Lattice Boltzmann based PDE solver on the GPU

In this paper, we propose a hardware-accelerated PDE (partial differential equation) solver based on the lattice Boltzmann model (LBM). The LBM is initially designed to solve fluid dynamics by constructing simplified microscopic kinetic models. As an explicit numerical scheme with only local operations, it has the advantage of being easy to implement and especially suitable for graphics hardware (GPU) acceleration. Beyond the Navier–Stokes equation of fluid mechanics, a typical LBM can be modified to solve the parabolic diffusion equation, which is further used to solve the elliptic Laplace and Poisson equations with a diffusion process. These PDEs are widely used in modeling and manipulating images, surfaces and volumetric data sets. Therefore, the LBM scheme can be used as an GPU-based numerical solver to provide a fast and convenient alternative to traditional implicit iterative solvers. We apply this method to several examples in volume smoothing, surface fairing and image editing, achieving outstanding performance on contemporary graphics hardware. It has the great potential to be used as a general GPU computing framework for efficiently solving PDEs in image processing, computer graphics and visualization.     

基于各向异性扩散活动轮廓模型的左心室MRI分割

结合各向异性扩散算法与梯度矢量流活动轮廓模型,提出了基于各向异性扩散活动轮廓模型并应用于心脏核磁共振图像分割;模型采用各向异性扩散方程构造活动轮廓模型的外部能量函数,得到边界更加清晰的分段平滑图像,运用梯度矢量流将边缘图梯度散射到平坦区域,可以有效抑制噪声,同时保持了目标边界;对左心室核磁共振图像的分割实验表明,该模型可以克服噪声和伪影的干扰,与原梯度矢量流模型相比具有更高的精确性和可靠性,有利于实现自动分割.     

Adjoint lattice Boltzmann equation for parameter identification

The lattice Boltzmann equation is briefly introduced using moments to clearly separate the propagation and collision steps in the dynamics. In order to identify unknown parameters we introduce a cost function and adapt control theory to the lattice Boltzmann equation to get expressions for the derivatives of the cost function vs. parameters. This leads to an equivalent of the adjoint method with the definition of an adjoint lattice Boltzmann equation.To verify the general expressions for the derivatives, we consider two elementary situations: a linearized Poiseuille flow to show that the method can be used to optimize parameters, and a nonlinear situation in which a transverse shear wave is advected by a mean uniform flow. We indicate in the conclusion how the method can be used for more realistic situations.     

Lattice Boltzmann Models for Anisotropic Diffusion of Images

The lattice Boltzmann method has attracted more and more attention as an alternative numerical scheme to traditional numerical methods for solving partial differential equations and modeling physical systems. The idea of the lattice Boltzmann method is to construct a simplified discrete microscopic dynamics to simulate the macroscopic model described by the partial differential equations. The use of the lattice Boltzmann method has allowed the study of a broad class of systems that would have been difficult by other means. The advantage of the lattice Boltzmann method is that it provides easily implemented fully parallel algorithms and the capability of handling complicated boundaries. In this paper, we present two lattice Boltzmann models for nonlinear anisotropic diffusion of images. We show that image feature selective diffusion (smoothing) can be achieved by making the relaxation parameter in the lattice Boltzmann equation be image feature and direction dependent. The models naturally lead to the numerical algorithms that are easy to implement. Experimental results on both synthetic and real images are described.     

Gibbs Field Approaches in Image Processing Problems

In this paper, we address the problem of image denoising using a stochastic differential equation approach. Proposed stochastic dynamics schemes are based on the property of diffusion dynamics to converge to a distribution on global minima of the energy function of the model, under a special cooling schedule (the annealing procedure). To derive algorithms for computer simulations, we consider discrete-time approximations of the stochastic differential equation. We study convergence of the corresponding Markov chains to the diffusion process. We give conditions for the ergodicity of the Euler approximation scheme. In the conclusion, we compare results of computer simulations using the diffusion dynamics algorithms and the standard Metropolis–Hasting algorithm. Results are shown on synthetic and real data.     

