基于偏微分方程的误差分散逆半调改进算法

结合误差分散半调噪声特征,提出一种基于偏微分方程的逆半调改进算法。通过研究偏微分方程的去噪原理,以3次B样条函数作为扩散函数,采用迭代求解偏微分方程的方法估计逆半调图像,计算每次迭代前后图像梯度模值的增量以确定平滑度的调节参数,解决偏微分方程在应用中的参数选择自适应问题。实验结果表明,该算法在图像整体平滑度和细节保持能力上都具有较好的效果。     

一种基于偏微分方程的图像平滑技术

图像平滑是大多数图像分析和计算机视觉问题中必需的环节。文中探讨了噪声图像的噪声抑制方法,利用了基于偏微分方程的平滑技术。该方法的优点在于可以在消除噪声的同时有效地保持空间分辨率。最后采用数据验证了方法的有效性。     

一种基于偏微分方程的图像平滑技术

图像平滑是大多数图像分析和计算机视觉问题中必需的环节.文中探讨了噪声图像的噪声抑制方法,利用了基于偏微分方程的平滑技术.该方法的优点在于可以在消除噪声的同时有效地保持空间分辨率.最后采用数据验证了方法的有效性.     

基于PDE''''s的图像平滑方法

传统的图像平滑方法在去除噪声的同时往往会破坏边缘、线务、纹理等图像特征，而基于偏微分方程(PDE’s)的各向异性扩散算法则在抑制噪声的同时能够保持这些特征。本文在Perona ＆ Malik模型基础上引入梯度阈值和高斯平滑核，实验结果表明改进后的平滑方法既能更有效消除孤立噪声点，又可以更好地保持边缘。     

基于前向和后向扩散的图像增强算法的改进

图像去噪和增强是图像处理和计算机视觉领域中的基本问题,而偏微分方程已经广泛应用于模糊图像的复原。针对P-M方法和原FAB方法的不足,通过区分图像的平坦区和边界区,综合这两种方法得出了新的扩散系数方程,并通过有限差分法将对应的偏微分方程离散化后得到了它的数值解。这种改进的各向异性的扩散方法,在平滑图像的同时能够保持和增强边界,对实际图像的滤波结果表明了该算法是有效的。     

基于前向和后向扩散的图像增强算法的改进

图像去噪和增强是图像处理和计算机视觉领域中的基本问题,而偏微分方程已经广泛应用于模糊图像的复原.针对P-M方法和原FAB方法的不足,通过区分图像的平坦区和边界区,综合这两种方法得出了新的扩散系数方程,并通过有限差分法将对应的偏微分方程离散化后得到了它的数值解.这种改进的各向异性的扩散方法,在平滑图像的同时能够保持和增强边界,对实际图像的滤波结果表明了该算法是有效的.     

基于PDE正则化的超分辨率图像重构方法

采用非线性扩散模型建立超分辨率图像重构的偏微分方程，利用各向异性扩散方程的方向选择平滑的特性，在重构高分辨率图像的同时能够很好地消除系统噪声，保持细节信息。实验结果表明，该方法有效地提高了重构的图像质量，在视觉观察和数值评价上都优于原有正则化方法，并且对不同噪声水平的图像具有很好的鲁棒性。     

基于图像局部最大中值差和梯度的非线性扩散

分析了图像平滑中几种基于非线性扩散模型存在的问题,提出一种改进的非线性扩散方法。该方法用图像局部最大中值差和像素的梯度幅值联合度量图像的不平滑度,由此控制偏微分方程（PDE）的扩散行为,达到既去除噪声又保持图像边缘的目的。实验结果表明,用该方法既可以去除图像噪声又可以保持图像边缘,并且收敛速度较快。     

基于自适应参数高阶偏微分方程的图像平滑

为消除经典P-M方法在图像平滑时引起的"阶梯"效应,提出了基于自适应参数的高阶偏微分方程图像平滑方法,并且利用Mean Shift的核密度估计方法来确定各点阈值参数.与固定阈值参数的各向异性扩散方法相比,该方法有效地保持了图像的边缘等重要信息,能够更大程度地抑制孤立噪声,从而得到更高的PSNR值和更好的视觉效果.     

