full-reference IQA methods and state-of-the-art general purpose NR-IQA algorithms.     

Fusion of multiparametric SAR images based on SW-nonsubsampled contourlet and PCNN

In this paper, a new fusion rule based on a pulse coupled neural network (PCNN) and the clarity of images is proposed for multi-band synthetic aperture radar (SAR) image fusion. By using a stationary wavelet-based nonsubsampled contourlet transform (SW-NSCT), we can calculate a flexible multiscale, multidirectional, anisotropy and shift-invariant representation of registered SAR images. A weighted fusion rule is performed on the low frequency subbands to calculate the fused lowpass band. For the fusion of high frequency directional subband images, a PCNN model is constructed, where the linking strength of each neuron is determined by the clarity of the decomposed subband images. The fusion approach exploits the advantages of both SW-NSCT in multiscale geometric representations and that of PCNN in the determination of fusion rules; as predicted, the obtained fusion image can preserve much more information regarding textures and edges of the images, compared to its counterparts. Some experiments are performed by comparing the new algorithm with other existing fusion rules and methods. The experimental results show that the proposed fusion approach is effective and can provide better performance in fusing multi-band SAR images than some current methods.     

结合无下采样Shearlet模极大值和改进尺度积的有噪图像边缘检测

为从噪声污染的图像中提取出更为清晰、连续的边缘,进一步改善边缘检测效果,本文提出了一种基于无下采样Shearlet模极大值和改进尺度积的边缘检测方法。首先对含噪图像进行多尺度、多方向无下采样Shearlet变换（Non-subsampled Shearlet Transform, NSST）,得到图像在NSST域的高频系数;然后选取相邻的两个较大尺度的高频系数进行改进的尺度积运算,并经NSST模极大值处理得到边缘二值图像;最后使用区域连通方法去除二值图像中的孤立点,得到准确的边缘图像。大量实验结果表明,与小波模极大值、小波尺度积、基于无下采样Contourlet变换（Non-subsampled Contourlet Transform, NSCT）模极大值和尺度积、NSST模极大值等4种边缘检测方法相比,本文提出的方法具有更强的抗噪能力,且有效地避免了纹理的影响,检测出的边缘完整清晰,连续性好。      

乳腺X线图像的增强与噪声抑制研究

提出了一种基于多尺度几何分析的乳腺X线图像增强与噪声抑制的新方法.首先对乳腺X线图像进行非下采样Contourlet变换分解,得到相应尺度和子带信息;然后根据变换系数的统计特性,应用广义高斯混合模型对其进行建模,并在此基础上引入贝叶斯分类方法将建模后的系数分为强弱边缘及噪声;再根据各个子带系数的类别属性,分别设计相应的非线性映射函数来对不同的系数进行自适应增强和抑制;最后采用增强和抑制后的系数对原图像进行重构,从而得到凸显病变区域特征的增强图像.实验结果表明,该方法具有良好的实用性和鲁棒性.     

基于子波变换极大值描述的图像压缩编码方法

本文给出了玫种有效的从图像子波变换模局部极大值点链接图像多尺度边缘曲线的跟踪算法。研究了基于基图像子波变换局部极大值描述的压缩编码方法。     

The contourlet transform: an efficient directional multiresolution image representation.