国画水墨扩散的LBE计算机模拟

为了满足人们在美工设计中对计算机国画艺术效果仿真的需求,研究和分析了水墨扩散LBE(lattice Boltzmann equation,网格波尔兹曼)算法,提出运用亮度决定水粒子的初始分布,用CMY粒子进行扩散模拟.通过对LBE算法进一步推导而提出疑问,并对扩散及受阻方程进行修正.使用Wintab 1.1压感设备接口完成用户压感数据的读取,借助图像处理函数库IPL98 2.0进行扩散实验数据结构和实验流程设计,实现了国画水墨扩散效果的模拟,证明了该方法的可行性和有效性.     

一种有效的最优序参量重构方法

针对模式识别中协同方法存在的问题,提出了一种协同神经网络中序参量重构的方法,该方法是利用遗传算法的全局最优搜索能力,通过对训练样本集的学习,然后再通过在序参量的构建参数空间进行全局搜索来获得最优重构参数。利用实际采样得到的样本对新算法进行的测试表明,新方法确定能找到一组序参量重构参数,并能使识别性能有较大提高。     

Adjoint-based fluid flow control and optimisation with lattice Boltzmann methods

A lattice Boltzmann (LB) framework to solve fluid flow control and optimisation problems numerically is presented. Problems are formulated on a mesoscopic basis. In a side condition, the dynamics of a Newtonian fluid is described by a family of simplified Boltzmann-like equations, namely BGK–Boltzmann equations, which are linked to an incompressible Navier–Stokes equation. It is proposed to solve the non-linear optimisation problem by a line search algorithm. The needed derivatives are obtained by deriving the adjoint equations, referred to as adjoint BGK–Boltzmann equations. The primal equations are discretised by standard lattice Boltzmann methods (LBM) while for the adjoint equations a novel discretisation strategy is introduced. The approach follows the main ideas behind LBM and is therefore referred to as adjoint lattice Boltzmann methods (ALBM). The corresponding algorithm retains most of the basic features of LB algorithms. In particular, it enables a highly-efficient parallel implementation and thus solving large-scale fluid flow control and optimisation problems. The overall solution strategy, the derivation of a prototype adjoint BGK–Boltzmann equation, the novel ALBM and its parallel realisation as well as its validation are discussed in detail in this article. Numerical and performance results are presented for a series of steady-state distributed control problems with up to approximately 1.6 million unknown control parameters obtained on a high performance computer with up to 256 processing units.     

Diffusion network architectures for implementation of Gibbssamplers with applications to assignment problems

In this paper, analog circuit designs for implementations of Gibbs samplers are presented, which offer fully parallel computation. The Gibbs sampler for a discrete solution space (or Boltzmann machine) can be used to solve both deterministic and probabilistic assignment (association) problems. The primary drawback to the use of a Boltzmann machine for optimization is its computational complexity, since updating of the neurons is typically performed sequentially. We first consider the diffusion equation emulation of a Boltzmann machine introduced by Roysam and Miller (1991), which employs a parallel network of nonlinear amplifiers. It is shown that an analog circuit implementation of the diffusion equation requires a complex neural structure incorporating matched nonlinear feedback amplifiers and current multipliers. We introduce a simpler implementation of the Boltzmann machine, using a "constant gradient" diffusion equation, which eliminates the need for a matched feedback amplifier. The performance of the Roysam and Miller network and the new constant gradient (CG) network is compared using simulations for the multiple-neuron case, and integration of the Chapman-Kolmogorov equation for a single neuron. Based on the simulation results, heuristic criteria for establishing the diffusion equation boundaries, and neuron sigmoidal gain are obtained. The final CG analog circuit is suitable for VLSI implementation, and hence may offer rapid convergence.     

Adaptive noise-reducing anisotropic diffusion filter

In image processing and computer vision, the denoising process is an important step before several processing tasks. This paper presents a new adaptive noise-reducing anisotropic diffusion (ANRAD) method to improve the image quality, which can be considered as a modified version of a speckle-reducing anisotropic diffusion (SRAD) filter. The SRAD works very well for monochrome images with speckle noise. However, in the case of images corrupted with other types of noise, it cannot provide optimal image quality due to the inaccurate noise model. The ANRAD method introduces an automatic RGB noise model estimator in a partial differential equation system similar to the SRAD diffusion, which estimates at each iteration an upper bound of the real noise level function by fitting a lower envelope to the standard deviations of pre-segment image variances. Compared to the conventional SRAD filter, the proposed filter has the advantage of being adapted to the color noise produced by today’s CCD digital camera. The simulation results show that the ANRAD filter can reduce the noise while preserving image edges and fine details very well. Also, it is favorably compared to the fast non-local means filter, showing an improvement in the quality of the restored image. A quantitative comparison measure is given by the parameters like the mean structural similarity index and the peak signal-to-noise ratio.     

