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.     

An empirical study of the simulation of various models used forimages

Markov random fields are typically used as priors in Bayesian image restoration methods to represent spatial information in the image. Commonly used Markov random fields are not in fact capable of representing the moderate-to-large scale clustering present in naturally occurring images and can also be time consuming to simulate, requiring iterative algorithms which can take hundreds of thousands of sweeps of the image to converge. Markov mesh models, a causal subclass of Markov random fields, are, however, readily simulated. We describe an empirical study of simulated realizations from various models used in the literature, and we introduce some new mesh-type models. We conclude, however, that while large-scale clustering may be represented by such models, strong directional effects are also present for all but very limited parameterizations. It is emphasized that the results do not detract from the use of Markov random fields as representers of local spatial properties, which is their main purpose in the implementation of Bayesian statistical approaches to image analysis. Brief allusion is made to the issue of parameter estimation     

图像分割中的马尔可夫随机场方法综述

马尔可夫随机场方法是图像分割中一个极为活跃的研究方向。本文介绍了基于马尔可夫随机场模型的一般理论与图像的关系,给出它在图像分割中的通用框架:包括空域和小波域图像模型的建立、最优准则的选取、标号数的确定、图像模型参数的估计和图像分割的实现,评述了其在图像分割中的应用,展望其发展的方向。     

图模型在彩色纹理分类中的应用

纹理分析中往往将彩色图像转换为灰度图以降低计算复杂度,这样就忽略了颜色信息。而利用主成分分析 的方法来降维彩色纹理,则可以尽可能地保留颜色和纹理信息。高斯图模型(Uaussian Graphical Models, GGM)可以 很好地描述有交互作用的高维数据,因此可用来建立图像纹理模型。根据局部马尔可夫性和高斯变量的条件回归之 间的关系,可将复杂的模型选择转变为较简单的变量选择。通过惩罚正则化方法,其部域选择和参数佑计可同步进 行,然后提取纹理特征进行彩色纹理分类,实验显示其具有很好的效果。因此,结合主成分分析和高斯图模型来构建 彩色纹理模型有很好的发展前景。     

An adaptive surrogate modeling-based sampling strategy for parameter optimization and distribution estimation (ASMO-PODE)

Parameter distribution estimation has long been a hot issue for the uncertainty quantification of environmental models. Traditional approaches such as MCMC (Markov Chain Monte Carlo) are prohibitive to be applied to large complex dynamic models because of the high computational cost of computing resources. To reduce the number of model evaluations required, we proposed an adaptive surrogate modeling-based sampling strategy for parameter distribution estimation, named ASMO-PODE (Adaptive Surrogate Modeling-based Optimization – Parameter Optimization and Distribution Estimation). The ASMO-PODE can provide an estimation of the parameter distribution using as little as one percent of the model evaluations required by a regular MCMC approach. The effectiveness and efficiency of the ASMO-PODE approach have been evaluated with 2 test problems and one land surface model, the Common Land Model. The results demonstrated that the ASMO-PODE method is an economic way for parameter optimization and distribution estimation.     

Maximum likelihood estimation methods for multispectral randomfield image models

Considers the problem of estimating parameters of multispectral random field (RF) image models using maximum likelihood (ML) methods. For images with an assumed Gaussian distribution, analytical results are developed for multispectral simultaneous autoregressive (MSAR) and Markov random field (MMRF) models which lead to practical procedures for calculating ML estimates. Although previous work has provided least squares methods for parameter estimation, the superiority of the ML method is evidenced by experimental results provided in this work. The effectiveness of multispectral RF models using ML estimates in modeling color texture images is also demonstrated     

Modeling textured images using generalized long correlation models

The long correlation (LC) models are a general class of random field (RF) models which are able to model correlations, extending over large image regions with few model parameters. The LC models have seen limited use, due to lack of an effective method for estimating the model parameters. In this work, we develop an estimation scheme for a very general form of this model and demonstrate its applicability to texture modeling applications. The relationship of the generalized LC models to other classes of RF models, namely the simultaneous autoregressive (SAR) and Markov random field (MRF) models, is shown. While it is known that the SAR model is a special case of the LC model, we show that the MRF model is also encompassed by this model. Consequently, the LC model may be considered as a generalization of the SAR and MRF models     

