基于张量空间中的均值漂移聚类的极化SAR图像分割

提出了一种基于均值漂移(Mean Shift, MS)聚类的全极化合成孔径雷达(Polarimetric Synthetic Aperture Radar, PolSAR)图像无监督分割算法. 已有的工作在将MS算法应用于全PolSAR图像分割时, 仅使用每个像素点的极化总功率值作为该像素点的特征值, 没有充分利用极化协方差矩阵或者相干矩阵所包含的完整的极化散射信息. 但是如果直接利用每个像素点的极化协方差矩阵作为特征向量, 则这些特征向量构成的空间不再是一个欧氏空间, 而原始的MS算法是定义在欧氏空间中的. 因此, 本文首先将每一个像素点的厄尔米特正定极化协方差矩阵也称为一个张量, 而且使用黎曼流形来描述该张量空间. 然后, 原始的MS算法被扩展到该张量空间中. 直接扩展得到的算法每一步具有明确的含义, 但是运算复杂度较高. 所以本文又进一步对该算法进行了简化, 从而得到了一个实用的分割算法. 通过使用真实的全PolSAR数据以及仿真数据进行实验, 结果验证了新方法的有效性.     

Fitting smoothing splines to time-indexed,noisy points on nonlinear manifolds

We address the problem of estimating full curves/paths on certain nonlinear manifolds using only a set of time-indexed points, for use in interpolation, smoothing, and prediction of dynamic systems. These curves are analogous to smoothing splines in Euclidean spaces as they are optimal under a similar objective function, which is a weighted sum of a fitting-related (data term) and a regularity-related (smoothing term) cost functions. The search for smoothing splines on manifolds is based on a Palais metric-based steepest-decent algorithm developed in Samir et al. [38]. Using three representative manifolds: the rotation group for pose tracking, the space of symmetric positive-definite matrices for DTI image analysis, and Kendall's shape space for video-based activity recognition, we demonstrate the effectiveness of the proposed algorithm for optimal curve fitting. This paper derives certain geometrical elements, namely the exponential map and its inverse, parallel transport of tangents, and the curvature tensor, on these manifolds, that are needed in the gradient-based search for smoothing splines. These ideas are illustrated using experimental results involving both simulated and real data, and comparing the results to some current algorithms such as piecewise geodesic curves and splines on tangent spaces, including the method by Kume et al. [24].     

基于虚拟样本图像集的多流形鉴别学习算法

为了丰富训练样本的类内变化信息,提出了基于通用训练样本集的虚拟样本生成方法。进一步,为了利用生成的虚拟样本中的类内变化信息有效地完成单样本人脸识别任务,提出了基于虚拟样本图像集的多流行鉴别学习算法。该算法首先将每类仅有的单个训练样本图像和该类的虚拟样本图像划分为互补重叠的局部块并构建流形,然后为每个流形学习一个投影矩阵,使得相同流形内的局部块在投影后的低维特征空间间隔最小化,不同流形中的局部块在投影后的低维特征空间中间隔最大化。实验结果表明,所提算法能够准确地预测测试样本中的类内变化,是一种有效的单样本人脸识别算法。     

Reusable components for partitioning clustering algorithms

Clustering algorithms are well-established and widely used for solving data-mining tasks. Every clustering algorithm is composed of several solutions for specific sub-problems in the clustering process. These solutions are linked together in a clustering algorithm, and they define the process and the structure of the algorithm. Frequently, many of these solutions occur in more than one clustering algorithm. Mostly, new clustering algorithms include frequently occurring solutions to typical sub-problems from clustering, as well as from other machine-learning algorithms. The problem is that these solutions are usually integrated in their algorithms, and that original algorithms are not designed to share solutions to sub-problems outside the original algorithm easily. We propose a way of designing cluster algorithms and to improve existing ones, based on reusable components. Reusable components are well-documented, frequently occurring solutions to specific sub-problems in a specific area. Thus we identify reusable components, first, as solutions to characteristic sub-problems in partitioning cluster algorithms, and, further, identify a generic structure for the design of partitioning cluster algorithms. We analyze some partitioning algorithms (K-means, X-means, MPCK-means, and Kohonen SOM), and identify reusable components in them. We give examples of how new cluster algorithms can be designed based on them.     