一种改进You-Kaveh模型扩散系数的图像去噪方法

将前向后向扩散系数引入到You和Kaveh提出的四阶偏微分方程去噪模型中,前向扩散用于对噪声进行平滑,后向扩散则对图像特征进行强化.同时,改进了模型中拉普拉斯算子的离散形式,使其包含更多的图像信息,能够更准确的判断图像的特征.新方法处理后的图像,避免了二阶偏微分方程处理图像常出现的"阶梯"效应,同时,和同类的四阶偏微分方程去噪模型相比,该方法的处理结果不会出现"斑"点,因此视觉效果更加理想.最后,通过实验证明了该方法的有效性.     

基于CDD模型的快速图像修复算法

为对图像的缺损部分进行快速自动修复,提出了一种基于曲率驱动修复模型的快速图像修复算法.曲率驱动修复模型由于引入了曲率项,使其偏微分方程为高阶,修复时需要数值求解偏微分方程,大量迭代运算导致修复速度非常缓慢.为加快修复速度.算法将模型的偏微分方程数值化,进一步改造成加权平均形式,利用邻近已知像素直接合成损坏像素,加权系数由曲率和梯度共同确定,使修复按照图像等照度线方向进行,在曲率大的地方将等照度线拉伸,同时由待修复点邻域内已知像素的梯度方差确定修复次序.实验结果表明,显著减小了运算时间,一定程度满足"连接性准则",并且对于较小破损区域修复效果好于曲率驱动修复模型.     

根据最佳预测模式概率进行帧内预测的快速方法

为了减少视频编码中帧内预测的计算量，提出一种称为AOPDE的快速算法．该算法利用H．26L中帧内预测编码的最佳预测模式概率模型来自适应调整预测过程，结合PDE方法，达到加快帧内图像编码速度的目的．基于H．26L参考模型TML8的实验结果表明，文中提出的算法具有很好的效果．     

Direct Manipulation and Interactive Sculpting of PDE Surfaces

This paper presents an integrated approach and a unified algorithm that combine the benefits of PDE surfaces and powerful physics-based modeling techniques within one single modeling framework, in order to realize the full potential of PDE surfaces. We have developed a novel system that allows direct manipulation and interactive sculpting of PDE surfaces at arbitrary location, hence supporting various interactive techniques beyond the conventional boundary control. Our prototype software affords users to interactively modify point, normal, curvature, and arbitrary region of PDE surfaces in a predictable way. We employ several simple, yet effective numerical techniques including the finite-difference discretization of the PDE surface, the multigrid-like subdivision on the PDE surface, the mass-spring approximation of the elastic PDE surface, etc. to achieve real-time performance. In addition, our dynamic PDE surfaces can also be approximated using standard bivariate B-spline finite elements, which can subsequently be sculpted and deformed directly in real-time subject to intrinsic PDE constraints. Our experiments demonstrate many attractive advantages of our dynamic PDE formulation such as intuitive control, real-time feedback, and usability to the general public.     

Mode Decomposition Evolution Equations

Partial differential equation (PDE) based methods have become some of the most powerful tools for exploring the fundamental problems in signal processing, image processing, computer vision, machine vision and artificial intelligence in the past two decades. The advantages of PDE based approaches are that they can be made fully automatic, robust for the analysis of images, videos and high dimensional data. A fundamental question is whether one can use PDEs to perform all the basic tasks in the image processing. If one can devise PDEs to perform full-scale mode decomposition for signals and images, the modes thus generated would be very useful for secondary processing to meet the needs in various types of signal and image processing. Despite of great progress in PDE based image analysis in the past two decades, the basic roles of PDEs in image/signal analysis are only limited to PDE based low-pass filters, and their applications to noise removal, edge detection, segmentation, etc. At present, it is not clear how to construct PDE based methods for full-scale mode decomposition. The above-mentioned limitation of most current PDE based image/signal processing methods is addressed in the proposed work, in which we introduce a family of mode decomposition evolution equations (MoDEEs) for a vast variety of applications. The MoDEEs are constructed as an extension of a PDE based high-pass filter (Wei and Jia in Europhys. Lett. 59(6):814–819, 2002) by using arbitrarily high order PDE based low-pass filters introduced by Wei (IEEE Signal Process. Lett. 6(7):165–167, 1999). The use of arbitrarily high order PDEs is essential to the frequency localization in the mode decomposition. Similar to the wavelet transform, the present MoDEEs have a controllable time-frequency localization and allow a perfect reconstruction of the original function. Therefore, the MoDEE operation is also called a PDE transform. However, modes generated from the present approach are in the spatial or time domain and can be easily used for secondary processing. Various simplifications of the proposed MoDEEs, including a linearized version, and an algebraic version, are discussed for computational convenience. The Fourier pseudospectral method, which is unconditionally stable for linearized high order MoDEEs, is utilized in our computation. Validation is carried out to mode separation of high frequency adjacent modes. Applications are considered to signal and image denoising, image edge detection, feature extraction, enhancement etc. It is hoped that this work enhances the understanding of high order PDEs and yields robust and useful tools for image and signal analysis.     