The limitations of commonly used separable extensions of one-dimensional transforms, such as the Fourier and wavelet transforms, in capturing the geometry of image edges are well known. In this paper, we pursue a "true" two-dimensional transform that can capture the intrinsic geometrical structure that is key in visual information. The main challenge in exploring geometry in images comes from the discrete nature of the data. Thus, unlike other approaches, such as curvelets, that first develop a transform in the continuous domain and then discretize for sampled data, our approach starts with a discrete-domain construction and then studies its convergence to an expansion in the continuous domain. Specifically, we construct a discrete-domain multiresolution and multidirection expansion using nonseparable filter banks, in much the same way that wavelets were derived from filter banks. This construction results in a flexible multiresolution, local, and directional image expansion using contour segments, and, thus, it is named the contourlet transform. The discrete contourlet transform has a fast iterated filter bank algorithm that requires an order N operations for N-pixel images. Furthermore, we establish a precise link between the developed filter bank and the associated continuous-domain contourlet expansion via a directional multiresolution analysis framework. We show that with parabolic scaling and sufficient directional vanishing moments, contourlets achieve the optimal approximation rate for piecewise smooth functions with discontinuities along twice continuously differentiable curves. Finally, we show some numerical experiments demonstrating the potential of contourlets in several image processing applications. Index Terms-Contourlets, contours, filter banks, geometric image processing, multidirection, multiresolution, sparse representation, wavelets.     

基于多尺度方向局部极值滤波和ASR的图像融合

为了更好地提取源图像的边缘和方向信息,充分利用边缘保持滤波器的保边缘特性和方向滤波器有效提取方向信息的能力,提出一种基于局部极值滤波和非下采样方向滤波器的多尺度方向局部极值滤波图像融合方法。源图像经多尺度方向局部极值滤波,得到低频子带以及一系列的高频方向细节子带,对低频子带系数提出一种基于自适应稀疏表示(ASR)的融合规则,采用空间频率与l1范数相结合的策略得到融合的稀疏表示系数,对高频方向细节子带系数提出一种基于改进拉普拉斯能量和匹配度的选择与加权平均相结合的融合策略。实验结果表明,本方法能够有效提取源图像的边缘等细节信息,融合结果对比度更高,具有更好的主观视觉效果,其客观评价指标也优于传统的图像融合方法。     

Multiscale image segmentation using wavelet-domain hidden Markovmodels

We introduce a new image texture segmentation algorithm, HMTseg, based on wavelets and the hidden Markov tree (HMT) model. The HMT is a tree-structured probabilistic graph that captures the statistical properties of the coefficients of the wavelet transform. Since the HMT is particularly well suited to images containing singularities (edges and ridges), it provides a good classifier for distinguishing between textures. Utilizing the inherent tree structure of the wavelet HMT and its fast training and likelihood computation algorithms, we perform texture classification at a range of different scales. We then fuse these multiscale classifications using a Bayesian probabilistic graph to obtain reliable final segmentations. Since HMTseg works on the wavelet transform of the image, it can directly segment wavelet-compressed images without the need for decompression into the space domain. We demonstrate the performance of HMTseg with synthetic, aerial photo, and document image segmentations.     

Multiscale estimation of multiple orientations based on morphological directional openings

This paper introduces a novel approach to estimate multiple orientations at each pixel of a gray image at different scales. The main orientations are provided by a bank of directional openings. Gathering the responses of the filtered directional openings provide at each pixel a discrete sequence which is the directional signature. Then, the directional signature is interpolated by cubic B-splines, and the multiple orientations at each pixel are obtained by means of peak detection in the continuous directional signature. This procedure is performed using structuring elements with different lengths which results in a multiscale approach. The comparison with other existing methods as well as the experimental results on images shows the ability of the proposed method to detect multiple orientations in textured images at different scales with high accuracy.     

New fast smoothers for multiscale systems

We consider the smoothing problem for multiscale stochastic systems based on the wavelet transform. These models involve processes indexed by the nodes of a dyadic tree. Each level of the dyadic tree represents one scale or resolution of the process; therefore, moving upward on the tree divides the resolution by 2, whereas moving downward multiplies it by 2. The processes are built according to a recursion in scale from coarse to fine to which random details are added. To operate the change in scale, one must perform an interpolation. This is achieved using the QMF pair of operators attached to a wavelet transform. These models have proved to be of great value to capture textures or fractal-like processes as well as to perform multiresolution sensor fusion (an example of which is given here). Up to now however, only subclasses of multiscale systems were amenable to fast algorithms and through different formalisms: those relying on Haar's wavelet and those involving only one of the two wavelet interpolators. We provide here a unifying framework that handles any system based on orthogonal wavelets. A smoothing theory is presented to define the field of fast algorithms for Markov random fields and give intuition on how to design them. This theory reveals the difficulties arising with general multiscale systems. We then prove that orthogonality properties of wavelets are the gate to fastness     