Nonparametric discriminant analysis

A nonparametric method of discriminant analysis is proposed. It is based on nonparametric extensions of commonly used scatter matrices. Two advantages result from the use of the proposed nonparametric scatter matrices. First, they are generally of full rank. This provides the ability to specify the number of extracted features desired. This is in contrast to parametric discriminant analysis, which for an L class problem typically can determine at most L 1 features. Second, the nonparametric nature of the scatter matrices allows the procedure to work well even for non-Gaussian data sets. Using the same basic framework, a procedure is proposed to test the structural similarity of two distributions. The procedure works in high-dimensional space. It specifies a linear decomposition of the original data space in which a relative indication of dissimilarity along each new basis vector is provided. The nonparametric scatter matrices are also used to derive a clustering procedure, which is recognized as a k-nearest neighbor version of the nonparametric valley seeking algorithm. The form which results provides a unified view of the parametric nearest mean reclassification algorithm and the nonparametric valley seeking algorithm.     

On mean shift-based clustering for circular data

Cluster analysis is a useful tool for data analysis. Clustering methods are used to partition a data set into clusters such that the data points in the same cluster are the most similar to each other and the data points in the different clusters are the most dissimilar. The mean shift was originally used as a kernel-type weighted mean procedure that had been proposed as a clustering algorithm. However, most mean shift-based clustering (MSBC) algorithms are used for numeric data. The circular data that are the directional data on the plane have been widely used in data analysis. In this paper, we propose a MSBC algorithm for circular data. Three types of mean shift implementation procedures with nonblurring, blurring and general methods are furthermore compared in which the blurring mean shift procedure is the best and recommended. The proposed MSBC for circular data is not necessary to give the number of cluster. It can automatically find a final cluster number with good clustering centers. Several numerical examples and comparisons with some existing clustering methods are used to demonstrate its effectiveness and superiority of the proposed method.     

A new fuzzy K-EVD orthogonal complement space clustering method

This paper studies the problem of underdetermined blind source separation with the nonstrictly sparse condition. Different from current approaches in literature, we propose a new and more effective algorithm to estimate the mixing matrices resulted from noise output data sets. After we introduce a clustering prototype of orthogonal complement space and give an extension of the normal vector clustering prototype, a new method combing the fuzzy clustering and eigenvalue decomposition technique to estimate the mixing matrix is presented in order to deal with the nonstrictly sparse situation. A convergent algorithm for estimating the mixing matrices is established, and numerical simulations are given to demonstrate the effectiveness of the proposed approach.     

基于最小二乘回归的分块加权子空间聚类*

传统子空间聚类算法向量化时忽略样本的自然结构信息,并且容易造成高维度小样本问题,从而导致聚类信息损失.为了弥补该缺陷,文中提出基于最小二乘回归的分块加权子空间聚类(WB-LSR).首先,将样本按维度分成若干块,并求得各个块对应的仿射矩阵.然后,通过相互投票方式对各仿射矩阵设置权重,将加权和作为最终的仿射矩阵.在图像数据和视频数据上的实验表明,文中方法能有效提升聚类准确率.     

Learning the Geometric Structure of Manifolds with Singularities Using the Tensor Voting Graph

We present a general framework that addresses manifolds with singularities and multiple intersecting manifolds, which is also robust against a large number of outliers. We suggest a hybrid local–global method that leverages the algorithmic capabilities of the tensor voting framework and, unlike tensor voting, is capable of reliably inferring the global structure of complex manifolds by using a unique graph construction, called the tensor voting graph (TVG). Moreover, we propose to explicitly and directly resolve the ambiguities near the intersections with a novel algorithm, which uses the TVG and the positions of the points near the manifold intersections. Experimental results in estimating geodesic distances and clustering demonstrate that our framework outperforms the state of the art, especially on geometric complex settings such as when the tangent spaces at the intersections points are not orthogonal and in the presence of a large amount of outliers.     

基于量子行为粒子群优化的软子空间聚类算法*

针对软子空间聚类算法搜寻聚类中心点容易陷入局部最优的缺点,提出在软子空间聚类框架下,结合量子行为粒子群优化(QPSO)和梯度下降法优化软子空间聚类目标函数的模糊聚类算法.根据QPSO全局寻优的特点,求解子空间中全局最优中心点,利用梯度下降法收敛速度快的特点,求解样本点的模糊权重和隶属度矩阵,最终获取样本点的最优聚类结果.在UCI数据集上的实验表明,文中算法可提高聚类精度和聚类结果的稳定性.     