一种基于四阶偏微分方程的噪声消除方法

介绍了一种基于四阶偏微分方程(PDE)噪声消除方法。采用分片平面图像逼近被处理图像。在噪声消除同时保持良好边缘,避免了使用二阶偏微分方程处理图像常常出现的块效应。实验结果表明该方法是行之有效的。     

Low dimensional disturbance observer‐based control for nonlinear parabolic PDE systems with spatio‐temporal disturbances

In this paper, a design problem of low dimensional disturbance observer‐based control (DOBC) is considered for a class of nonlinear parabolic partial differential equation (PDE) systems with the spatio‐temporal disturbance modeled by an infinite dimensional exosystem of parabolic PDE. Motivated by the fact that the dominant structure of the parabolic PDE is usually characterized by a finite number of degrees of freedom, the modal decomposition method is initially applied to both the PDE system and the PDE exosystem to derive a low dimensional slow system and a low dimensional slow exosystem, which accurately capture the dominant dynamics of the PDE system and the PDE exosystem, respectively. Then, the definition of input‐to‐state stability for the PDE system with the spatio‐temporal disturbance is given to formulate the design objective. Subsequently, based on the derived slow system and slow exosystem, a low dimensional disturbance observer (DO) is constructed to estimate the state of the slow exosystem, and then a low dimensional DOBC is given to compensate the effect of the slow exosystem in order to reject approximately the spatio‐temporal disturbance. Then, a design method of low dimensional DOBC is developed in terms of linear matrix inequality to guarantee that not only the closed‐loop slow system is exponentially stable in the presence of the slow exosystem but also the closed‐loop PDE system is input‐to‐state stable in the presence of the spatio‐temporal disturbance. Finally, simulation results on the control of temperature profile for catalytic rod demonstrate the effectiveness of the proposed method. Copyright © 2015 John Wiley & Sons, Ltd.     

融合偏微分方程和中值滤波的图像去噪模型

针对基于偏微分方程(PDE)的图像去噪模型不能有效地去除脉冲噪声,并且低阶偏微分方程在去噪的同时会出现“块效应”现象的问题,提出一种融合偏微分方程和自适应中值滤波的图像去噪模型。该模型通过对图像梯度的分析,在梯度变化剧烈区域和梯度变化微小区域利用二阶模型去噪以提高去噪效率;而在梯度渐变区域利用四阶模型平滑图像以避免出现“块效应”现象。同时,利用脉冲噪声梯度值远大于边缘梯度值的特点,定位脉冲噪声所在区域,在该区域利用自适应中值滤波消除脉冲噪声。该方法能有效去除脉冲噪声,保护图像边缘并消除“块效应”现象,同时提高了去噪效率。实验表明了该模型的有效性。     

An Improved Hybrid Model for Molecular Image Denoising

In this paper an improved hybrid method for removing noise from low SNR molecular images is introduced. The method provides an improvement over the one suggested by Jian Ling and Alan C. Bovik (IEEE Trans. Med. Imaging, 21(4), [2002]). The proposed model consists of two stages. The first stage consists of a fourth order PDE and the second stage is a relaxed median filter, which processes the output of fourth order PDE. The model enjoys the benefit of both nonlinear fourth order PDE and relaxed median filter. Apart from the method suggested by Ling and Bovik, the proposed method will not introduce any staircase effect and preserves fine details, sharp corners, curved structures and thin lines. Experiments were done on molecular images (fluorescence microscopic images) and standard test images and the results shows that the proposed model performs better even at higher levels of noise.