Morphological analysis of discrete random shapes

In this paper I discuss a number of theoretical issues regarding the morphological analysis of discrete random shapes by means of Matheron's random set theory. I revisit this theory by limiting myself to the discrete case, since most image data are available in a discrete form. Although it may seem that the transition from the continuous to the discrete case is straightforward (since most of Matheron's theory is general enough to incorporate the discrete case as a special case), this transition is often challenging and full of exciting and, surprisingly, pleasant results. I introduce the concept of the cumulative-distribution functional of a discrete random set and review some fundamental properties of the capacity functional (a fundamental statistical quantity that uniquely defines a random set and relates random set theory to mathematical morphology). In analogy to a recent result and under a natural boundness condition, I show that there exists a one-to-one correspondence between the probability-mass function of a discrete binary random field and the corresponding cumulative-distribution functional. The relationship between the cumulative-distribution functional and the capacity functional of a discrete random set is also established. The cumulative-distribution and capacity functionals are related to the higher-order moments of a discrete binary random field, and, therefore, their computation is equivalent to computing these moments. A brief discussion of how to perform such computations for a certain class of discrete random sets is provided. The capacity functional of a morphologically transformed, continuous random set cannot be associated to the capacity functional of the random set itself, except in the case of dilation. I show that the derivation of such an association is possible in the discrete case and for the cases of dilation and erosion and more complicated morphological transformations, such as opening and closing. These relationships are then used to derive a fundamental result regarding the statistical behavior of opening and closing morphological filters. I also show that the probability-mass function of a discrete binary random field may be expressed in terms of the cumulative-distribution functional or the capacity functional of a morphologically transformed discrete random set by means of a hit-or-miss transformation. I also introduce moments for discrete random sets, which permit generalization of the concepts of autocorrelation and contact distribution. Furthermore, I demonstrate the fact that the class of opening-based size distributions, introduced axiomatically by Matheron, are higher-order moments of a discrete random set, therefore statistically demonstrating that size distributions are good statistical summaries for shape. Finally, convex random sets are viewed in the discrete domain. My final result regarding convexity, is similar to Matheron's. However, the tools used here for the derivation of such a result are different from the ones used by Matheron, whose approach to this subject is limited to the continuous case.     

基于马尔可夫随机场的图像分割方法综述

系统地综述了基于MRF的图像分割方法。介绍了基于MRF模型的图像分割理论框架, 给出了当前MRF图像建模研究的热点问题。概括了基于MRF模型的图像分割算法, 包括图割算法、归一化割算法、置信度传播算法等, 指出了这些算法的发展方向。     

基于LDA的条件随机场主题模型研究

使用主题模型对文本建模,提取文本的隐含主题,进而进行词性标注和文本分类等工作,是机器学习和文本挖掘领域的研究热点。提出一个基于LDA的主题模型,它基于“段袋“假设--文本中的段落具有相同的主题,且连续的段落更倾向于具有相同的主题。对于文章的段落,采用条件随机场（CRF）模型划分并判断它们是否具有相同主题。实验表明,新模型相比LDA模型能更好得提取主题并具有更低的困惑度,同时,能够较好地进行词性标注和文本分类工作。     

Identifying and constructing elemental parts of shafts based on conditional random fields model

Semantic information is very important for understanding 2D engineering drawings. However, this kind of information is implicit so that it is hard to be extracted and understood by computers. In this paper, we aim to identify the semantic information of shafts from their 2D drawings, and then reconstruct the 3D models. The 2D representations of shafts are diverse. By analyzing the characteristics of 2D drawings of shafts, we find that there is always a view which represents the projected outline of the shaft, and each loop in this view corresponds to an elemental part. The conditional random fields (CRFs) model is a classification technique which can automatically integrate various features, rather than manually organizing of heuristic rules. We first use a CRFs model to identify elemental parts with semantic information. The 3D elemental parts are then constructed by a parameters template method. Compared with the existing 3D reconstruction methods, our approach can obtain both geometrical information and semantic information of each part of shafts from 2D drawings. Several examples are provided to demonstrate that our algorithm can accurately handle diverse 2D drawings of shafts.     

