Speeding up the EM algorithm for mixture model-based segmentation of magnetic resonance images

Mixture models implemented via the expectation-maximization (EM) algorithm are being increasingly used in a wide range of problems in pattern recognition such as image segmentation. However, the EM algorithm requires considerable computational time in its application to huge data sets such as a three-dimensional magnetic resonance (MR) image of over 10 million voxels. Recently, it was shown that a sparse, incremental version of the EM algorithm could improve its rate of convergence. In this paper, we show how this modified EM algorithm can be speeded up further by adopting a multiresolution kd-tree structure in performing the E-step. The proposed algorithm outperforms some other variants of the EM algorithm for segmenting MR images of the human brain.     

Unsupervised image segmentation using triplet Markov fields

Hidden Markov fields (HMF) models are widely applied to various problems arising in image processing. In these models, the hidden process of interest X is a Markov field and must be estimated from its observable noisy version Y. The success of HMF is mainly due to the fact that the conditional probability distribution of the hidden process with respect to the observed one remains Markovian, which facilitates different processing strategies such as Bayesian restoration. HMF have been recently generalized to “pairwise” Markov fields (PMF), which offer similar processing advantages and superior modeling capabilities. In PMF one directly assumes the Markovianity of the pair (X, Y). Afterwards, “triplet” Markov fields (TMF), in which the distribution of the pair (X, Y) is the marginal distribution of a Markov field (X, U, Y), where U is an auxiliary process, have been proposed and still allow restoration processing. The aim of this paper is to propose a new parameter estimation method adapted to TMF, and to study the corresponding unsupervised image segmentation methods. The latter are validated via experiments and real image processing.     

Adaptive pixon represented segmentation (APRS) for 3D MR brain images based on mean shift and Markov random fields

In this paper, we proposed an adaptive pixon represented segmentation (APRS) algorithm for 3D magnetic resonance (MR) brain images. Different from traditional method, an adaptive mean shift algorithm was adopted to adaptively smooth the query image and create a pixon-based image representation. Then K-means algorithm was employed to provide an initial segmentation by classifying the pixons in image into a predefined number of tissue classes. By using this segmentation as initialization, expectation-maximization (EM) iterations composed of bias correction, a priori digital brain atlas information, and Markov random field (MRF) segmentation were processed. Pixons were assigned with final labels when the algorithm converges. The adoption of bias correction and brain atlas made the current method more suitable for brain image segmentation than the previous pixon based segmentation algorithm. The proposed method was validated on both simulated normal brain images from BrainWeb and real brain images from the IBSR public dataset. Compared with some other popular MRI segmentation methods, the proposed method exhibited a higher degree of accuracy in segmenting both simulated and real 3D MRI brain data. The experimental results were numerically assessed using Dice and Tanimoto coefficients.     

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.     

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.     

Global optimization of wavelet-domain hidden Markov tree for image segmentation

This work presents a global energy minimization method for multiscale image segmentation using convex optimization theory. The construction of energy function is motivated by the intuition that the larger the entropy, the less a priori information one has on the value of the random variables. First, we represent the wavelet-domain hidden Markov tree (WHMT) model of the original image as a structured energy function, which is proved convex in marginal distributions. Next, we derive the maximum lower bound of the energy function through Lagrange dual transform for the purpose of incorporating marginal constraints into optimization. Finally, a modified belief propagation optimization algorithm is used to perform global energy minimization of the dual convex energy function. Experiments on real image segmentation problems demonstrate the superior performance of this new algorithm when compared with nonconvex ones.     

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.     

MRF model and FRAME model-based unsupervised image segmentation

This paper presents a method for unsupervised segmentation of images consisting of multiple textures. The images under study are modeled by a proposed hierarchical random field model, which has two layers. The first layer is modeled as a Markov Random Field (MRF) representing an unobservable region image and the second layer uses "Filters, Random and Maximum Entropy (Abb. FRAME)" model to represent multiple textures which cover each region. Compared with the traditional Hierarchical Markov Random Field (HMRF), the FRAME can use a bigger neighborhood system and model more complex patterns. The segmentation problem is formulated as Maximum a Posteriori (MAP) estimation according to the Bayesian rule. The iterated conditional modes (ICM) algorithm is carried out to find the solution of the MAP estimation. An algorithm based on the local entropy rate is proposed to simplify the estimation of the parameters of MRF. The parameters of FRAME are estimated by the ExpectationMaximum (EM) algorithm. Finally, an exp     

