2D shape deformation using nonlinear least squares optimization

This paper presents a novel 2D shape deformation algorithm based on nonlinear least squares optimization. The algorithm aims to preserve two local shape properties: the Laplacian coordinates of the boundary curve and the local area of the shape interior, which are together represented in a non-quadratic energy function. An iterative Gauss–Newton method is used to minimize this nonlinear energy function. The result is an interactive shape deformation system that can achieve physically plausible results that are difficult to achieve with previous linear least squares methods. In addition to this algorithm that preserves local shape properties, we also introduce a scheme to preserve the global area of the shape, which is useful for deforming incompressible objects.     

偏最小二乘改进算法与特征抽取

采用基于正交约束的非迭代PLS可以实现PLS成分的快速有效抽取,但不能保证所抽取的成分之间不相关。而基于统计不相关约束的非迭代PLS建模方法所抽取的成分之间是无关的,从而可以保证图像识别时的有效性和稳定性。基于2DPCA思想的2DPLS特征抽取技术,直接从图像矩阵中抽取特征,能有效地解决小样本问题。但在使用PLS对单特征数据进行维数压缩时,传统的类标编码过于简单,为了充分利用数据分布信息,采用模糊k-近邻法对每个样本赋予一个样本标号,将近邻样本类别信息反映在该样本的类编码中,从而提出了基于样本标号的PLS及2DPLS改进算法。在ORL人脸库上的实验结果表明,该改进算法优于传统的PLS,能够更有效地抽取识别特征,其识别率要高于传统的PLS算法。     

基于偏最小二乘回归的性别识别

在现有研究中,人脸图像往往局限于简单的受控场景,忽略了自然场景中光照、姿态、表情等因素的影响.针对此问题,重点研究了自然场景下的性别识别问题,并提出了基于偏最小二乘回归(PLS)的性别识别算法.在人脸特征提取阶段,提出了一种新的特征描述算子多尺度方差局部二元模式(MBV-LBP),并与多尺度局部二元模式(MB-LBP)结合作为最终的人脸特征表示,采用PLS模型同时完成特征降维和性别识别,简化了计算过程.通过在LFW数据库和一个Web人脸图像库上进行实验,实验结果表明了算法的优越性.     

基于最小二乘法的高维目标减少算法

多目标进化算法在许多领域有广泛的应用,大部分文献都只针对二维与三维的测试问题,目标减少成为高维优化的热点之一．本文从决策者角度考虑冗余目标问题,提出了基于最小二乘法的目标减少算法（ORLSM）,该方法将每个目标函数分段拟合为若干条直线段,然后比较各直线段之间的斜率来确定最冗余目标对,进而确定冗余目标．同时针对目标减少前后个体支配关系的变化情况,提出了支配关系改变率的评价方法．通过3个测试函数,分别用逆世代距离（IGD）、支配关系改变率（CDR）和时间效率3个方面,对同类的两个算法进行了性能测试．结果表明,ORLSM在总体上具有最好的性能：CDR和IGD具有基本一致的评价结果．     

An iterative algorithm for least squares problem in quaternionic quantum theory

Quaternionic least squares (QLS) problem is one method of solving overdetermined sets of quaternion linear equations AXB=E that is appropriate when there is error in the matrix E. In this paper, by means of real representation of a quaternion matrix, we introduce a concept of norm of quaternion matrices, which is different from that in [T. Jiang, L. Chen, Algebraic algorithms for least squares problem in quaternionic quantum theory, Comput. Phys. Comm. 176 (2007) 481-485; T. Jiang, M. Wei, Equality constrained least squares problem over quaternion field, Appl. Math. Lett. 16 (2003) 883-888], and derive an iterative method for finding the minimum-norm solution of the QLS problem in quaternionic quantum theory.     

统一最小二乘规则的单幅图像超分辨算法

基于机器学习的超分辨方法是一个很有发展前景的单幅图像超分辨方法,稀疏表达和字典学习是其中的研究热点。针对比较耗时的字典训练与恢复精度不高图像重建,从减小低分辨率(LR)和高分辨率(HR)特征空间之间差异性的角度提出了一种使用迭代最小二乘字典学习算法(ILS-DLA),并使用锚定邻域回归(ANR)进行图像重建的单幅图像超分辨算法。迭代最小二乘法的整体优化过程极大地缩短了低分辨字典/高分辨字典的训练时间,它采用了与锚定邻域回归相同的优化规则,有效地保证了字典学习和图像重建在理论上的一致性。实验结果表明,所提算法的字典学习效果比K-均值奇异值分解(K-SVD)和Beta过程联合字典学习(BPJDL)等算法更高效,图像重建的效果也优于许多优秀的超分辨算法。     

