小波域中的PDE指纹图像增强

提出了一种基于偏微分方程的小波域指纹增强算法。分析了一致性扩散方程的缺陷,改为使用方向扩散使方程严格沿着指纹纹路扩散;进而提出了一种基于方向扩散的小波域指纹增强算法。该算法利用小波域低频系数图增强指纹,抑制了噪声的影响,将增强子图利用小波逆变换实现重构。通过对FVC2002的dB4指纹库中部分低质量图像的增强结果比较,表明该算法对低质量指纹图像的增强效果明显,且处理速度比现存的基于PDE的增强方法快。     

基于各向异性扩散方程的并行图像去噪研究

各向异性扩散方程是一种非线性PDE模型,在图像去噪中,通过非线性扩散因子来滤除噪声,同时能保留原有的边缘和纹理。但是当图像很大时,求解PDE的差分运算量将很大,满足不了实时系统的要求。针对该模型,在MPI并行编程环境下,利用图像像素的独立性和PDE求解的并发性,采用并行方式对图像去噪,在保证去噪性能的同时,极大地降低计算时间。     

同向平均梯度的各向异性扩散模型

遥感图像成像过程中经常会产生包括高斯噪声和椒盐噪声的图像噪声,这些噪声在很大程度上降低了图像的清晰度,影响了图像的实际应用。如何在有效的去除图像噪声的同时又能够很好的保留图像的纹理信息,成为遥感图像去噪追求的目标。针对林石算子和基于非线性小波阈值的各向异性扩散方程存在的不足,提出一种基于同向平均梯度值的各向异性扩散去噪模型,该模型克服了林石算子和基于非线性小波阈值的各向异性扩散方程无法去除强高斯噪声和椒盐噪声的不足,在有效去除遥感图像噪声的同时,很好的保持了图像的边缘和纹理信息。实验结果表明,提出模型的稳定性和有效性,并且去噪后的图像信噪比较林石算子和基于非线性小波阈值的各向异性扩散方程分别提高了24 dB。     

Slow and fast diffusion effects in image processing

A mathematical model for a nonlinear image multiscale analysis is studied. Processing of an image is based on a solution of the strongly nonlinear parabolic partial differential equation, which can degenerate depending on values of the greylevel intensity function. The governing PDE is a generalization of the regularized (in the sense of Catté, Lions, Morel and Coll) Perona-Malik anisotropic diffusion equation. We present numerical techniques for solving the suggested initial-boundary value problem and also existence and convergence results. Numerical experiments are discussed. Received: 6 May 1998 / Accepted: 27 July 2000     

The canny detector with edge region focusing using an anisotropic diffusion process

This paper proposes a methodology for edge detection in digital images using the Canny detector, but associated with a priori edge structure focusing by a nonlinear anisotropic diffusion via the partial differential equation (PDE). This strategy aims at minimizing the effect of the well-known duality of the Canny detector, under which is not possible to simultaneously enhance the insensitivity to image noise and the localization precision of detected edges. The process of anisotropic diffusion via thePDE is used to a priori focus the edge structure due to its notable characteristic in selectively smoothing the image, leaving the homogeneous regions strongly smoothed and mainly preserving the physical edges, i.e., those that are actually related to objects presented in the image. The solution for the mentioned duality consists in applying the Canny detector to a fine gaussian scale but only along the edge regions focused by the process of anisotropic diffusion via the PDE. The results have shown that the method is appropriate for applications involving automatic feature extraction, since it allowed the high-precision localization of thinned edges, which are usually related to objects present in the image.     

