Efficient Bayesian spatial prediction with mobile sensor networks using Gaussian Markov random fields

In this paper, we consider the problem of predicting a large scale spatial field using successive noisy measurements obtained by mobile sensing agents. The physical spatial field of interest is discretized and modeled by a Gaussian Markov random field (GMRF) with uncertain hyperparameters. From a Bayesian perspective, we design a sequential prediction algorithm to exactly compute the predictive inference of the random field. The main advantages of the proposed algorithm are: (1) the computational efficiency due to the sparse structure of the precision matrix, and (2) the scalability as the number of measurements increases. Thus, the prediction algorithm correctly takes into account the uncertainty in hyperparameters in a Bayesian way and is also scalable to be usable for mobile sensor networks with limited resources. We also present a distributed version of the prediction algorithm for a special case. An adaptive sampling strategy is presented for mobile sensing agents to find the most informative locations in taking future measurements in order to minimize the prediction error and the uncertainty in hyperparameters simultaneously. The effectiveness of the proposed algorithms is illustrated by numerical experiments.     

Bayesian multiscale analysis of images modeled as Gaussian Markov random fields

A Bayesian multiscale technique for the detection of statistically significant features in noisy images is proposed. The prior is defined as a stationary intrinsic Gaussian Markov random field on a toroidal graph, which enables efficient computation of the relevant posterior marginals. Hence the method is applicable to large images produced by modern digital cameras. The technique is demonstrated in two examples from medical imaging.     

Fast kriging of large data sets with Gaussian Markov random fields

Spatial data sets are analysed in many scientific disciplines. Kriging, i.e. minimum mean squared error linear prediction, is probably the most widely used method of spatial prediction. Computation time and memory requirement can be an obstacle for kriging for data sets with many observations. Calculations are accelerated and memory requirements decreased by using a Gaussian Markov random field on a lattice as an approximation of a Gaussian field. The algorithms are well suited also for nonlattice data when exploiting a bilinear interpolation at nonlattice locations.     

Parallel and interacting Markov chain Monte Carlo algorithm

In many situations it is important to be able to propose N independent realizations of a given distribution law. We propose a strategy for making N parallel Monte Carlo Markov chains (MCMC) interact in order to get an approximation of an independent N-sample of a given target law. In this method each individual chain proposes candidates for all other chains. We prove that the set of interacting chains is itself a MCMC method for the product of N target measures. Compared to independent parallel chains this method is more time consuming, but we show through examples that it possesses many advantages. This approach is applied to a biomass evolution model.     

Parallel use of multiplicative congruential random number generators

On parallel processors or in distributed computing environments, generating and sharing one stream of random numbers for all parallel processing elements is usually impractical. A more attractive method is to allow each processing element to generate random numbers independently. This paper investigates parallel use of multiplicative congruential generators. We analyze the leapfrog, the regular spacing, and the random spacing methods. Our results show: (1) The leapfrog method can result in multipliers of low spectral values. (2) In the random spacing method, the minimal distance between n substreams is only 1/n² of cycle length in average. (3) The regular spacing method can result in strong correlation between substreams if the starting points αjx₀ () are poorly selected. We then suggest selecting multiplier a and factor α based on their k-dimensional spectral values and the minimal distance between substreams of these generators.     

Markov random fields for catadioptric image processing

Images obtained with catadioptric sensors contain significant deformations which prevent the direct use of classical image treatments. Thus, Markov random fields (MRF) whose usefulness is now obvious for projective image processing, cannot be used directly on catadioptric images because of the inadequacy of the neighborhood. In this paper, we propose to define a new neighborhood for MRF by using the equivalence theorem developed for central catadioptric sensors. We show the importance of this adaptation for segmentation, image restoration and motion detection.     

Pattern analysis of dermoscopic images based on Markov random fields

In this paper a method for detecting different patterns in dermoscopic images is presented. In order to diagnose a possible skin cancer, physicians assess the lesion based on different rules. While the most famous one is the ABCD rule (asymmetry, border, colour, diameter), the new tendency in dermatology is to classify the lesion performing a pattern analysis. Due to the colour textured appearance of these patterns, this paper presents a novel method based on Markov random field (MRF) extended for colour images that classifies images representing different dermatologic patterns. First, each image plane in L^*a^*b^* colour space is modelled as a MRF following a finite symmetric conditional model (FSCM). Coupling of colour components is taken into account by supposing that features of the MRF in the three colour planes follow a multivariate Normal distribution. Performance is analysed in different colour spaces. The best classification rate is 86% on average.     

