Recursive algorithms for the Bayes solution of the fixed-point and fixed-lag smoothing problems

Recursive algorithms for the Bayes solutions of the fixed-point and fixed-lag smoothing problems are obtained. Recursive algorithms for the respective smoothed a posteriori densities are derived under assumptions that the signal to be estimated is a Markov process and the observation is a signal embedded in independent noise (not necessarily additive) which is also independent of the signal. The recursive algorithm for the fixed-point smoothing is applied to a binary Markov signal corrupted by an independent noise in a nonlinear manner.     

Scene segmentation from visual motion using global optimization

This paper presents results from computer experiments with an algorithm to perform scene disposition and motion segmentation from visual motion or optic flow. The maximum a posteriori (MAP) criterion is used to formulate what the best segmentation or interpretation of the scene should be, where the scene is assumed to be made up of some fixed number of moving planar surface patches. The Bayesian approach requires, first, specification of prior expectations for the optic flow field, which here is modeled as spatial and temporal Markov random fields; and, secondly, a way of measuring how well the segmentation predicts the measured flow field. The Markov random fields incorporate the physical constraints that objects and their images are probably spatially continuous, and that their images are likely to move quite smoothly across the image plane. To compute the flow predicted by the segmentation, a recent method for reconstructing the motion and orientation of planar surface facets is used. The search for the globally optimal segmentation is performed using simulated annealing.     

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.     

VBI-MRF model for image segmentation

In statistical image segmentation, the distribution of pixel values is usually assumed to be Gaussian and the optimal result is believed to be the one that has maximum a posteriori (MAP) probability. In spite of its prevalence and computational efficiency, the Gaussian assumption, however, is not always strictly followed, and hence may lead to less accurate results. Although the variational Bayes inference (VBI), in which statistical model parameters are also assumed to be random variables, has been widely used, it can hardly handle the spatial information embedded in pixels. In this paper, we incorporate spatial smoothness constraints on pixels labels interpreted by the Markov random field (MRF) model into the VBI process, and thus propose a novel statistical model called VBI-MRF for image segmentation. We evaluated our algorithm against the variational expectation-maximization (VEM) algorithm and the hidden Markov random field (HMRF) model and MAP-MRF model based algorithms on both noise-corrupted synthetic images and mosaics of natural texture. Our pilot results suggest that the proposed algorithm can segment images more accurately than other three methods and is capable of producing robust image segmentation.     

Multiple resolution segmentation of textured images

A multiple resolution algorithm is presented for segmenting images into regions with differing statistical behavior. In addition, an algorithm is developed for determining the number of statistically distinct regions in an image and estimating the parameters of those regions. Both algorithms use a causal Gaussian autoregressive model to describe the mean, variance, and spatial correlation of the image textures. Together, the algorithms can be used to perform unsupervised texture segmentation. The multiple resolution segmentation algorithm first segments images at coarse resolution and then progresses to finer resolutions until individual pixels are classified. This method results in accurate segmentations and requires significantly less computation than some previously known methods. The field containing the classification of each pixel in the image is modeled as a Markov random field. Segmentation at each resolution is then performed by maximizing the a posteriori probability of this field subject to the resolution constraint. At each resolution, the a posteriori probability is maximized by a deterministic greedy algorithm which iteratively chooses the classification of individual pixels or pixel blocks. The unsupervised parameter estimation algorithm determines both the number of textures and their parameters by minimizing a global criterion based on the AIC information criterion. Clusters corresponding to the individual textures are formed by alternately estimating the cluster parameters and repartitioning the data into those clusters. Concurrently, the number of distinct textures is estimated by combining clusters until a minimum of the criterion is reached     

Image smoothing with generalized random walks: Algorithm and applications

A novel generalized random walks model based algorithm for image smoothing is presented. Unlike previous image smoothing methods, the proposed method performs image smoothing in a global weighted way based on graph notation, which can preserve important features and edges as much as possible. Based on the new random walks model, input image information and user defined smoothing scale information are projected to a graph, our method calculates the probability that a random walker starting at each pixel node position will first reach one of the pre-defined terminal node to achieve image smoothing, which goes to solving a system of linear equations, the system can be solved efficiently by lots of methods. Theoretical analysis and experimental results are reported to illustrate the usefulness and potential applicability of our algorithm on various computer vision fields, including image enhancement, edge detection, image decomposition, high dynamic range (HDR) image tone mapping and other applications.     