Texture-based segmentation using markov random field models and approximate Bayesian estimators based on trees

We describe segmentation based on textures using the label and image model of D. Gemanet al., Boundary Detection by Constrained Optimization,IEEE Trans. Pattern Analysis and Machine Intelligence, 12(7):609–628, July 1990. We replace their maximuma posteriori estimation criterion with a Bayesian estimator that minimizes the sum of the pixel misclassification probabilities. The new estimation goal allows the use of a different computational algorithm, which is deterministic rather than random, based on approximating lattices by trees. An example demonstrating an accurate segmentation of a collage of Brodatz textures is included.This work was supported by the Purdue Research Foundation, a Whirlpool Faculty Fellowship, U. S. National Science Foundation grant MIP-9110919, and the School of Electrical Engineering, Purdue University.     

基于模糊马尔可夫场的脑部MR图像分割算法

在传统马尔可夫场模型的基础上,建立了模糊马尔可夫场模型。通过对模型的分析得出图像像素对不同类的隶属度计算公式,提出了一种高效、无监督的图像分割算法,从而实现了对脑部MR图像的精确分割。通过对模拟脑部MR图像和临床脑部MR图像分割实验,表明新算法比传统的基于马尔可夫场的图像分割算法和模糊C-均值等图像分割算法有更精确的图像分割能力。     

基于马尔可夫随机场的快速图象分割

根据卫星遥感图象的特点,讨论了基于马可夫随机场的图象分割方法,建立了相应的基于马可夫随机场的图象分割模型,以实现复杂遥感图象的快速分割,并由此将图象分割问题转化成图象标记问题,进而转化成求解图象的最大后验概率估计的问题。虽然传统的模拟退火算法（SA）能达到后验概率的全局最大,但是时间复杂度太高,实际分割中经常采用次优算法,文中还引进了一种基于博弈理论的决定性退火算法（GSA）和一种基于竞争理论的算法（CA）,取得了快速分割图象的效果。试验证明,该两种算法完全可应用于复杂遥感图象的快速分割。     

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。     

形态小波域多尺度马尔可夫模型在纹理图像分割中的应用

针对图像分割中小波域多尺度马尔可夫模型(MRMRF-W)无法有效描述图像非线性特征,提出了一种在形态小波域下的多尺度MRF模型（MRMRF-MW）,实现纹理图像分割。该模型结合了形态小波和MRF各自的优势,能够对图像进行非线性多尺度分解,并在各尺度上进行空间关系建模。通过对两个纹理图像库（Brodatz纹理库、Prague纹理库）中图像的分割实验,验证了该模型的有效性。     

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。     

Unsupervised image segmentation using a simple MRF model with a new implementation scheme

A simple Markov random field model with a new implementation scheme is proposed for unsupervised image segmentation based on image features. The traditional two-component MRF model for segmentation requires training data to estimate necessary model parameters and is thus unsuitable for unsupervised segmentation. The new implementation scheme solves this problem by introducing a function-based weighting parameter between the two components. Using this method, the simple MRF model is able to automatically estimate model parameters and produce accurate unsupervised segmentation results. Experiments demonstrate that the proposed algorithm is able to segment various types of images (gray scale, color, texture) and achieves an improvement over the traditional method.     

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.     

基于PSO的Markov随机场在医学图像分割中的应用

研究了应用粒子群优化算法（PSO）优化Markov随机场方法对磁共振图像进行分割的算法。建立了基于马尔可夫随机场的图像分割模型,针对马尔可夫随机场图像模型的局部相关特性和最大后验概率估计,将粒子群优化算法应用于该模型,快速获得图像分割目标的全局最优解。实验数据表明该方法的高效性。     

Phonetic segmentation using multiple speech features

In this paper we propose a method for improving the performance of the segmentation of speech waveforms to phonetic units. The proposed method is based on the well known Viterbi time-alignment algorithm and utilizes the phonetic boundary predictions from multiple speech parameterization techniques. Specifically, we utilize the most appropriate, with respect to boundary type, phone transition position prediction as initial point to start Viterbi time-alignment for the prediction of the successor phonetic boundary. The proposed method was evaluated on the TIMIT database, with the exploitation of several, well known in the area of speech processing, Fourier-based and wavelet-based speech parameterization algorithms. The experimental results for the tolerance of 20 milliseconds indicated an improvement of the absolute segmentation accuracy of approximately 0.70%, when compared to the baseline speech segmentation scheme.