Mean fields and two-dimensional Markov random fields in image analysis

In this paper we compare two iterative approaches to the problem of pixel-level image restoration when the model contains unknown parameters. Pairwise interaction models are assumed to represent the local associations in the true scene. The first approach is a variation on the EM algorithm in which Mean-field approximations are used in the E-step and a variational approximation is used in the M-step. In the second approach, each iteration involves first restoring the image using the Iterated Conditional Modes (ICM) algorithm and then updating the parameter estimates by maximising the so-called pseudolikelihood. In addition, refinemenrs are made to the Mean-field approximation, and these are also used for restoration. The methods are compared empirically using both artificial and real noise-corrupted binary scenes. Within the comparisons the effects of using different convergence criteria for deciding when to stop the algorithms are also investigated.     

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.     

并行马尔可夫随机场计算变分光流方法

目的 基于马尔可夫随机场（MRF）的变分光流计算是一种较为鲁棒的光流计算方法,但是计算效率很低。置信传播算法（BP） 是一种针对MRF较为高效的全局优化算法。本文提出一种MRF变分光流计算模型并采用并行BP方法实现,极大提高计算效率。方法 提出的MRF变分光流计算模型中的数据项采用了Horn等人根据灰度守恒假设得到的光流基本约束方程,并采用非平方惩罚函数进行调整以平滑边界影响。为在CUDA平台上实现高效并行处理,本文提出了一种优化的基于置信传播的MRF并行光流计算方法。该优化方法在采用置信传播最小化MRF光流能量函数时,采用了一种4层的3维网络结构进行并行计算,每层对应MRF4邻域模型中的一个方向的信息传播,同时在每层中为每个像素分配多个线程采用并行降维法计算所要传递的信息,大大降低单线程计算负荷,大幅度提高计算效率。结果 采用旋转小球图像序列进行实验,计算效率提高314倍;采用旋转小球、Yosemite山谷和RubberWhale 3种不同图像序列,与Horn算法、Weickert算法、Hossen并行Lucas算法、Grauer-Gray并行MRF算法进行对比实验,本文方法得到最低的平均端点误差（AEE）,分别为0.13、0.55和0.34。结论 本文提出了一种新的MRF光流计算模型,并在CUDA平台上实现了并行优化计算。实验结果表明,本文提出的并行计算方法在保持计算精度的同时极大提高了计算效率。本文方法对内存需求巨大,在处理高分辨率图像时,限制了采样点数,难以计算大位移。     

学习高阶马尔可夫随机场：评分匹配方法

传统的马尔可夫随机场模型有两个内在的缺陷：邻域的低阶性和参数的手动选择。提出一种新的机器学习方法——评分匹配法,从训练图像数据中学习得到一组高阶马尔可夫随机场模型参数。为了验证通过学习得到的马尔可夫随机场模型的能力,将学习得到的参数向量通过贝叶斯规则应用于图像去噪。实验结果表明：不管是根据峰值信噪比的大小还是根据主观视觉,都能取得优秀的去噪效果,从而表明该学习方法的有效性。     

基于马尔可夫随机场的纹理图像并行分割

基于消息传递接口（Message Passing Interface,MPI）和消息传递并行编程模型,提出了一种针对计算机集群（Cluster）的纹理图像并行分割算法。该算法使用马尔可夫随机场作为纹理特征,通过将图像分块,把特征提取的计算量均匀的分布到并行系统中的各个节点上,从而极大地减少了计算时间。在遥感图像上的实验发现,该算法在4机并行的环境下可以取得与单机串行程序一样精确的分割,而耗时仅为串行程序的31.95％。令人满意的实验结果表明该并行算法不但可以有效的应用于纹理图像分割,而且也为使用计算机集群实现高时间复杂度的图像处理提供了有益的启示。     

Multiscale Bayesian texture segmentation using neural networks and Markov random fields

This paper presents a wavelet-based texture segmentation method using multilayer perceptron (MLP) networks and Markov random fields (MRF) in a multi-scale Bayesian framework. Inputs and outputs of MLP networks are constructed to estimate a posterior probability. The multi-scale features produced by multi-level wavelet decompositions of textured images are classified at each scale by maximum a posterior (MAP) classification and the posterior probabilities from MLP networks. An MRF model is used in order to model the prior distribution of each texture class, and a factor, which fuses the classification information through scales and acts as a guide for the labeling decision, is incorporated into the MAP classification of each scale. By fusing the multi-scale MAP classifications sequentially from coarse to fine scales, our proposed method gets the final and improved segmentation result at the finest scale. In this fusion process, the MRF model serves as the smoothness constraint and the Gibbs sampler acts as the MAP classifier. Our texture segmentation method was applied to segmentation of gray-level textured images. The proposed segmentation method shows better performance than texture segmentation using the hidden Markov trees (HMT) model and the HMTseg algorithm, which is a multi-scale Bayesian image segmentation algorithm.     