Stabilization of a class of nonlinear uncertain ordinary differential equation by parabolic partial differential equation controller

This article is concerned with stabilization for a class of uncertain nonlinear ordinary differential equation (ODE) with dynamic controller governed by linear 1?d heat partial differential equation (PDE). The control input acts at the one boundary of the heat's controller domain and the second boundary injects a Dirichlet term in ODE plant. The main contribution of this article is the use of the recent infinite‐dimensional backstepping design for state feedback stabilization design of coupled PDE‐ODE systems, to stabilize exponentially the nonlinear uncertain systems, under the restrictions that (a) the right‐hand side of the ODE equation has the classical particular form: linear controllable part with an additive nonlinear uncertain function satisfying lower triangular linear growth condition, and (b) the length of the PDE domain has to be restricted. We solve the stabilization problem despite the fact that all known backstepping transformation in the literature cannot decouple the PDE and the ODE subsystems. Such difficulty is due to the presence of a nonlinear uncertain term in the ODE system. This is done by introducing a new globally exponentially stable target system for which the PDE and ODE subsystems are strongly coupled. Finally, an example is given to illustrate the design procedure of the proposed method.     

各向异性扩散平滑滤波的改进算法

图像的噪声过滤和增强是数字图像处理中非常重要的组成部分.在图像处理过程中,为了既有效地去除噪声,又能够较好地保持图像的边缘和重要的细节信息,在Perona-Malik各向异性扩散模型（PM模型）的基础上,通过对变分方法的扩散方程中扩散系数的改进,提出了一个对噪声图像更有效更具有适应性的去噪扩散模型.该模型针对不同的梯度大小采用了不同的扩散系数.在实际处理过程中该模型不仅能够有效地保持图像的边缘,而且还能够克服PM模型对小尺度噪声敏感和部分边缘和细节失真的问题.实验结果表明,改进的扩散模型的性能优于PM模型,是一种较为理想的保边缘平滑模型.     

基于改进复扩散自适应耦合非局部变换域模型的图像放大

针对二阶偏微分方程（PDE）放大算法丢失弱边缘和纹理细节的不足,提出一种改进复扩散自适应耦合非局部变换域模型的图像放大算法。利用复扩散具有边缘定位准确的特点耦合冲击滤波器,改进复扩散模型能够较好地增强强边缘;而通过对相似图像块构成图像组的三维变换系数的稀疏特性进行建模,非局部变换域模型能够很好地利用图像中相似图像块的非局部信息,对弱边缘和纹理细节有较好的处理效果;最后利用复扩散得到图像的二阶导数作为参数实现改进复扩散模型和非局部变换域模型自适应耦合。所提算法与偏微分方程放大算法、非局部变换域放大算法和偏微分方程耦合空域非局部模型放大算法进行仿真实验比较,在强边缘、弱边缘和细节纹理具有较好的放大效果,弱边缘和纹理细节图像在平均结构相似性测度上高于改进复扩散放大算法、非局部变换域放大算法。所提算法验证了空域模型和变换域模型、局部模型和非局部模型耦合结合的有效性。     

基于时间变化的鲁棒各向异性扩散模型

建立性能稳定的扩散模型一直以来都是各向异性扩散技术研究的关键问题. 尽管许多改进的扩散模型陆续提出, 这些方法仍旧难以有效解决两个核心问题: 梯度阈值和迭代停止时间的确定. 针对以上问题, 本文提出了基于时间变化的鲁棒各向异性扩散模型. 在该模型中, 作者设定高斯尺度因子和梯度阈值随时间单调递减, 这有利于在多个尺度下准确提取边缘和边界特征信息. 此外, 利用逐次迭代信噪比能够有效地确定迭代停止时间, 减少不必要的过量平滑. 为了验证本文模型的有效性, 采用Pinecone灰度图像进行了图像增强平滑处理. 实验结果表明, 本文模型在性能上优于传统扩散模型, 能够有效地消除噪声和保持边缘.     

Learning an integral equation approximation to nonlinearanisotropic diffusion in image processing

Multiscale image enhancement and representation is an important part of biological and machine early vision systems. The process of constructing this representation must be both rapid and insensitive to noise, while retaining image structure at all scales. This is a complex task as small scale structure is difficult to distinguish from noise, while larger scale structure requires more computational effort. In both cases, good localization can be problematic. Errors can also arise when conflicting results at different scales require cross-scale arbitration. Structure sensitive multiscale techniques attempt to analyze an image at a variety of scales within a single image. Various techniques are compared. In this paper, we present a technique which obtains an approximate solution to the partial differential equation (PDE) for a specific time, via the solution of an integral equation which is the nonlinear analog of convolution. The kernel function of the integral equation plays the same role that a Green's function does for a linear PDE, allowing the direct solution of the nonlinear PDE for a specific time without requiring integration through intermediate times. We then use a learning technique to approximate the kernel function for arbitrary input images. The result is an improvement in speed and noise-sensitivity, as well as providing a means to parallelize an otherwise serial algorithm     

