Hidden Markov random field models for TCA image analysis

Tooth Cementum Annulation (TCA) is an age estimation method carried out on thin cross sections of the root of mammalian teeth. Age is computed by adding the tooth eruption age to the count of annual incremental lines which are called tooth rings and appear in the cementum band. The number of rings is computed from an intensity (gray scale) image of the cementum band, by estimating the average ring width and then dividing the area of the cementum band by this estimate. The ring width is estimated by modelling the image by a hidden Markov random field, where intensities are assumed to be pixelwise conditionally independent and normally distributed, given a Markov random field of hidden binary labels, representing the“true scene”. To incorporate image macro-features (the long-range dependence among intensities and the quasi-periodicity in the placement of tooth rings), the label random field is defined by an energy function that depends on a parametric Gabor filter, convolved with the true scene. The filter parameter represents the unknown of main interest, i.e. the average width of the rings. The model is estimated through an EM algorithm, relying on the mean field approximation of the hidden label distribution and allows to predict the locations of the rings in the image.     

核空间隐马尔可夫随机场图像模糊聚类

针对模糊C均值算法未考虑图像邻域信息,导致其分割效果不好的不足,结合隐马尔可夫随机场和高斯核函数,提出核空间隐马尔可夫随机场模糊C均值聚类算法。引入隐马尔可夫随机场,在目标函数中引入像素的空间邻域信息,使得分割算法对噪声鲁棒性增强;引入核函数,将样本点非线性变换映射到高维特征空间,增强图像分割的抗干扰能力,保持图像的细节信息。对标准灰度图像添加噪声,用以验证算法的性能。视觉效果及分割图像的峰值信噪比均显示,改进算法具有更好的抗噪能力。     

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.     

基于遗传算法的分子场分析方法研究

将遗传算法引入比较分子场分析方法中进行最佳构象的选择。通过遗传算法的优化,可以得到一组统计最优的三维构效关系模型。计算结果表明,通过遗传算法优化得到的最优模型要优于用传统比较分子场分析方法得到的模型;同时,从这个最优构象中我们可以确定这线化合物的活性构象。     

Factorial Hidden Markov Models

Hidden Markov models (HMMs) have proven to be one of the most widely used tools for learning probabilistic models of time series data. In an HMM, information about the past is conveyed through a single discrete variable—the hidden state. We discuss a generalization of HMMs in which this state is factored into multiple state variables and is therefore represented in a distributed manner. We describe an exact algorithm for inferring the posterior probabilities of the hidden state variables given the observations, and relate it to the forward–backward algorithm for HMMs and to algorithms for more general graphical models. Due to the combinatorial nature of the hidden state representation, this exact algorithm is intractable. As in other intractable systems, approximate inference can be carried out using Gibbs sampling or variational methods. Within the variational framework, we present a structured approximation in which the the state variables are decoupled, yielding a tractable algorithm for learning the parameters of the model. Empirical comparisons suggest that these approximations are efficient and provide accurate alternatives to the exact methods. Finally, we use the structured approximation to model Bach's chorales and show that factorial HMMs can capture statistical structure in this data set which an unconstrained HMM cannot.     

An automatic statistical segmentation algorithm for extraction of fire and smoke regions

Estimation of the extent and spread of wildland fires is an important application of high spatial resolution multispectral images. This work addresses a fuzzy segmentation algorithm to map fire extent, active fire front, hot burn scar, and smoke regions based on a statistical model. The fuzzy results are useful data sources for integrated fire behavior and propagation models built using Dynamic Data Driven Applications Systems (DDDAS) concepts that use data assimilation techniques which require error estimates or probabilities for the data parameters. The Hidden Markov Random Field (HMRF) model has been used widely in image segmentation, but it is assumed that each pixel has a particular class label belonging to a prescribed finite set. The mixed pixel problem can be addressed by modeling the fuzzy membership process as a continuous Multivariate Gaussian Markov Random Field. Techniques for estimating the class membership and model parameters are discussed. Experimental results obtained by applying this technique to two Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) images show that the proposed methodology is robust with regard to noise and variation in fire characteristics as well as background. The segmentation results of our algorithm are compared with the results of a K-means algorithm, an Expectation Maximization (EM) algorithm (which is very similar to the Fuzzy C-Means Clustering algorithm with entropy regularization), and an MRF-MAP algorithm. Our fuzzy algorithm achieves more consistent segmentation results than the comparison algorithms for these test images with the added advantage of simultaneously providing a proportion or error map needed for the data assimilation problem.     