Curvelet based face recognition via dimension reduction

Multiresolution ideas, notably the wavelet transform, have been proved quite useful for analyzing the information content of facial images. Numerous papers and research articles have discussed the application of wavelet transform in face recognition. However, little attention has been paid to the newly developed multiresolution tools (contourlet, curvelet, etc.) despite their improved directional elements and other promising abilities compared to traditional wavelet transform. In this article we introduce the application of digital curvelet transform in conjunction with different dimensionality reduction tools, looking particularly at the problem of facial feature extraction from 2D images. The purpose of this paper is exploratory. We do not claim that the results achieved here are the best possible. Rather, we aim at showing that curvelets can serve as an effective alternative to wavelets as a feature extraction tool. This work can be seen as a stepping stone for further research in this direction. Our methods have been evaluated on well-known databases like ORL, Essex Grimace and Yale face. Curvelet based results have been compared with that achieved using wavelets and other existing techniques to show that curvelets indeed has the potential to supersede wavelet based results.     

抗混叠轮廓波变换及其在图像融合中的应用

研究了原始轮廓波变换的频谱混叠问题,设计出能抑制混叠的多尺度分解方案,结合方向滤波器组,实现了一种抗混叠的轮廓波变换.在此基础上,提出了新颖的基于抗混叠轮廓波变换的图像融合算法.该算法通过邻域一致性测度的计算,实现了变换系数的局部自适应融合.实验结果表明,所提出的方法在视觉质量及定量指标上都优于基于小波变换和轮廓波变换的传统方法.     

Curvelet-Based Snake for Multiscale Detection and Tracking of Geophysical Fluids

Detection and target tracking have an application to many scientific problems. The approach developed in this paper is motivated by the applications of detection and tracking characteristic deformable structures in geophysical fluids. We develop an integrated detection and tracking method of geophysical fluids based on a discrete curvelet representation of the information characterizing the targets. Curvelets are in some sense geometric wavelets, allowing an optimal sparse representation of two-dimensional piecewise continuous objects with C ²-singularities. The proposed approach first identifies a consistent vortex by a curvelet-based gradient-vector-flow snake and then establishes the motion correspondence of the snaxels between successive time frames by a constructed so-called semi-T or comp-T multiscale motion-estimation method based on the geometric wavelets. Furthermore, a combination of total-variation regularization and cycle-spinning techniques effectively removes false matches and improves significantly the estimation. Numerical experiments at each stage demonstrate the performance of the proposed tracking methodology for temporal oceanographic satellite image sequences corrupted by noise, with weak edges and submitted to large deformations, in comparison to conventional methods     

反对称双正交小波应用于多尺度边缘提取的研究

本文对反对称双正交小波所具有的多尺度边缘提取能力进行了理论分析，提出了一种反对称双正交小波变换域内的多尺度边缘提取算法，并通过实验进行了验证。该结果为在基于小波变换的压缩数据域内利用边缘信息实现图像检索提供了依据。     

Inverse halftoning using wavelets

This work introduces a new approach to inverse halftoning using nonorthogonal wavelets. The distinct features of this wavelet-based approach are: (1) edge information in the highpass wavelet images of a halftone image is extracted and used to assist inverse halftoning, (2) cross-scale correlations in the multiscale wavelet decomposition are used for removing background halftoning noise while preserving important edges in the wavelet lowpass image, and (3) experiments show that our simple wavelet-based approach outperforms the best results obtained from inverse halftoning methods published in the literature, which are iterative in nature.