各向异性扩散与高斯差分模型的多聚焦图像融合方法

利用各向异性扩散模型具有良好的边缘保持特性,提出一种基于各向异性扩散滤波与高斯滤波差分规则的图像融合算法。各向异性扩散方程对图像进行滤波操作,在图像的同质区域实施正向扩散以平滑图像,而在图像边缘实行较弱平滑以保护边缘细节信息。将通过各向异性扩散模型处理的图像与经过高斯函数滤波的结果图像进行差分操作,可以得到图像的高频系数信息。为提高健壮性,对高频系数进行小窗口累加,其作为像素选择准则,再分别从原始图像中直接获取对应的像素值组成融合结果图像。实验结果表明,所提出的方法可以有效地融合源图像信息,非常适合多聚焦     

一种高阶各向异性扩散小波收缩图像降噪算法

图像可以看作是一个曲面,描述曲面上某点相对于球面的弯曲程度可以用高斯曲率.提出用高斯曲率来定义在图像上的能量泛函,并得到相应的欧拉方程,利用梯度下降法推出基于高斯曲率的高阶各向异性扩散方程.进而根据小波收缩与各向异性扩散等价性框架,提出一种高阶各向异性扩散小波收缩图像降噪算法.实验表明,此算法在去除噪声的同时能够很好地保持高频特征和边缘形状.     

Multispectral image denoising by well-posed anisotropic diffusion scheme with channel coupling

A novel way to denoise multispectral images is proposed via an anisotropic diffusion based partial differential equation (PDE). A coupling term is added to the divergence term and it facilitates the modelling of interchannel relations in multidimensional image data. A total variation function is used to model the intrachannel smoothing and gives a piecewise smooth result with edge preservation. The coupling term uses weights computed from different bands of the input image and balances the interchannel information in the diffusion process. It aligns edges from different channels and stops the diffusion transfer using the weights. Well-posedness of the PDE is proved in the space of bounded variation functions. Comparison with the previous approaches is provided to demonstrate the advantages of the proposed scheme. The simulation results show that the proposed scheme effectively removes noise and preserves the main features of multispectral image data by taking channel coupling into consideration.     

Vector-valued image regularization with PDEs: a common framework for different applications

In this paper, we focus on techniques for vector-valued image regularization, based on variational methods and PDE. Starting from the study of PDE-based formalisms previously proposed in the literature for the regularization of scalar and vector-valued data, we propose a unifying expression that gathers the majority of these previous frameworks into a single generic anisotropic diffusion equation. On one hand, the resulting expression provides a simple interpretation of the regularization process in terms of local filtering with spatially adaptive Gaussian kernels. On the other hand, it naturally disassembles any regularization scheme into the smoothing process itself and the underlying geometry that drives the smoothing. Thus, we can easily specialize our generic expression into different regularization PDE that fulfill desired smoothing behaviors, depending on the considered application: image restoration, inpainting, magnification, flow visualization, etc. Specific numerical schemes are also proposed, allowing us to implement our regularization framework with accuracy by taking the local filtering properties of the proposed equations into account. Finally, we illustrate the wide range of applications handled by our selected anisotropic diffusion equations with application results on color images.     