Deriving non-homogeneous DNA Markov chain models by cluster analysis algorithm minimizing multiple alignment entropy

Non-homogeneous Markov chain models can represent biologically important regions of DNA sequences. The statistical pattern that is described by these models is usually weak and was found primarily because of strong biological indications. The general method for extracting similar patterns is presented in the current paper. The algorithm incorporates cluster analysis, multiple alignment and entropy minimization.The method was first tested using the set of DNA sequences produced by Markov chain generators. It was shown that artificial gene sequences, which initially have been randomly set up along the multiple alignment panels, are aligned according to the hidden triplet phase. Then the method was applied to real protein-coding sequences and the resulting alignment clearly indicated the triplet phase and produced the parameters of the optimal 3-periodic non-homogeneous Markov chain model. These Markov models were already employed in the GeneMark gene prediction algorithm, which is used in genome sequencing projects.The algorithm can also handle the case in which the sequences to be aligned reveal different statistical patterns, such as Escherichia coli protein-coding sequences belonging to Class II and Class III. The algorithm accepts a random mix of sequences from different classes, and is able to separate them into two groups (clusters), align each cluster separately, and define a non-homogeneous Markov chain model for each sequence cluster.     

基于小波域层次Markov模型的图像分割

针对两个状态的有限高斯混合模型逼近小波系数的不足和小波域隐马尔可夫树标号场相互独立的缺点,提出了一种基于小波域层次马尔可夫模型的图像分割算法,这种模型用有限通用混合模型逼近小波系数的分布,使有限高斯混合模型只是其一种特殊情况;在标号场的先验模型确定上,利用马尔可夫模型描述标号场的局部作用关系,给出标号场的具体表达式,克服了小波域马尔可夫树模型标号场相互独立的不足,然后利用贝叶斯准则,给出相应的分割因果算法。该模型不仅具有空域马尔可夫模型有效的递归算法的优点,同时具有小波域隐马尔可夫树模型中的马尔可夫参数变尺度行为。最后用真实的图像和合成图像同几种分割方法进行了对比实验,实验结果表明了本文算法的有效性和优异性。     

一种分层马尔可夫图像模型及其推导算法

离散分层马尔可夫随机场(MRF)模型由于层间具有了因果性,因而其非迭代的推导算法比非因果的马尔可夫随机场模型的迭代算法复杂度低得多,结果更精确.针对图像分割问题中观测数据有限的情况,提出了一种新的基于离散分层MRF的半树模型,推导出了它的最大后验边缘概率(MPM)算法.半树模型不仅继承了一般分层模型快速、误分类少的优点,还避免了计算中遇到的数值下溢问题,减轻了分层模型带来的块现象,尤其适合大幅面图像的处理.     

Approximate steady-state analysis of large Markov models based on the structure of their decision diagram encoding

We propose a new approximate numerical algorithm for the steady-state solution of general structured ergodic Markov models. The approximation uses a state-space encoding based on multiway decision diagrams and a transition rate encoding based on a new class of edge-valued decision diagrams. The new method retains the favorable properties of a previously proposed Kronecker-based approximation, while eliminating the need for a Kronecker-consistent model decomposition. Removing this restriction allows for a greater utilization of event locality, which facilitates the generation of both the state-space and the transition rate matrix, thus extends the applicability of this algorithm to larger and more complex models.     

基于分水岭-隐马尔可夫模型联合的语义视频对象提取技术

针对3C无线网络的增值服务业务,提出一种语义对象基于分水岭算法的视频帧内的分割,及基于隐马尔可夫模型的视频帧间跟踪提取技术.其主要的特点是首先采用基于标识集的分水岭算法来进行初始帧内语义视频对象的标定和分割处理,随后再进行二值化掩膜处理,最后借助隐马尔可夫测量场模型,将后续帧中视频对象的跟踪处理演化为跟踪区域与非跟踪区域的二值离散化标定问题.实验结果证明,该算法能很好地实现视频帧序列中语义视频对象的连续提取.     

一种低信噪比图像的模拟退火恢复算法

本文根据马尔可夫(Markov)随机场模型和全局最大后验概率估计技术提出了一种模拟退火图像恢复算法.应用这种算法对混入可加性独立高斯噪声的试验图像进行恢复的实验结果表明,该算法对低信噪比图像数据的恢复处理非常有效.     

Unsupervised statistical segmentation of nonstationary images using triplet Markov fields

Recent developments in statistical theory and associated computational techniques have opened new avenues for image modeling as well as for image segmentation techniques. Thus, a host of models have been proposed and the ones which have probably received considerable attention are the hidden Markov fields (HMF) models. This is due to their simplicity of handling and their potential for providing improved image quality. Although these models provide satisfying results in the stationary case, they can fail in the nonstationary one. In this paper, we tackle the problem of modeling a nonstationary hidden random field and its effect on the unsupervised statistical image segmentation. We propose an original approach, based on the recent triplet Markov field (TMF) model, which enables one to deal with nonstationary class fields. Moreover, the noise can be correlated and possibly non-Gaussian. An original parameter estimation method which uses the Pearson system to find the natures of the noise margins, which can vary with the class, is also proposed and used to perform unsupervised segmentation of such images. Experiments indicate that the new model and related processing algorithm can improve the results obtained with the classical ones.     

