EM enhancement of 3D head pose estimated by point at infinity

Head pose estimation is a key task for visual surveillance, HCI and face recognition applications. In this paper, a new approach is proposed for estimating 3D head pose from a monocular image. The approach assumes the full perspective projection camera model. Our approach employs general prior knowledge of face structure and the corresponding geometrical constraints provided by the location of a certain vanishing point to determine the pose of human faces. To achieve this, eye-lines, formed from the far and near eye corners, and mouth-line of the mouth corners are assumed parallel in 3D space. Then the vanishing point of these parallel lines found by the intersection of the eye-line and mouth-line in the image can be used to infer the 3D orientation and location of the human face. In order to deal with the variance of the facial model parameters, e.g. ratio between the eye-line and the mouth-line, an EM framework is applied to update the parameters. We first compute the 3D pose using some initially learnt parameters (such as ratio and length) and then adapt the parameters statistically for individual persons and their facial expressions by minimizing the residual errors between the projection of the model features points and the actual features on the image. In doing so, we assume every facial feature point can be associated to each of features points in 3D model with some a posteriori probability. The expectation step of the EM algorithm provides an iterative framework for computing the a posterori probabilities using Gaussian mixtures defined over the parameters. The robustness analysis of the algorithm on synthetic data and some real images with known ground-truth are included.     

概率二维主分量分析

二维主分量分析是一种直接面向图像矩阵表达方式的特征抽取与降维方法. 提出了一个基于二维主分量分析的概率模型. 首先, 通过对此产生式概率模型参数的最大似然估计得到主分量(矢量); 然后, 考虑到缺失数据问题, 利用期望最大化算法迭代估计模型参数和主分量. 混合概率二维主分量分析模型在人脸聚类问题上的应用表明概率二维主分量分析模型能作为图像矩阵的密度估计工具. 含有缺失值的人脸图像重构实验阐述了此模型及迭代算法的有效性.     

用于图像分割的滤波EM算法

利用邻近像素类别上的相关性,在采用EM算法对模型参数求解的过程中,以滤波方法引入像素的空间位置信息,降低了EM对初始值选择的敏感性.该算法在引入了像素的位置信息的同时,保持了EM算法的简单性,并为混合分量个数的选择提供了一种新的实现途径.对实际图像的分割结果证实了算法的有效性.     

一种快速、贪心的高斯混合模型EM算法研究

针对传统EM算法存在初始模型成分数目需要预先指定以及收敛速度随样本数目的增长而急剧减慢等问题,提出了一种快速、贪心的高斯混合模型EM算法。该算法采用贪心的策略以及对隐含参数设置适当阈值的方法,使算法能够快速收敛,从而在很少的迭代次数内获取高斯混合模型的模型成分数。该算法通过与传统EM算法、无监督EM算法和鲁棒EM算法的聚类结果进行比较,实验结果证明该算法具有很强的鲁棒性,并且能够提高算法的效率以及模型成分数的准确性。     

混合聚类彩色图像分割方法研究

提出了一种基于K-均值算法和EM算法混合聚类的彩色图像分割方法。首先将待分割的RGB彩色图像转化成YUV空间模型,然后将该图像分割成n小块,对每个块的颜色分量用改进的K-均值聚类算法进行聚类分析,最后用EM聚类算法对每个块进行聚类,分割源图像。对K-均值算法和EM算法的初始聚类中心引进了改进算法,加快了算法的收敛速度。并与相似的分割方法进行了比较实验,给出了详细的实验结果与分析。实验表明该方法分割速度快,效果好,具有较高的实用价值。     

一种半监督机器学习的EM算法改进方法

EM(Expectation Maximization)算法是含有隐变量(latent variable)的概率参数模型最大似然估计、极大后验概率估计最有效的算法,但很容易进入局部最优现象,对此提出基于半监督机器学习机制的EM算法.本文方法是在最大似然函数中加入惩罚最小二乘因子,同时引入非负约束作为先验信息,结合半监督机器学习方法,将EM算法改进转化为最小化求解问题,再采用最大似然方法求解EM模型,有效估计了混合矩阵和高斯混合模型参数,实现EM算法的改进.仿真结果表明,该方法能够很好地解决了EM算法容易局部最优化问题.     