Fundamental relationship between bilateral filtering, adaptivesmoothing, and the nonlinear diffusion equation

In this paper, the relationship between bilateral filtering and anisotropic diffusion is examined. The bilateral filtering approach represents a large class of nonlinear digital image filters. We first explore the connection between anisotropic diffusion and adaptive smoothing, and then the connection between adaptive smoothing and bilateral filtering. Previously, adaptive smoothing was considered to be an inconsistent approximation to the nonlinear diffusion equation. We extend adaptive smoothing to make it consistent, thus enabling a unified viewpoint that relates nonlinear digital image filters and the nonlinear diffusion equation     

基于偏微分方程的稠密视差图获取方法

立体匹配是计算机视觉领域中的一个重要的热门研究课题,为了获得性能更优的稠密视差图,通过把偏微分方程理论运用于机器视觉中,提出了一种新的基于能量函数获取稠密视差图(disparity map)的方法,并首先分析了匹配点对在不同相对位置下对匹配项产生的影响;接着提出了适用于视差图的各向异性的热扩散方程,它不仅继承了Alvarez定义的正则项对初始视差图内部平滑和保持边缘不连续的特性,还通过引入图像的噪声屏蔽函数和二阶方向导数来分别控制对应视差图中不同区域的扩散速度和角点处的扩散方向;最后通过定义的正则项和匹配项来构造新的能量函数,并把基于区域匹配算法得到的视差图作为初始值,再利用最速下降法求解相应的最小能量泛函。实验结果表明,无论从视觉效果上,还是重构深度图的判别上,该新算法都取得了更优的性能。     

小波方向子带偏微分方程遥感图像去噪

针对小波阈值法在去除遥感图像高斯噪声时,所存在的由于过度"扼杀"小波系数而引起的模糊边缘问题,以及P-M模型通常会使图像的灰度趋于分段常量而产生所谓的"块状"效应问题。提出小波域偏微分方程(PDE)遥感图像去噪模型,该模型通过对遥感图像进行小波分解,保持低频子带信息,而只对含有噪声、图像边缘的高频子带进行基于子带方向特性的非线性异性扩散,使模型在有效去除高斯噪声的同时,能够很好地保护遥感图像中的边缘特征和细节纹理信息,避免了去噪后的结果图像出现分段常量现象。实验结果表明,对于相同的遥感图像高斯噪声,基于所提出混合模型的去噪图像的PSNR较基于类零树的Bayes阈值法和P-M模型提高了1～2dB。     

基于图像特征方向的各向异性扩散滤波方法

传统的各向异性扩散滤波方法都是从偏微分方程本身出发的,理论上的分析较为复杂.本文研究了基于图像特征方向的内在正交坐标系,分析了在此框架下的扩散滤波机制,然后直接从该坐标系下建立各向异性扩散滤波方案.这样的扩散滤波方法更加直观,可以简化理论分析.在此框架下,提出了一种新的各向异性扩散滤波方法.数值实验结果表明,新的扩散滤波方法可以更好地考虑图像的局部特性,从而完成细节保护和噪声消除的双重功能.所以,基于图像特征方向建立的各向异性扩散滤波方法更能达到我们预期的效果,该设计方法是有效的.     

Adaptive nonlocal filtering: a fast alternative to anisotropicdiffusion for image enhancement

Nonlinear anisotropic diffusion algorithms provide significant improvement in image enhancement as compared to linear filters. However, the excessive computational cost of solving nonlinear PDEs precludes their use in real-time vision applications. We show that two orders of magnitude speed improvement is provided by a new image filtering paradigm in which an adaptively determined vector field specifies nonlocal application points for an image filter     

Alternating Schwarz methods for partial differential equation-based mesh generation

To solve boundary value problems with moving fronts or sharp variations, moving mesh methods can be used to achieve reasonable solution resolution with a fixed, moderate number of mesh points. Such meshes are obtained by solving a nonlinear elliptic differential equation in the steady case, and a nonlinear parabolic equation in the time-dependent case. To reduce the potential overhead of adaptive partial differential equation-(PDE) based mesh generation, we consider solving the mesh PDE by various alternating Schwarz domain decomposition methods. Convergence results are established for alternating iterations with classical and optimal transmission conditions on an arbitrary number of subdomains. An analysis of a colouring algorithm is given which allows the subdomains to be grouped for parallel computation. A first result is provided for the generation of time-dependent meshes by an alternating Schwarz algorithm on an arbitrary number of subdomains. The paper concludes with numerical experiments illustrating the relative contraction rates of the iterations discussed.