新的声纳图像自动分割方法

对水下声纳图像进行目标分割是非常复杂的,它不仅取决于被分割的不同目标,还与海底混响噪声、背景区域有着紧密的联系。通过分析声纳图像的特点,提出了一种新的声纳图像自动分割方法,即利用一种快速的模糊C均值聚类方法来完成初始分割,然后利用初始分割结果对马尔可夫模型的初始参数进行估计,最后,根据马尔可夫理论进行迭代条件估计,得到精确的图像分割结果。最后利用实测数据,验证了此种算法的可行性和有效性。     

Hidden Markov models with factored Gaussian mixtures densities

We present a factorial representation of Gaussian mixture models for observation densities in hidden Markov models (HMMs), which uses the factorial learning in the HMM framework. We derive the reestimation formulas for estimating the factorized parameters by the Expectation Maximization (EM) algorithm and propose a novel method for initializing them. To compare the performances of the proposed models with that of the factorial hidden Markov models and HMMs, we have carried out extensive experiments which show that this modelling approach is effective and robust.     

Turbo segmentation of textured images

We consider the problem of semi-supervised segmentation of textured images. Existing model-based approaches model the intensity field of textured images as a Gauss-Markov random field to take into account the local spatial dependencies between the pixels. Classical Bayesian segmentation consists of also modeling the label field as a Markov random field to ensure that neighboring pixels correspond to the same texture class with high probability. Well-known relaxation techniques are available which find the optimal label field with respect to the maximum a posteriori or the maximum posterior mode criterion. But, these techniques are usually computationally intensive because they require a large number of iterations to converge. In this paper, we propose a new Bayesian framework by modeling two-dimensional textured images as the concatenation of two one-dimensional hidden Markov autoregressive models for the lines and the columns, respectively. A segmentation algorithm, which is similar to turbo decoding in the context of error-correcting codes, is obtained based on a factor graph approach. The proposed method estimates the unknown parameters using the Expectation-Maximization algorithm.     

Two design methods of hyperparameters in variational Bayes learning for Bernoulli mixtures

Variational Bayes learning or mean field approximation is widely used in statistical models which are made of mixtures of exponential distributions, for example, normal mixtures, binomial mixtures, and hidden Markov models. To derive variational Bayes learning algorithm, we need to determine the hyperparameters in the a priori distribution; however, the design method of hyperparameters has not yet been established. In the present paper, we propose two different design methods of hyperparameters which are applied to the different purposes. In the former method, the hyperparameter is determined for minimization of the generalization error. In the latter method, it is chosen so that candidates of hidden structure in training data are extracted. It is experimentally shown that the optimal hyperparameters for two purposes are different from each other.     

Parallel and deterministic algorithms from MRFs: surfacereconstruction

Deterministic approximations to Markov random field (MRF) models are derived. One of the models is shown to give in a natural way the graduated nonconvexity (GNC) algorithm proposed by A. Blake and A. Zisserman (1987). This model can be applied to smooth a field preserving its discontinuities. A class of more complex models is then proposed in order to deal with a variety of vision problems. All the theoretical results are obtained in the framework of statistical mechanics and mean field techniques. A parallel, iterative algorithm to solve the deterministic equations of the two models is presented, together with some experiments on synthetic and real images     

A genetic algorithm for MRF-based segmentation of multi-spectral textured images

A segmentation approach based on a Markov random field (MRF) model is an iterative algorithm; it needs many iteration steps to approximate a near optimal solution or gets a non-suitable solution with a few iteration steps. In this paper, we use a genetic algorithm (GA) to improve an unsupervised MRF-based segmentation approach for multi-spectral textured images. The proposed hybrid approach has the advantage that combines the fast convergence of the MRF-based iterative algorithm and the powerful global exploration of the GA. In experiments, synthesized color textured images and multi-spectral remote-sensing images were processed by the proposed approach to evaluate the segmentation performance. The experimental results reveal that the proposed approach really improves the MRF-based segmentation for the multi-spectral textured images.     

Distributed genetic algorithm for Gaussian mixture model based speaker identification

This paper presents a novel algorithm for reducing the computational complexity of identifying a speaker within a Gaussian mixture speaker model (GMM) framework. We have combined distributed genetic algorithm (DGA) and the Markov random field (MRF) to avoid typical local minima for speaker vector quantization. To improve the computation efficiency, only unstable chromosomes corresponding to speaker data parts are evolved. Identification accuracies of 93% were achieved for 100 Mandarin speakers.