纹理分析中的图模型

纹理作为一种重要的视觉特征,广泛应用于图像分析。高斯图模型（GGM）可以很好地描述有交互作用的高维数据,因此可用来建立图像纹理模型。根据纹理特征的局部马尔可夫性和高斯变量的条件回归之间的关系,将复杂的模型选择转变为较简单的变量选择,应用惩罚正则化技巧同步选择邻域和估计参数。提取基于图模型的纹理特征分析纹理,实验显示了很好的效果。因此,利用高斯图模型来构建纹理模型有很好的发展前景。     

Pairwise Markov chains

We propose a model called a pairwise Markov chain (PMC), which generalizes the classical hidden Markov chain (HMC) model. The generalization, which allows one to model more complex situations, in particular implies that in PMC the hidden process is not necessarily a Markov process. However, PMC allows one to use the classical Bayesian restoration methods like maximum a posteriori (MAP), or maximal posterior mode (MPM). So, akin to HMC, PMC allows one to restore hidden stochastic processes, with numerous applications to signal and image processing, such as speech recognition, image segmentation, and symbol detection or classification, among others. Furthermore, we propose an original method of parameter estimation, which generalizes the classical iterative conditional estimation (ICE) valid for a classical hidden Markov chain model, and whose extension to possibly non-Gaussian and correlated noise is briefly treated. Some preliminary experiments validate the interest of the new model.     

Estimating degradation model parameters using neighborhood pattern distributions: an optimization approach

Noise models are crucial for designing image restoration algorithms, generating synthetic training data, and predicting algorithm performance. There are two related but distinct estimation scenarios. The first is model calibration, where it is assumed that the input ideal bitmap and the output of the degradation process are both known. The second is the general estimation problem, where only the image from the output of the degradation process is given. While researchers have addressed the problem of calibration of models, issues with the general estimation problems have not been addressed in the literature. In this paper, we describe a parameter estimation algorithm for a morphological, binary, page-level image degradation model. The inputs to the estimation algorithm are 1) the degraded image and 2) information regarding the font type (italic, bold, serif, sans serif). We simulate degraded images using our model and search for the optimal parameter by looking for a parameter value for which the local neighborhood pattern distributions in the simulated image and the given degraded image are most similar. The parameter space is searched using a direct search optimization algorithm. We use the p-value of the Kolmogorov-Smirnov test as the measure of similarity between the two neighborhood pattern distributions. We show results of our algorithm on degraded document images.     

Multispectral textured image segmentation using a multi-resolution fuzzy Markov random field model on variable scales in the wavelet domain

This article proposes a new multispectral image texture segmentation algorithm using a multi-resolution fuzzy Markov random field model for a variable scale in the wavelet domain. The algorithm considers multi-scalar information in both vertical and lateral directions. The feature field of the scalable wavelet coefficients is modelled, combining with the fuzzy label field describing the spatially constrained correlations between neighbourhood features to achieve a more accurate parameter estimation. The extended scalable label field models the label data from different scales to obtain more homogeneous areas; image segmentation results are finally obtained according to the Bayesian rule from a coarser to a finer scale. Multispectral texture images and remote-sensing images are used to test the effectiveness of the the proposed method. Segmentation results show that the new method simultaneously presents a better performance in achieving the homogeneity of the region and accuracy of detected boundaries compared with existing image segmentation algorithms.     

基于多尺度Markov模型的SAR图像上下文融合分割方法

在多尺度Markov模型的基础上,提出了一种新的用于SAR图像无监督分割的上下文融合分割方法。该方法充分考虑了SAR图像分布的统计特性,用基于混合Rayleigh分布的多尺度Markov模型对待分割图像建模,并直接根据待分割图像用迭代条件估计算法来训练模型的参数。然后以上下文向量的形式提出了四种不同的上下文模型,并用这四种上下文模型分别对待分割图像的多尺度图像信息进行自上而下的融合,最终得到四种不同的分割结果。实验表明,该方法进一步提高了SAR图像分割结果的精度。     

Pairwise likelihood inference for ordinal categorical time series

Ordinal categorical time series may be analyzed as censored observations from a suitable latent stochastic process, which describes the underlying evolution of the system. This approach may be considered as an alternative to Markov chain models or to regression methods for categorical time series data. The problem of parameter estimation is solved through a simple pseudolikelihood, called pairwise likelihood. This inferential methodology is successfully applied to the class of autoregressive ordered probit models. Potential usefulness for inference and model selection within more general classes of models are also emphasized. Illustrations include simulation studies and two simple real data applications.     