Parallel iterative refinement linear least squares solvers based on all-reduce operations

We present the novel parallel linear least squares solvers ARPLS-IR and ARPLS-MPIR for dense overdetermined linear systems. All internode communication of our ARPLS solvers arises in the context of all-reduce operations across the parallel system and therefore they benefit directly from efficient implementations of such operations. Our approach is based on the semi-normal equations, which are in general not backward stable. However, the method is stabilised by using iterative refinement. We show that performing iterative refinement in mixed precision also increases the parallel performance of the algorithm. We consider different variants of the ARPLS algorithm depending on the conditioning of the problem and in this context also evaluate the method of normal equations with iterative refinement. For ill-conditioned systems, we demonstrate that the semi-normal equations with standard iterative refinement achieve the best accuracy compared to other parallel solvers.We discuss the conceptual advantages of ARPLS-IR and ARPLS-MPIR over alternative parallel approaches based on QR factorisation or the normal equations. Moreover, we analytically compare the communication cost to an approach based on communication-avoiding QR factorisation. Numerical experiments on a high performance cluster illustrate speed-ups up to 3820 on 2048 cores for ill-conditioned tall and skinny matrices over state-of-the-art solvers from DPLASMA or ScaLAPACK.     

基于最小二乘优化的加权DV-Hop改进算法

针对传统DV-Hop算法定位精度差的问题,加权DV-Hop算法优化了待计算节点的平均单跳距离。在存在GPS定位误差的情况下,对加权DV-Hop算法进行了改进,利用最小二乘法优化全网信标节点的平均单跳距离,利用二次曲线算法代替三边测量法。随机单次仿真的平均定位误差较传统算法降低13.01%,较加权DV-Hop算法降低8.94%,重复实验仿真结果同样表明算法精度、稳定性有显著提高。     

Interactive mesh deformation using equality-constrained least squares

Mesh deformation techniques that preserve the differential properties have been intensively studied. In this paper, we propose an equality-constrained least squares approach for stably deforming mesh models while approximately preserving mean curvature normals and strictly satisfying other constraints such as positional constraints. We solve the combination of hard and soft constraints by constructing a typical least squares system using QR decomposition. A well-known problem of hard constraints is over-constraints. We show that the equality-constrained least squares approach is useful for resolving such over-constrained situations. In our framework, the rotations of mean curvature normals are treated using the logarithms of unit quaternions in . During deformation, mean curvature normals can be rotated while preserving their magnitudes. In addition, we introduce a new modeling constraints called rigidity constraints and show that rigidity constraints can effectively preserve the shapes of feature regions during deformation. Our framework achieves good performance for interactive deformation of mesh models.     

Face recognition using partial least squares components

The paper considers partial least squares (PLS) as a new dimension reduction technique for the feature vector to overcome the small sample size problem in face recognition. Principal component analysis (PCA), a conventional dimension reduction method, selects the components with maximum variability, irrespective of the class information. So PCA does not necessarily extract features that are important for the discrimination of classes. PLS, on the other hand, constructs the components so that the correlation between the class variable and themselves is maximized. Therefore PLS components are more predictive than PCA components in classification. The experimental results on Manchester and ORL databases show that PLS is to be preferred over PCA when classification is the goal and dimension reduction is needed.     

迭代最小二乘椭圆拟合的锥套图像检测与跟踪

目的 针对自主空中加油过程中锥套图像目标识别与定位问题,以锥套内部加油口作为匹配特征,提出一种基于圆形特征的锥套检测与跟踪方法。方法 锥套跟踪采用行列扫描法获取锥套内部边缘,并通过迭代最小二乘拟合确定精确的椭圆形状参数,而锥套检测采用多方位最近点区域搜索法提取锥套所在的所有可能图像区域,并采用锥套跟踪进行精匹配和最终决策。结果 实验结果表明,该方法下锥套精确定位的成功率高达94.71%,锥套检测耗时小于500 ms,锥套跟踪的最大耗时为21.59 ms,平均耗时4.18 ms。结论 本文方法无须在锥套上额外安装光学标记,且能够实时、精确地确定锥套所在的图像位置和大小。     

An iterative algorithm for a least squares solution of a matrix equation

In this article, we propose an iterative algorithm to compute the minimum norm least-squares solution of AXB+CYD=E, based on a matrix form of the algorithm LSQR for solving the least squares problem. We then apply this algorithm to compute the minimum norm least-squares centrosymmetric solution of min _X ‖AXB?E‖ _F . Numerical results are provided to verify the efficiency of the proposed method.     