Computation of the exact Cramer–Rao lower bound for the parameters of a nonsymmetric half-plane 2-D ARMA model

The Cramer–Rao lower bound (CRLB) that gives the minimal achievable variance/standard deviation for any unbiased estimator offers a useful tool for an assessment of the consistency of parameter estimation techniques. In this paper, a closed-form expression for the computation of the exact CRLB on unbiased estimates of the parameters of a two-dimensional (2-D) autoregressive moving average (ARMA) model with a nonsymmetric half-plane (NSHP) region of support is developed. The proposed formulation is mainly based on a matrix representation of 2-D real-valued discrete and homogeneous random field characterized by the NSHP ARMA model. Assuming that the random field is Gaussian, the covariance matrix of the NSHP ARMA random field is first expressed in terms of the model parameters. Then, using this matrix structure, a closed-form expression of the exact Fisher information matrix required for the CRLB computation of the NSHP ARMA model parameters is developed. Finally, the main formulas derived for the NSHP ARMA model are rearranged for its autoregressive and moving average counterparts, separately. Numerical simulations are included to demonstrate the behavior of the derived CRLB formulas.     

基于条件随机场进行蛋白质二级结构预测*

使用一种新的概率图模型——条件随机场对蛋白质二级结构进行预测,并给出了模型的构建、训练以及解码的算法。应用这一模型对一个典型的蛋白质数据集CB513的二级结构进行了预测,并将预测结果与其他方法进行比较,预测准确度有明显的提高。     

基于修正的分段模糊吉伯斯随机场模型的图像分割

模糊随机场模型在解决多值模糊分割方面主要存在算法的稳定性和效率问题。针对这些不足,提出一种简单、方便有效的多值模糊分割新算法--修正的分段模糊吉伯斯分割算法。该算法利用修正的模糊C均值来提供良好的初始分类,结合传统的二值模糊算法来完成对复杂多值图像的快速、精确分割。实验表明,该修正算法比传统的随机场模型有更好的图像分割能力,能较好地解决目前多值模糊分割算法所面临的稳定性和效率问题。     

结合深度学习与条件随机场的遥感图像分类

目的 为进一步提高遥感影像的分类精度,将卷积神经网络（CNN）与条件随机场（CRF）两个模型结合,提出一种新的分类方法。方法 首先采用CNN对遥感图像进行预分类,并将其类成员概率定义为CRF模型的一阶势函数;然后利用高斯核函数的线性组合定义CRF模型的二阶势函数,用全连接的邻域结构代替常见的4邻域或8邻域;接着加入区域约束,使用Mean-shift分割方法得到超像素,通过计算超像素的后验概率均值修正各像素的分类结果,鼓励连通区域结果的一致性;最后采用平均场近似算法实现整个模型的推断。结果 选用3组高分辨率遥感图像进行地物分类实验。本文方法不仅能抑制更多的分类噪声,同时还可以改善过平滑现象,保护各类地物的边缘信息。实验采用类精度、总体分类精度OA、平均分类精度AA,以及Kappa系数4个指标进行定量分析,与支持向量机（SVM）、CNN和全连接CRF相比,最终获得的各项精度均得到显著提升,其中,AA提高3.28个百分点,OA提高3.22个百分点,Kappa提高5.07个百分点。结论 将CNN与CRF两种模型融合,不仅可以获得像元本质化的特征,而且同时还考虑了图像的空间上下文信息,使分类更加准确,后加入的约束条件还能进一步保留地物目标的局部信息。本文方法适用于遥感图像分类领域,是一种精确有效的分类方法。     

关于第二类Fornasini-Marchesini模糊的2-D动态规划

为了求解用正常或奇异的第二类Fornasini-Marchesini模型(FMM Ⅱ)描述的2-D线性离散系统的最优控制问题, 首先将2-D FMM Ⅱ用变结构1-D形式表示, 再利用1-D动态规划的方法, 给出使给定指标函数最小的2-D控制序列、最优轨线及性能指标的最优值的计算方法.     