Robust Bayesian analysis of heavy-tailed stochastic volatility models using scale mixtures of normal distributions

A Bayesian analysis of stochastic volatility (SV) models using the class of symmetric scale mixtures of normal (SMN) distributions is considered. In the face of non-normality, this provides an appealing robust alternative to the routine use of the normal distribution. Specific distributions examined include the normal, student-t, slash and the variance gamma distributions. Using a Bayesian paradigm, an efficient Markov chain Monte Carlo (MCMC) algorithm is introduced for parameter estimation. Moreover, the mixing parameters obtained as a by-product of the scale mixture representation can be used to identify outliers. The methods developed are applied to analyze daily stock returns data on S&P500 index. Bayesian model selection criteria as well as out-of-sample forecasting results reveal that the SV models based on heavy-tailed SMN distributions provide significant improvement in model fit as well as prediction to the S&P500 index data over the usual normal model.     

基于平均场退火的二值纹理图象恢复

本文根据平均场退火技术，提出了一种二值纹理图象的估计和恢复算法，纹理图象描述为一个马尔可夫随机场模型和噪声过程的综合结果，算法递归地进行模型参数估计和图象恢复，其核心是一个统计松驰搜索算法，平均场方法将统计松驰方程转化为一组确定性方程，从而有效地提高了计算效率，对二值噪声纹理图象的实验结果说明了算法的有效性。     

EM procedures using mean field-like approximations for Markov model-based image segmentation

Image segmentation using Markov random fields involves parameter estimation in hidden Markov models for which the EM algorithm is widely used. In practice, difficulties arise due to the dependence structure in the models and approximations are required. Using ideas from the mean field approximation principle, we propose a class of EM-like algorithms in which the computation reduces to dealing with systems of independent variables. Within this class, the simulated field algorithm is a new stochastic algorithm which appears to be the most promising for its good performance and speed, on synthetic and real image experiments.     

Input-output HMMs for sequence processing

We consider problems of sequence processing and propose a solution based on a discrete-state model in order to represent past context. We introduce a recurrent connectionist architecture having a modular structure that associates a subnetwork to each state. The model has a statistical interpretation we call input-output hidden Markov model (IOHMM). It can be trained by the estimation-maximization (EM) or generalized EM (GEM) algorithms, considering state trajectories as missing data, which decouples temporal credit assignment and actual parameter estimation. The model presents similarities to hidden Markov models (HMMs), but allows us to map input sequences to output sequences, using the same processing style as recurrent neural networks. IOHMMs are trained using a more discriminant learning paradigm than HMMs, while potentially taking advantage of the EM algorithm. We demonstrate that IOHMMs are well suited for solving grammatical inference problems on a benchmark problem. Experimental results are presented for the seven Tomita grammars, showing that these adaptive models can attain excellent generalization.     

Factorial hidden Markov models and the generalized backfitting algorithm

Previous researchers developed new learning architectures for sequential data by extending conventional hidden Markov models through the use of distributed state representations. Although exact inference and parameter estimation in these architectures is computationally intractable, Ghahramani and Jordan (1997) showed that approximate inference and parameter estimation in one such architecture, factorial hidden Markov models (FHMMs), is feasible in certain circumstances. However, the learning algorithm proposed by these investigators, based on variational techniques, is difficult to understand and implement and is limited to the study of real-valued data sets. This chapter proposes an alternative method for approximate inference and parameter estimation in FHMMs based on the perspective that FHMMs are a generalization of a well-known class of statistical models known as generalized additive models (GAMs; Hastie & Tibshirani, 1990). Using existing statistical techniques for GAMs as a guide, we have developed the generalized backfitting algorithm. This algorithm computes customized error signals for each hidden Markov chain of an FHMM and then trains each chain one at a time using conventional techniques from the hidden Markov models literature. Relative to previous perspectives on FHMMs, we believe that the viewpoint taken here has a number of advantages. First, it places FHMMs on firm statistical foundations by relating them to a class of models that are well studied in the statistics community, yet it generalizes this class of models in an interesting way. Second, it leads to an understanding of how FHMMs can be applied to many different types of time-series data, including Bernoulli and multinomial data, not just data that are real valued. Finally, it leads to an effective learning procedure for FHMMs that is easier to understand and easier to implement than existing learning procedures. Simulation results suggest that FHMMs trained with the generalized backfitting algorithm are a practical and powerful tool for analyzing sequential data.