基于EM算法的混合模型医学图像分割

医学图像分割中的期望最大化(EM)算法在求解混合模型参数时存在局限性。为此,提出一种模糊约束的混合模型图像分割算法。该算法以像素的独立性假设为前提,在采用EM算法对模型参数进行求解的过程中,通过模糊集合论方法,引入像素空间信息。实验结果表明,该算法没有引入新的模型参数,能够保持独立混合模型的简单性,且具有自动模型选择能力,可以获得较理想的分割结果。     

聚类模型参数自动选择的图库索引

提出一种基于模式聚类和混合模型参数自动选择的图库索引方法。因为传统的EM（Expectation Maximization）算法为混合模型聚类问题中的参数估计提供了一个很好的解决方法,但需要事先指定聚类数,影响了高维数据索引的精度和效率。综合利用改进的CEM2（Component-wise EM of Mixture）混合模型自动选择算法、矢量量化和概率近似的索引机制,在保证准确率同时有效提高了检索效率。     

基于遗传算法的SAR图像多尺度分割

基于最大期望（EM）算法与遗传算法（GA）,提出一种有效的多尺度SAR图像无监督分割方法。该方法首先利用混合多尺度自回归（MMAR）模型描述SAR图像中由于雷达斑点所引起的不同尺度和同一尺度内像素之间的统计相依性; 然后将GA与EM结合给出MMAR模型的参数估计算法。这种算法利用最小描述长度（MDL）准则,能够选择模型的分量数;最后利用Bayes分类器实现图像的分割。该方法集遗传算法和EM算法的优点,对初始值有较少的敏感性,避免局部最优解,提高了分割精度。实验结果表明GA EM方法优于EM算法。     

基于自适应变异混沌粒子群优化和SVM的导弹命中预测模型

针对国内外关于导弹命中预测方面存在的研究深度不足、算法寻优能力不强、模型预测精度不高等缺陷,提出一种基于自适应变异混沌粒子群算法（AMCPSO）和支持向量机（SVM）的导弹命中预测模型。首先,对空战数据进行特征提取,构建模型训练所需样本库;然后,采用改进的AMCPSO算法对SVM中的惩罚因子C和核函数参数g进行寻优,并用优化后的模型对样本进行预测;最后,与经典PSO算法、BP神经网络法、网格法构建的预测模型进行了对比实验。实验结果表明,所提算法的全局寻优能力与局部寻优能力均得到提高,模型预测精度较高,可为导弹命中预测研究提供一定的参考依据。     

Speaker identification using multi-step clustering algorithm with transformation-based GMM

To improve the performance of speaker recognition, the embedded linear transformation is used to integrate both transformation and diagonal-covariance Caussian mixture into a unified framework. In the case, the mixture number of GMM must be fixed in model training. The cluster expectation-maximization (EM) algorithm is a well-known technique in which the mixture number is regarded as an estimated parameter. This paper presents a new model structure that integrates a multi-step cluster algorithm into the estimating process of GMM with the embedded transformation. In the approach, the transformation matrix, the mixture number and model parameters are simultaneously estimated according to a maximum likelihood criterion. The proposed method is demonstrated on a database of three data sessions for text independent speaker identification. The experiments show that this method outperforms the traditional GMM with cluster EM algorithm. This text was submitted by the authors in English.     

Fuzzy clustering to estimate the parameters of block mixture models

Finite mixture models are being increasingly used to provide model-based cluster analysis. To tackle the problem of block clustering which aims to organize the data into homogeneous blocks, recently we have proposed a block mixture model; we have considered this model under the classification maximum likelihood approach and we have developed a new algorithm for simultaneous partitioning based on the classification EM algorithm. From the estimation point of view, classification maximum likelihood approach yields inconsistent estimates of the parameters and in this paper we consider the block clustering problem under the maximum likelihood approach; unfortunately, the application of the classical EM algorithm for the block mixture model is not direct: difficulties arise due to the dependence structure in the model and approximations are required. Considering the block clustering problem under a fuzzy approach, we propose a fuzzy block clustering algorithm to approximate the EM algorithm. To illustrate our approach, we study the case of binary data by using a Bernoulli block mixture.     

空间约束层次加权Gamma混合模型的SAR图像分割

目的 合成孔径雷达（SAR）图像中像素强度统计分布呈现出复杂的特性,而传统混合模型难以建模非对称、重尾或多峰等特性的分布。为了准确建模SAR图像统计分布并得到高精度分割结果,本文提出一种利用空间约束层次加权Gamma混合模型（HWGaMM）的SAR图像分割算法。方法 采用Gamma分布的加权和定义混合组份;考虑到同质区域内像素强度的差异性和异质区域间像素强度的相似性,采用混合组份加权和定义HWGaMM结构。采用马尔可夫随机场（MRF）建模像素空间位置关系,利用中心像素及其邻域像素的后验概率定义混合权重以将像素邻域关系引入HWGaMM,构建空间约束HWGaMM,以降低SAR图像内固有斑点噪声的影响。提出算法结合M-H（Metropolis-Hastings）和期望最大化算法（EM）求解模型参数,以实现快速SAR图像分割。该求解方法避免了M-H算法效率低的缺陷,同时克服了EM算法难以求解Gamma分布中形状参数的问题。结果 采用3种传统混合模型分割算法作为对比算法进行分割实验。拟合直方图结果表明本文算法具有准确建模复杂统计分布的能力。在分割精度上,本文算法比基于高斯混合模型（GMM）、Gamma分布和Gamma混合模型（GaMM）分割算法分别提高33%,29%和9%。在分割时间上,本文算法虽然比GMM算法多64 s,但与基于Gamma分布和GaMM算法相比较分别快600 s和420 s。因此,本文算法比传统M-H算法的分割效率有很大的提高。结论 提出一种空间约束HWGaMM的SAR图像分割算法,实验结果表明提出的HWGaMM算法具有准确建模复杂统计分布的能力,且具有较高的精度和效率。     