基于黎曼流形的多视角谱聚类算法

现有的多视角谱聚类算法大多只线性结合了各视角的基拉普拉斯矩阵,未考虑不同视角数据的差异性对最优拉普拉斯矩阵的影响,存在聚类性能受限的问题。提出一种基于黎曼几何均值与高阶拉普拉斯矩阵的谱聚类算法(RMMSC),挖掘多视角数据中的高阶连接信息与流形信息,提高最优拉普拉斯矩阵对各视角的信息利用率。按一定的权重线性结合数据单一视角的各阶拉普拉斯矩阵,得到每个视角的基拉普拉斯矩阵,通过低阶与高阶连接信息的结合使用,充分体现多视角数据集的全局结构。在此基础上,计算各视角基拉普拉斯矩阵的黎曼几何均值,将其作为最优拉普拉斯矩阵输入谱聚类算法,得到聚类结果。相比于传统矩阵算数均值的计算,基于黎曼流形的黎曼几何均值能够更好地恢复互补层数据的流形信息。实验结果表明,RMMSC在多组标准数据集上聚类效果优于ONMSC、MLAN、AMGL等算法。其中,在Flower17数据集上,精确度较基准算法ONMSC提高了2.14%,纯度提高了1.7%,且收敛性较好。     

基于均值漂移法进行多光谱遥感聚类研究

传统的聚类方法大都是基于空间划分的方法,一般都假设数据符合混合高斯模型。这在实际应用中往往是不成立的。在大部分模式分类的问题中,常见的参数形式不适合实际遇到的概率密度,特别是所有经典的参数密度都是单峰的,而一般遥感图像都是包含多峰的密度,因此分类结果往往不够精确。用于模式分类的非参数方法正是解决这类问题的一个重要途径,可以从本质上克服这一缺陷,而且可以发现任意形状的聚类。均值漂移方法是基于密度估计的非参数聚类方法,遥感图像的聚类分析可以通过均值漂移方法来实现,而且均值漂移过程不需要预先给出地物的类别数目,在聚类过程中自动确定类别数,这对于图像中类别数目不易确定的情况,给非监督遥感图像聚类带来方便。     

Advances in matrix manifolds for computer vision

The attention paid to matrix manifolds has grown considerably in the computer vision community in recent years. There are a wide range of important applications including face recognition, action recognition, clustering, visual tracking, and motion grouping and segmentation. The increased popularity of matrix manifolds is due partly to the need to characterize image features in non-Euclidean spaces. Matrix manifolds provide rigorous formulations allowing patterns to be naturally expressed and classified in a particular parameter space. This paper gives an overview of common matrix manifolds employed in computer vision and presents a summary of related applications. Researchers in computer vision should find this survey beneficial due to the overview of matrix manifolds, the discussion as well as the collective references.     

Intrinsic Statistics on Riemannian Manifolds: Basic Tools for Geometric Measurements

In medical image analysis and high level computer vision, there is an intensive use of geometric features like orientations, lines, and geometric transformations ranging from simple ones (orientations, lines, rigid body or affine transformations, etc.) to very complex ones like curves, surfaces, or general diffeomorphic transformations. The measurement of such geometric primitives is generally noisy in real applications and we need to use statistics either to reduce the uncertainty (estimation), to compare observations, or to test hypotheses. Unfortunately, even simple geometric primitives often belong to manifolds that are not vector spaces. In previous works [1, 2], we investigated invariance requirements to build some statistical tools on transformation groups and homogeneous manifolds that avoids paradoxes. In this paper, we consider finite dimensional manifolds with a Riemannian metric as the basic structure. Based on this metric, we develop the notions of mean value and covariance matrix of a random element, normal law, Mahalanobis distance and χ² law. We provide a new proof of the characterization of Riemannian centers of mass and an original gradient descent algorithm to efficiently compute them. The notion of Normal law we propose is based on the maximization of the entropy knowing the mean and covariance of the distribution. The resulting family of pdfs spans the whole range from uniform (on compact manifolds) to the point mass distribution. Moreover, we were able to provide tractable approximations (with their limits) for small variances which show that we can effectively implement and work with these definitions.     