Simultaneous estimation of super-resolved scene and depth map from low resolution defocused observations

This paper presents a novel technique to simultaneously estimate the depth map and the focused image of a scene, both at a super-resolution, from its defocused observations. Super-resolution refers to the generation of high spatial resolution images from a sequence of low resolution images. Hitherto, the super-resolution technique has been restricted mostly to the intensity domain. In this paper, we extend the scope of super-resolution imaging to acquire depth estimates at high spatial resolution simultaneously. Given a sequence of low resolution, blurred, and noisy observations of a static scene, the problem is to generate a dense depth map at a resolution higher than one that can be generated from the observations as well as to estimate the true high resolution focused image. Both the depth and the image are modeled as separate Markov random fields (MRF) and a maximum a posteriori estimation method is used to recover the high resolution fields. Since there is no relative motion between the scene and the camera, as is the case with most of the super-resolution and structure recovery techniques, we do away with the correspondence problem.     

基于MRF的复杂图像抠图

所谓复杂图像抠图就是从复杂图像中抠取出目标物体的一种图像处理算法。为了取得更好的抠图效果,提出了一种基于马尔可夫随机场的自然图像抠图方法。该方法首先手工把图像分成3个区域:前景区域、背景区域和未知区域;然后,再将未知区域用手工粗略地划分成几个相交的小区域;接着在每一个小区域内,以其中的未知区域的像素点为节点,定义抠图标号,同时在这些节点上面建立MRF抠图模型,并把这些标号赋给这些节点,这样抠图问题被定义为在这个MRF模型和它的Gibbs分布上MAP估计问题;继而再计算出每个小区域的掩像;最后把这些掩像合并,即得到输入图像最终的掩像。和其他算法相比,对复杂图像的抠图问题,该方法可以取得更好的抠图效果。     

贝叶斯框架下的非参数估计Graph Cuts分割算法

假设图像中各像素灰度值是具有一定概率分布的随机变量,由贝叶斯定理,正确分割观测图像等价于求出具有最大后验概率的实际图像估计。在此框架下,提出了一种改进型Graph Cuts图像分割算法。与传统Graph Cuts分割算法相比,该算法在模型建立上有两个方面的改进：1)将模糊C均值聚类引入数据约束能量函数来得到各像素在某个标记下的概率,改善了收敛性能;2)使用非参数方法估计图像的统计分布,然后用此统计量构成图像分割的先验概率,并保证分割结果的局部平滑。由于非参数估计是由样本直接估计得到的结果,特别适用于小样本和分布函数不恒定的情况,因此拓展了算法的适用范围。实验结果表明,改进算法在遥感图像分割和医学图像分割中均提高了分割精度,证明了该算法的有效性。     

一种鲁棒的MRF-MAP图象分割框架研究

提出了一种新颖的基于马尔可夫随机场(MRF)空间上下文信息的图象分割方法。该方法利用马尔可夫随机场表示图象标记场,并在传统的邻域势函数基础上,引入观测场中邻域像素间强度关系,由此描述像素被分入同一类的可能性。通过贝叶斯(Bayes)定理将分割问题转化为最大后验(MAP)估计的问题。运用迭代条件模型(ICM)求取最大后验估计的解。用人工合成图象及真实图象进行实验,同时与传统的期望最大化(EM)方法以及传统的马尔可夫随机场方法相比较,由实验结果及信噪比(SNR)-误分率(MCR)曲线可以看出,该文的方法对噪声图象分割更为有效。     

模糊马尔可夫随机场理论在阴影检测中的应用

阴影的检测是目标检测、目标跟踪、视频监控等领域的一个关键问题。提出了一种基于模糊马尔可夫随机场的阴影检测算法。该算法把阴影检测问题看做是一个求最优化的像素点分类问题。对于输入的视频,提取背景图像,找出阴影和前景目标物体区域。通过计算阴影概率分布,前景概率分布,隶属度函数,建立模糊马尔可夫随机场。应用贝叶斯准则,最大后验(MAP)估计和条件迭代模式(ICM)算法,寻找最优化的模糊马尔可夫随机场,并利用最大隶属度原则消除模糊性,得到阴影检测的结果。实验证明,文中算法具有较好的阴影检测率和目标检测率。     

Recursive algorithms for Bayes smoothing with uncertain observations

Recursive algorithms for the Bayes solution of fixed-interval, fixed-point, and fixed-lag smoothing under uncertain observations are presented. The Bayes smoothing algorithms are obtained for a Markovian system model with Markov uncertainty, a model more general than the one used in linear smoothing algorithms. The Bayes fixed-interval smoothing algorithm is applied to a Gauss-Markov example. The simulation results for this example indicate that the MSE performance of the Bayes smoother is significantly better than that of the linear smoother.     

上下文场景识别模型的稀疏贝叶斯判别学习方法

在机器人场景识别问题中,将连续场景的相关性通过基于隐马尔可夫模型的上下文模型进行描述.采用不同于传统的使用生成模型方法学习上下文场景识别模型的方式,首先引入稀疏贝叶斯学习机对上下文模型中图像特征的后验概率进行建模,然后通过贝叶斯原理将稀疏贝叶斯模型与隐马尔可夫模型结合,提出一种能够实现上下文场景识别模型的判别学习方法.在真实场景数据库上的实验结果表明,由该方法得到的上下文场景识别系统具有很好的场景识别能力和泛化特性.     