基于正则化约束最小二乘的稳健频率不变波束形成器设计方法

频率不变波束形成器(Frequency invariant beamformer,FIB)在无畸变宽带声信号采集等方面具有重要应用.经典的FIB设计方法通常是在理想的模型条件下提出的,当存在由麦克风的幅度和相位响应不一致性所引起的阵列通道失配误差时,其性能会变差,无法满足实际的设计要求.本文提出了一种基于正则化约束最小二乘的稳健FIB设计方法,有效克服了麦克风阵列通道失配误差对FIB设计性能的影响.该方法适用于任意结构的阵列,并且具有闭式解,无需迭代步骤,计算复杂度较低.仿真实例证明了所提方法的有效性和理论分析的正确性.     

Learning-based super resolution using kernel partial least squares

In this paper, we propose a learning-based super resolution approach consisting of two steps. The first step uses the kernel partial least squares (KPLS) method to implement the regression between the low-resolution (LR) and high-resolution (HR) images in the training set. With the built KPLS regression model, a primitive super-resolved image can be obtained. However, this primitive HR image loses some detailed information and does not guarantee the compatibility with the LR one. Therefore, the second step compensates the primitive HR image with a residual HR image, which is the subtraction of the original and primitive HR images. Similarly, the residual LR image is obtained from the down-sampled version of the primitive HR and original LR image. The relation of the residual LR and HR images is again modeled with KPLS. Integration of the primitive and the residual HR image will achieve the final super-resolved image. The experiments with face, vehicle plate, and natural scene images demonstrate the effectiveness of the proposed approach in terms of visual quality and selected image quality metrics.     

使用线约束运动最小二乘法的视差图像拼接

目的 图像配准是影响拼接质量的关键因素。已有的视差图象拼接方法没有解决匹配特征点对间的错误配准问题,容易引起不自然的拼接痕迹。针对这一问题,提出了使用线约束运动最小二乘法的配准算法,减少图像的配准误差,提高拼接质量。方法 首先,计算目标图像和参考图像的SIFT（scale-invariant feature transform）特征点,应用RANSAC（random sample consensus）方法建立特征点的匹配关系,由此计算目标到参考图像的最佳单应变换。然后,使用线约束运动最小二乘法分别配准两组图像：1）第1组是目标图像和参考图像;2）第2组是经单应变换后的目标图像和参考图像。第1组用逐点仿射变换进行配准,而第2组配准使用了单应变换加上逐点仿射变换。最后,在重叠区域,利用最大流最小割算法寻找最优拼接缝,沿着拼接缝评估两组配准的质量,选取最优的那组进行融合拼接。结果 自拍图库和公开数据集上的大量测试结果表明,本文算法的配准精度超过95%,透视扭曲比例小于17%。与近期拼接方法相比,本文配准算法精度提高3%,拼接结果中透视扭曲现象减少73%。结论 运动最小二乘法可以准确地配准特征点,但可能会扭曲图像中的结构对象。而线约束项则尽量保持结构,阻止扭曲。因此,线约束运动最小二乘法兼顾了图像结构的完整性和匹配特征点的对准精度,基于此配准模型的拼接方法能够有效减少重影和鬼影等人工痕迹,拼接结果真实自然。     

Orthogonal vs. uncorrelated least squares discriminant analysis for feature extraction

In this paper, a new discriminant analysis for feature extraction is derived from the perspective of least squares regression. To obtain great discriminative power between classes, all the data points in each class are expected to be regressed to a single vector, and the basic task is to find a transformation matrix such that the squared regression error is minimized. To this end, two least squares discriminant analysis methods are developed under the orthogonal or the uncorrelated constraint. We show that the orthogonal least squares discriminant analysis is an extension to the null space linear discriminant analysis, and the uncorrelated least squares discriminant analysis is exactly equivalent to the traditional linear discriminant analysis. Comparative experiments show that the orthogonal one is more preferable for real world applications.     

有理模型辨识的两类新方法——混合迭代与柔性最小二乘法

针对有理模型提出两类辨识方法.首先提出基于递阶辨识思想的混合辨识方法,将模型分解为分子和分母两个子模型,分别用最小二乘法辨识分子参数,用粒子群算法和智能多步长梯度迭代算法辨识分母参数.由于降低了模型维数,且信息向量与噪声不相关,相对于传统的偏差补偿最小二乘算法,混合迭代法可以提高辨识精度并降低计算量.然后,为消除模型结构已知的假设,且充分利用最新数据更新系统参数,提出柔性递推最小二乘辨识方法,将有理模型转化为时变参数系统,进而辨识出时变系统的参数.仿真例子验证了所提出方法的有效性.