Model-Driven Domain Adaptation on Product Manifolds for Unconstrained Face Recognition

Many classification algorithms see a reduction in performance when tested on data with properties different from that used for training. This problem arises very naturally in face recognition where images corresponding to the source domain (gallery, training data) and the target domain (probe, testing data) are acquired under varying degree of factors such as illumination, expression, blur and alignment. In this paper, we account for the domain shift by deriving a latent subspace or domain, which jointly characterizes the multifactor variations using appropriate image formation models for each factor. We formulate the latent domain as a product of Grassmann manifolds based on the underlying geometry of the tensor space, and perform recognition across domain shift using statistics consistent with the tensor geometry. More specifically, given a face image from the source or target domain, we first synthesize multiple images of that subject under different illuminations, blur conditions and 2D perturbations to form a tensor representation of the face. The orthogonal matrices obtained from the decomposition of this tensor, where each matrix corresponds to a factor variation, are used to characterize the subject as a point on a product of Grassmann manifolds. For cases with only one image per subject in the source domain, the identity of target domain faces is estimated using the geodesic distance on product manifolds. When multiple images per subject are available, an extension of kernel discriminant analysis is developed using a novel kernel based on the projection metric on product spaces. Furthermore, a probabilistic approach to the problem of classifying image sets on product manifolds is introduced. We demonstrate the effectiveness of our approach through comprehensive evaluations on constrained and unconstrained face datasets, including still images and videos.     

Mean shift-based clustering

In this paper, a mean shift-based clustering algorithm is proposed. The mean shift is a kernel-type weighted mean procedure. Herein, we first discuss three classes of Gaussian, Cauchy and generalized Epanechnikov kernels with their shadows. The robust properties of the mean shift based on these three kernels are then investigated. According to the mountain function concepts, we propose a graphical method of correlation comparisons as an estimation of defined stabilization parameters. The proposed method can solve these bandwidth selection problems from a different point of view. Some numerical examples and comparisons demonstrate the superiority of the proposed method including those of computational complexity, cluster validity and improvements of mean shift in large continuous, discrete data sets. We finally apply the mean shift-based clustering algorithm to image segmentation.     

基于多代表点近邻传播的大数据图像分割算法

基于多代表点近邻传播聚类算法,提出一种有效的大数据图像的快速分割算法。 该算法首先运用均值漂移算法将彩色图像分割成很多小的同质区域,然后计算每个区域中所有 像素的颜色向量平均值,并用区域数目代替原图像像素点数目,选用区域间的距离作为相似度 的测度指标,最后应用多代表点近邻传播聚类算法在区域相似度矩阵上进行二次聚类,得到最 终的图像分割结果。实验结果证明,提出的算法在大数据图像的分割中取得了较为满意的分割 效果,且分割效率较高。     

基于混沌特征的运动模式分割和动态纹理分类

采用混沌理论对动态纹理中的像素值序列建模,提取动态纹理中的像素值序列的相关特征量,将视频用特征向量矩阵表示. 通过均值漂移（Mean shift）算法对矩阵中的特征向量聚类,实现对视频中的运动模式分割. 然后,采用地球移动距离（Earth mover’s distance,EMD）度量不同视频的差异,对动态纹理视频分类. 本文对多个数据库测试表明:1）分割算法可以分割出视频中不同的运动模式;2）提出的特征向量可以很好地描述动态纹理系统;3）分类算法可以对动态纹理视频分类,且对视频中噪声干扰具有一定的鲁棒性.     

基于Contourlet变换和均值漂移的SAR图像分割

基于斑噪特性和纹理特征,提出了一种完全无监督的SAR图像分割算法。针对SAR图像的Contourlet变换,提出了子带选取的能量标准,对选定的子带计算能量特征和共生特征;依据特征向量的相似度剔除相近特征向量,用均值漂移算法获取纹理区域数和相应的中心特征,用像素的特征向量与相应中心特征向量的距离确定它们的分类。该文提出的方法不需要先验知识和训练样本。实验表明,基于Contourlet变换的均值漂移分割算法对混合Brodatz图像和SAR图像的分割取得了满意结果。