基于图像处理和模式识别的网络图像监控系统

随着科学技术和生活水平不断的提高,人们的财产和人身安全问题已经不仅仅来自于传统的经验,而是逐渐的转变到虚拟的网络当中;为此,提高人们的隐私安全和财产安全需要加强网络监控,其中图像监控是较为主要的方面;加强图像监控的可靠性和实时性,是实现社会稳步发展和人民网络隐私安全的首要目标;应用计算机网络技术和现代化通讯技术相结合,综合图像处理技术和模式识别技术的应用,设计应用于网络图像监控系统是当前社会发展的安全技术保障之一;文章通过对图像监控进行简析,阐述图像处理技术和模式识别技术的相关方面,探讨研究网络图像监控中图像识别和处理方面的技术;通过对图像处理中的色彩均化和模糊识别实验,得出其对于网络中传播的图片辨识度和提取信息能力具有很高的发展。     

求解二维对流扩散方程的格子Boltzmann方法

针对二维对流扩散方程,基于D2Q4格子速度,用Chapman-Enskog多尺度分析技术,将时间尺度取为二阶,空间尺度取为一阶,推导了各个速度方向上的平衡态分布函数所满足的条件,给出了简单且对称的平衡态分布函数表达式,所得到的平衡态分布函数能正确地恢复出二维对流扩散方程,从而构建了一种新的求解二维对流扩散方程的D2Q4格子Boltzmann（LB）模型。用所给LB模型对扩散方程和两个不同初边界条件的对流扩散方程进行了数值求解,数值实验结果表明数值解与精确解吻合较好,与相关文献结果比较边界误差要小得多,验证了模型的有效性。     

基于梯度树的光学层析正则化重建

光学层析成像是一个病态重建过程,为降低重建过程中的病态特性,需加入合适的先验信息。目前,大多数重建都是基于扩散方程的,在某些情况下,这种重建会失败。直接基于玻耳兹曼传输模型,并以图像熵为正则化项的梯度迭代重建是一种有效的方法。该方法中,梯度计算是个难点。对此,提出一种基于梯度树的求解方法,降低光学层析图像重建的病态性,有效地重建光学层析图像。     

多松弛时间格子Boltzmann方法在GPU上的实现

近年来,随着统一计算设备构架(CUDA)的出现,高端图形处理器(GPU)在图像处理、计算流体力学等科学计算领域的应用得到了快速发展.属于介观数值方法的格子Boltzmann方法(LBM)是1种新的计算流体力学(CFD)方法,具有算法简单、能处理复杂边界条件、压力能够直接求解等优势,在多相流、湍流、渗流等领域得到了广泛应用.LBM由于具有内在的并行性,特别适合在GPU上计算.采用多松弛时间模型(MRT)的LBM,受松弛因子的影响较小并且数值稳定性较好.本文实现了MRT-LBM在基于CUDA的GPU上的计算,并通过计算流体力学经典算例--二维方腔流来验证计算的正确性.在雷诺数Re=[10,104]之间,计算了多达26种雷诺数的算例,并将Re=102,4×102,103,2×103,5×103,7.5×103算例对应的主涡中心坐标与文献中结果进行了对比.计算结果与文献数值实验符合较好,从而验证了算法实现的正确性,并显示出MRT-LBM具有更优的数值稳定性.本文还分析了在GPU上MRT-LBM的计算性能并与CPU的计算进行了比较,结果表明,GPU可以极大地加快MRT-LBM的计算,NVIDIA Tesla C2050相对于单核Intel Xeon 5430 CPU的加速比约为60倍.     

Application of Markov chains on image enhancement

Stochastic image processing tools have been widely used in digital image processing in order to improve the quality of the images. Markov process is one of the well-known mathematical modeling tools in stochastic theory. In this study, a Markov chain model has been developed and applied to image denoising. The transition probabilities were obtained from Fokker–Planck diffusion equation. According to the results, the proposed Markov chain model supplies very good peak signal to noise ratio values along with low computational cost.     