一种基于EM算法的图像分割改进技术

图像分割是计算机视觉的基础,该文结合EM算法和PCA降维技术,给出了一种有效快速的进行图象分割的方法。该方法利用高斯混合模型对原始图像进行建模,通过EM算法将分割问题转化为参数最大似然估计的问题,同时采用PCA降维技术和随机采样来降低计算量。通过人工合成图象及真实图象的实际测试结果,验证了该算法的有效性和快速性。     

Multivariate mixed normal conditional heteroskedasticity

A new multivariate volatility model where the conditional distribution of a vector time series is given by a mixture of multivariate normal distributions is proposed. Each of these distributions is allowed to have a time-varying covariance matrix. The process can be globally covariance stationary even though some components are not covariance stationary. Some theoretical properties of the model such as the unconditional covariance matrix and autocorrelations of squared returns are derived. The complexity of the model requires a powerful estimation algorithm. A simulation study compares estimation by maximum likelihood with the EM algorithm. Finally, the model is applied to daily US stock returns.     

一种基于EM算法的图像分割改进技术

图像分割是计算机视觉的基础,该文结合EM算法和PCA降维技术,给出了一种有效快速的进行图象分割的方法。该方法利用高斯混合模型对原始图像进行建模,通过EM算法将分割问题转化为参数最大似然估计的问题,同时采用PCA降维技术和随机采样来降低计算量。通过人工合成图象及真实图象的实际测试结果,验证了该算法的有效性和快速性。     

“Probability transforms” of digital pictures

Let g be any local property (e.g., gray level or gradient magnitude) defined on a digital picture. Let p_g(z) be the relative frequency with which g has value z. At each point (x,y) of the picture we can display p_g[g(x,y)], appropriately scaled; the result is called the p_g transform of the picture. Alternatively, we can use joint or conditional frequencies of pairs of local properties to define transforms. This note gives examples of such transforms for various gs and discusses their possible uses and limitations.     

Multimode process monitoring with PCA mixture model

For multimode processes, Gaussian mixture model (GMM) has been applied to estimate the probability density function of the process data under normal-operational condition in last few years. However, learning GMM with the expectation maximization (EM) algorithm from process data can be difficult or even infeasible for high-dimensional and collinear process variables. To address this issue, a novel multimode process monitoring approach based on PCA mixture model is proposed. First, the PCA technique is directly applied to the covariance matrix of each Gaussian component to reduce the dimension of process variables and to obtain nonsingular covariance matrices. Then the Bayesian Ying-Yang incremental EM algorithm is adopted to automatically optimize the number of mixture components. With the obtained PCA mixture model, a novel process monitoring scheme is derived for fault detection of multimode processes. Three case studies are provided to evaluate the monitoring performance of the proposed method.     

Sparse regression mixture modeling with the multi-kernel relevance vector machine

A regression mixture model is proposed where each mixture component is a multi-kernel version of the Relevance Vector Machine (RVM). This mixture model exploits the enhanced modeling capability of RVMs, due to their embedded sparsity enforcing properties. In order to deal with the selection problem of kernel parameters, a weighted multi-kernel scheme is employed, where the weights are estimated during training. The mixture model is trained using the maximum a posteriori approach, where the Expectation Maximization (EM) algorithm is applied offering closed form update equations for the model parameters. Moreover, an incremental learning methodology is also presented that tackles the parameter initialization problem of the EM algorithm along with a BIC-based model selection methodology to estimate the proper number of mixture components. We provide comparative experimental results using various artificial and real benchmark datasets that empirically illustrate the efficiency of the proposed mixture model.     

连续PH分布数据拟合的确定性退火EM算法

针对目前连续PH分布数据拟合EM(Expectation-Maximization)算法存在的初值敏感问题,提出运用确定性退火EM算法进行连续PH分布数据拟合,给出了详细的理论推导,并通过两个拟合实例与标准EM算法进行了对比.对比结果表明所提出的方法可以有效地避免初值选择的不同对EM算法结果的影响,减小陷入局部最优的可能性,能得到比标准EM算法更好的结果.