时滞2-D中立型离散状态模型正解的存在性

在Bandch空间中利用不动点定理研究了时滞 2 D二阶中立型离散时间状态模型正解的存在性.     

初始状态为正交的二维线性正系统的渐近稳定性

本文分析了初始状态为正交的二维线性正系统的渐近稳定性. 与一维系统不同, 初始状态为正交的二维系统的稳定性严格依赖于合适的初始条件. 首先, 当初始状态 绝对收敛时, 二维正FM I 模型的渐近稳定性判据被提出. 然后, 针对二维正Rosser模型, 在初始状态 绝对收敛时, 相似的结论被给出. 最后, 两个数字实例证实了这些判据的有效性.     

Stability analysis of 2-D linear discrete systems based on the Fornasini–Marchesini second model: Stability with asymmetric Lyapunov matrix

The stability of two-dimensional (2-D) linear discrete systems based on the Fornasini–Marchesini local state-space (LSS) model is considered. A stability criterion using the asymmetric Lyapunov matrix P is presented. A special case of the criterion is discussed.     

一类2-D不确定离散系统的弹性保成本控制

当被控系统的数学模型存在不确定性时,需要设计鲁棒控制器才能使得受控系统稳定,然而,如果控制器本身也存在不确定性时,系统就会变得复杂难以控制,使用传统的鲁棒控制方法很难达到期望的控制目标,甚至不能保证受控系统的稳定性.本研究就是针对当系统模型和控制器同时存在不确定性时,给出了设计稳定控制器的简便方法.通过将控制器的不确定性分别表示为加法式和乘法式摄动,研究了以上两种系统的弹性保成本控制问题,并给出了相应控制器的设计方法.在主要结果推导过程中,巧妙运用了各种矩阵不等式放缩和等价参数变换等数学方法,最终将主要结果表示为线性矩阵不等式(LMI),利用Matlab的LMI工具箱,可以很方便地设计所需要的控制器.最后,对同一个受控系统,分别施加利用本文结果和已有结果设计的控制器,发现前者可以很好地控制系统,而后者却不能使受控系统稳定,从而验证了所得结果的有效性.     

Parallel exact sampling and evaluation of Gaussian Markov random fields

Markov chain Monte Carlo algorithms are computationally expensive for large models. Especially, the so-called one-block Metropolis-Hastings (M-H) algorithm demands large computational resources, and parallel computing seems appealing. A parallel one-block M-H algorithm for latent Gaussian Markov random field (GMRF) models is introduced. Important parts of this algorithm are parallel exact sampling and evaluation of GMRFs. Parallelisation is achieved with parallel algorithms from linear algebra for sparse symmetric positive definite matrices. The parallel GMRF sampler is tested for GMRFs on lattices and irregular graphs, and gives both good speed-up and good scalability. The parallel one-block M-H algorithm is used to make inference for a geostatistical GMRF model with a latent spatial field of 31,500 variables.     

Global and componentwise extrapolations for accelerating training of Bayesian networks and conditional random fields