梯度矢量扩散控制实现边缘保持的彩色图像去噪

目的 在图像的获取过程中,由于受到噪声等因素影响,可能导致图像质量下降,给后期处理带来困难,为此提出一种梯度矢量扩散控制实现边缘保持的彩色图像去噪方法。方法 首先分析了彩色图像因灰度化带来的信息损失,为了更好地利用彩色图像信息,构造了RGB空间下的梯度矢量计算方法。其次分析了噪声邻域梯度矢量与边缘邻域梯度矢量间区域性结构差异,并指出现有扩散方程的不足,给出一种控制扩散矩阵的获取方法。最后通过推导矢量图像的边缘函数,给出了RGB空间下的PM方程,分解该模型去除法向扩散,并结合控制扩散矩阵改进边缘停止函数,以此获得更好的矢量扩散控制。结果 实验结果表明,采用这种方法得到的处理结果有着较高的信噪比,验证了该方法的有效性。结论 本文方法能够在去噪的同时,较好地保持图像对比度与边缘信息,具备一定的实用性。     

一种自适应的图像平滑技术

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，提出了基于各向异性分布方程的平滑技术。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。最后采用了真实数据验证了方法的有效性。     

Adaptive discrete neural observer design for nonlinear systems with unknown time‐delay

This paper focuses on the adaptive observer design for nonlinear discrete‐time MIMO systems with unknown time‐delay and nonlinear dynamics. The delayed states involved in the system are arguments of a nonlinear function and only the estimated delay is utilized. By constructing an appropriate Lyapunov–Krasovskii function, the delay estimation error is considered in the observer parameter design. The proposed method is then extended to the system with a nonlinear output measurement equation and the delayed dynamics. With the help of a high‐order neural network (HONN), the requirement for a precise system model, the linear‐in‐the‐parameters (LIP) assumption of the delayed states, the Lipschitz or norm‐boundedness assumption of unknown nonlinearities are removed. A novel converse Lyapunov technical lemma is also developed and used to prove the uniform ultimate boundedness of the proposed observer. The effectiveness of the proposed results is verified by simulations. Copyright © 2010 John Wiley & Sons, Ltd.     

基于CNN的分块自适应彩色图像边缘检测的研究*

利用细胞神经网络(CNN)模型对彩色图像边缘检测时,首先要解决彩色空间的选择以及颜色距离的计算问题,其次网络参数的选择也是一个重要问题。为了达到在确保边缘检测准确的同时有效抑制噪声的目的,对整幅图像进行分块自适应检测,采用熵来度量图像的各个子区域的不同性质,然后根据该区域的性质选择一组合适的网络参数,对提取该区域图像边缘的CNN 模板进行了理论分析和鲁棒性研究,提出一个设计符合相应功能要求的CNN 鲁棒性定理,它为设计相应的 CNN 模板参数提供了解析判据。仿真实验表明,该算法具有较好的健壮性。     

An SNN-Based Semantic Role Labeling Model with Its Network Parameters Optimized Using an Improved PSO Algorithm

Semantic role labeling (SRL) is a fundamental task in natural language processing to find a sentence-level semantic representation. The semantic role labeling procedure can be viewed as a process of competition between many order parameters, in which the strongest order parameter will win by competition and the desired pattern will be recognized. To realize the above-mentioned integrative SRL, we use synergetic neural network (SNN). Since the network parameters of SNN directly influence the synergetic recognition performance, it is important to optimize the parameters. In this paper, we propose an improved particle swarm optimization (PSO) algorithm based on log-linear model and use it to effectively determine the network parameters. Our contributions are two-folds: firstly, a log-linear model is introduced to PSO algorithm which can effectively make use of the advantages of a variety of different knowledge sources, and enhance the decision making ability of the model. Secondly, we propose an improved SNN model based on the improved PSO and show its effectiveness in the SRL task. The experimental results show that the proposed model has a higher performance for semantic role labeling with more powerful global exploration ability and faster convergence speed, and indicate that the proposed model has a promising future for other natural language processing tasks.