An MRF-Based Approach to Generation of Super-Resolution Images from Blurred Observations

This paper presents a new technique for generating a high resolution image from a blurred image sequence; this is also referred to as super-resolution restoration of images. The image sequence consists of decimated, blurred and noisy versions of the high resolution image. The high resolution image is modeled as a Markov random field (MRF) and a maximum a posteriori (MAP) estimation technique is used for super-resolution restoration. Unlike other super-resolution imaging methods, the proposed technique does not require sub-pixel registration of given observations. A simple gradient descent method is used to optimize the functional. The discontinuities in the intensity process can be preserved by introducing suitable line processes. Superiority of this technique to standard methods of image expansion like pixel replication and spline interpolation is illustrated.     

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。     

二维属性直方图的Fisher 准则图像分割及快速递推算法

利用图像中目标和背景之间类间方差和类内方差在类别分离性中的作用,提出了基于二维属性直方图 的Fisher 准则分割方法．首先,在考虑图像中心像素与邻域中非直接相邻像素的基础上,通过图像直方图的统计分 布特性构造属性集,建立新的二维属性直方图．然后根据最大化Fisher 准则,获取最优二维阈值向量．同时为降低 二维阈值算法的复杂性,提出了快速递推算法．该快速递推算法中,将二维Fisher 准则的计算写成递推的形式,减 少了大量的重复计算．实验结果表明,所提出的方法不仅能得到理想的分割结果,而且计算量大大减少,达到了快 速分割的目的．     

Bayesian estimation of motion vector fields

A stochastic approach to the estimation of 2D motion vector fields from time-varying images is presented. The formulation involves the specification of a deterministic structural model along with stochastic observation and motion field models. Two motion models are proposed: a globally smooth model based on vector Markov random fields and a piecewise smooth model derived from coupled vector-binary Markov random fields. Two estimation criteria are studied. In the maximum a posteriori probability (MAP) estimation, the a posteriori probability of motion given data is maximized, whereas in the minimum expected cost (MEC) estimation, the expectation of a certain cost function is minimized. Both algorithms generate sample fields by means of stochastic relaxation implemented via the Gibbs sampler. Two versions are developed: one for a discrete state space and the other for a continuous state space. The MAP estimation is incorporated into a hierarchical environment to deal efficiently with large displacements     

A colorization algorithm based on local MAP estimation

This paper presents a colorization algorithm which adds color to monochrome images. In this paper, the colorization problem is formulated as the maximum a posteriori (MAP) estimation of a color image given a monochrome image. Markov random field (MRF) is used for modeling a color image which is utilized as a prior for the MAP estimation. The MAP estimation problem for a whole image is decomposed into local MAP estimation problems for each pixel. Using 0.6% of whole pixels as references, the proposed method produced pretty high quality color images with 25.7-32.6 dB PSNR values for eight images.     

Nonparametric interpolation of the Markov sequence

Consideration was given to the problem of interpolation (smoothing) of the nonobservable component of the composite Markov process within the framework of the conditional Markov scheme. In the case of the dynamic observation models such as autoregression, equations were derived for the a posteriori interpolation density of the probability of the state of the nonobservable component. The aim of the present paper was to construct a smoothing algorithm for an unknown family of the distributions of the nonobservable component of the partially observable random Markov sequence. The result was obtained for the strictly stationary random Markov processes with mixing and for the conditional densities in the observation model from the exponential family of distributions. Computer-aided modeling within the framework of the Kalman scheme demonstrated that the sampled root-mean-square error of the nonparametric smoothing algorithm constructed for an unknown state equation was situated between the errors of the optimal linear filtration and the optimal linear interpolation.     

A probabilistic approach to the coupled reconstruction andrestoration of underwater acoustic images

Describes a probabilistic technique for the coupled reconstruction and restoration of underwater acoustic images. The technique is founded on the physics of the image-formation process. Beamforming, a method widely applied in acoustic imaging, is used to build a range image from backscattered echoes, associated point by point with another type of information representing the reliability (or confidence) of such an image. Unfortunately, this kind of images is plagued by problems due to the nature of the signal and to the related sensing system. In the proposed algorithm, the range and confidence images are modeled as Markov random fields whose associated probability distributions are specified by a single energy function. This function has been designed to fully embed the physics of the acoustic image-formation process by modeling a priori knowledge of the acoustic system, the considered scene, and the noise-affecting measures and also by integrating reliability information to allow the coupled and simultaneous reconstruction and restoration of both images. Optimal (in the maximum a posteriori probability sense) estimates of the reconstructed range image map and the restored confidence image are obtained by minimizing the energy function using simulated annealing. Experimental results show the improvement of the processed images over those obtained by other methods performing separate reconstruction and restoration processes that disregard reliability information