The triple jump extrapolation method is an effective approximation of Aitken’s acceleration that can accelerate the convergence of many algorithms for data mining, including EM and generalized iterative scaling (GIS). It has two options—global and componentwise extrapolation. Empirical studies showed that neither can dominate the other and it is not known which one is better under what condition. In this paper, we investigate this problem and conclude that, when the Jacobian is (block) diagonal, componentwise extrapolation will be more effective. We derive two hints to determine the block diagonality. The first hint is that when we have a highly sparse data set, the Jacobian of the EM mapping for training a Bayesian network will be block diagonal. The second is that the block diagonality of the Jacobian of the GIS mapping for training CRF is negatively correlated with the strength of feature dependencies. We empirically verify these hints with controlled and real-world data sets and show that our hints can accurately predict which method will be superior. We also show that both global and componentwise extrapolation can provide substantial acceleration. In particular, when applied to train large-scale CRF models, the GIS variant accelerated by componentwise extrapolation not only outperforms its global extrapolation counterpart, as our hint predicts, but can also compete with limited-memory BFGS (L-BFGS), the de facto standard for CRF training, in terms of both computational efficiency and F-scores. Though none of the above methods are as fast as stochastic gradient descent (SGD), careful tuning is required for SGD and the results given in this paper provide a useful foundation for automatic tuning.     

Cascade Markov random fields for stroke extraction of Chinese characters

Extracting perceptually meaningful strokes plays an essential role in modeling structures of handwritten Chinese characters for accurate character recognition. This paper proposes a cascade Markov random field (MRF) model that combines both bottom-up (BU) and top-down (TD) processes for stroke extraction. In the low-level stroke segmentation process, we use a BU MRF model with smoothness prior to segment the character skeleton into directional substrokes based on self-organization of pixel-based directional features. In the high-level stroke extraction process, the segmented substrokes are sent to a TD MRF-based character model that, in turn, feeds back to guide the merging of corresponding substrokes to produce reliable candidate strokes for character recognition. The merit of the cascade MRF model is due to its ability to encode the local statistical dependencies of neighboring stroke components as well as prior knowledge of Chinese character structures. Encouraging stroke extraction and character recognition results confirm the effectiveness of our method, which integrates both BU/TD vision processing streams within the unified MRF framework.     

具有时变状态滞后的非线性2-D 离散系统的稳定性与控制

考虑一类由局部状态空间Fornasini-Marchesini(FM LSS)第二模型描述的,具有时变状态滞后非线性二维(2-D)离散系统的稳定性分析和控制问题.时变状态滞后项的上、下界为正整数,非线性项满足Lipschitz条件.首先,通过引入一个含有时滞上、下界的新Lyapunov函数,给出了系统的稳定性准则;然后设计了状态反馈控制器以保证系统的稳定性,进而,状态反馈控制律可由线性矩阵不等式求得;最后通过数值算例表明了所得结果的有效性.     

基于条件随机场的网络评论与事件中命名实体匹配研究

为发现针对新闻事件中实体展开的网络评论,本文提出一种基于条件随机场的网络评论与新闻事件中命名实体匹配方法。提出使用Semi-Markov CRFs从评论语句中识别出片段粒度的命名实体。针对评论描述随意的特点,结合命名实体的模式特征、符号特征等特征识别出评论中实体的简称、缩写、昵称等变体形式。本文使用Linear-Chain CRFs结合多种匹配方法计算评论中命名实体与事件中命名实体的综合相似度,完成匹配。实验证明,提出的基于条件随机场的网络评论与事件中命名实体匹配方法能够准确根据命名实体匹配评论与事件。     

Non-fragile robust optimal guaranteed cost control of uncertain 2-D discrete state-delayed systems

This paper is concerned with the problem of non-fragile robust optimal guaranteed cost control for a class of uncertain two-dimensional (2-D) discrete state-delayed systems described by the general model with norm-bounded uncertainties. Our attention is focused on the design of non-fragile state feedback controllers such that the resulting closed-loop system is asymptotically stable and the closed-loop cost function value is not more than a specified upper bound for all admissible parameter uncertainties and controller gain variations. A sufficient condition for the existence of such controllers is established under the linear matrix inequality framework. Moreover, a convex optimisation problem is proposed to select a non-fragile robust optimal guaranteed cost controller stabilising the 2-D discrete state-delayed system as well as achieving the least guaranteed cost for the resulting closed-loop system. The proposed method is compared with the previously reported criterion. Finally, illustrative examples are given to show the potential of the proposed technique.