网页去重的改进算法

针对网页内容相似重复的特点,提出了一种改进算法对网页进行去重处理。该方法能够有效地对网页进行去重,并能对网页信息进行冗余识别处理。实验结果表明,与原有网页去重算法相比,该算法的执行效果提高了14.3%,对网页去重有了很明显的改善。     

Face detection and recognition of natural human emotion using Markov random fields

This paper presents an integrated system for emotion detection. In this research effort, we have taken into account the fact that emotions are most widely represented with eye and mouth expressions. The proposed system uses color images and it is consisted of three modules. The first module implements skin detection, using Markov random fields models for image segmentation and skin detection. A set of several colored images with human faces have been considered as the training set. A second module is responsible for eye and mouth detection and extraction. The specific module uses the HLV color space of the specified eye and mouth region. The third module detects the emotions pictured in the eyes and mouth, using edge detection and measuring the gradient of eyes’ and mouth’s region figure. The paper provides results from the system application, along with proposals for further research.     

Using local transition probability models in Markov random fields for forest change detection

Change detection based on the comparison of independently classified images (i.e. post-classification comparison) is well-known to be negatively affected by classification errors of individual maps. Incorporating spatial-temporal contextual information in the classification helps to reduce the classification errors, thus improving change detection results. In this paper, spatial-temporal Markov Random Fields (MRF) models were used to integrate spatial-temporal information with spectral information for multi-temporal classification in an attempt to mitigate the impacts of classification errors on change detection. One important component in spatial-temporal MRF models is the specification of transition probabilities. Traditionally, a global transition probability model is used that assumes spatial stationarity of transition probabilities across an image scene, which may be invalid if areas have varying transition probabilities. By relaxing the stationarity assumption, we developed two local transition probability models to make the transition model locally adaptive to spatially varying transition probabilities. The first model called locally adjusted global transition model adapts to the local variation by multiplying a pixel-wise probability of change with the global transition model. The second model called pixel-wise transition model was developed as a fully local model based on the estimation of the pixel-wise joint probabilities. When applied to the forest change detection in Paraguay, the two local models showed significant improvements in the accuracy of identifying the change from forest to non-forest compared with traditional models. This indicates that the local transition probability models can present temporal information more accurately in change detection algorithms based on spatial-temporal classification of multi-temporal images. The comparison between the two local transition models showed that the fully local model better captured the spatial heterogeneity of the transition probabilities and achieved more stable and consistent results over different regions of a large image scene.     

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。     

Some exact tests for manifest properties of latent trait models

Item response theory is one of the modern test theories with applications in educational and psychological testing. Recent developments made it possible to characterize some desired properties in terms of a collection of manifest ones, so that hypothesis tests on these traits can, in principle, be performed. But the existing test methodology is based on asymptotic approximation, which is impractical in most applications since the required sample sizes are often unrealistically huge. To overcome this problem, a class of tests is proposed for making exact statistical inference about four manifest properties: covariances given the sum are non-positive (CSN), manifest monotonicity (MM), conditional association (CA), and vanishing conditional dependence (VCD). One major advantage is that these exact tests do not require large sample sizes. As a result, tests for CSN and MM can be routinely performed in empirical studies. For testing CA and VCD, the exact methods are still impractical in most applications, due to the unusually large number of parameters to be tested. However, exact methods are still derived for them as an exploration toward practicality. Some numerical examples with applications of the exact tests for CSN and MM are provided.     

Image registration using Markov random coefficient and geometric transformation fields

Image registration is central to different applications such as medical analysis, biomedical systems, and image guidance. In this paper we propose a new algorithm for multimodal image registration. A Bayesian formulation is presented in which a likelihood term is defined using an observation model based on coefficient and geometric fields. These coefficients, which represent the local intensity polynomial transformations, as the local geometric transformations, are modeled as prior information by means of Markov random fields. This probabilistic approach allows one to find optimal estimators by minimizing an energy function in terms of both fields, making the registration between the images possible.