Camera-pose estimation via projective Newton optimization on the manifold

Determining the pose of a moving camera is an important task in computer vision. In this paper, we derive a projective Newton algorithm on the manifold to refine the pose estimate of a camera. The main idea is to benefit from the fact that the 3-D rigid motion is described by the special Euclidean group, which is a Riemannian manifold. The latter is equipped with a tangent space defined by the corresponding Lie algebra. This enables us to compute the optimization direction, i.e., the gradient and the Hessian, at each iteration of the projective Newton scheme on the tangent space of the manifold. Then, the motion is updated by projecting back the variables on the manifold itself. We also derive another version of the algorithm that employs homeomorphic parameterization to the special Euclidean group. We test the algorithm on several simulated and real image data sets. Compared with the standard Newton minimization scheme, we are now able to obtain the full numerical formula of the Hessian with a 60% decrease in computational complexity. Compared with Levenberg-Marquardt, the results obtained are more accurate while having a rather similar complexity.     

Genetic algorithm-based improved DOA estimation using fourth-order cumulants

Genetic algorithm (GA)-based direction of arrival (DOA) estimation is proposed using fourth-order cumulants (FOC) and ESPRIT principle which results in Multiple Invariance Cumulant ESPRIT algorithm. In the existing FOC ESPRIT formulations, only one invariance is utilised to estimate DOAs. The unused multiple invariances (MIs) must be exploited simultaneously in order to improve the estimation accuracy. In this paper, a fitness function based on a carefully designed cumulant matrix is developed which incorporates MIs present in the sensor array. Better DOA estimation can be achieved by minimising this fitness function. Moreover, the effectiveness of Newton’s method as well as GA for this optimisation problem has been illustrated. Simulation results show that the proposed algorithm provides improved estimation accuracy compared to existing algorithms, especially in the case of low SNR, less number of snapshots, closely spaced sources and high signal and noise correlation. Moreover, it is observed that the optimisation using Newton’s method is more likely to converge to false local optima resulting in erroneous results. However, GA-based optimisation has been found attractive due to its global optimisation capability.     

Geometrical Structures of FIR Manifold and Multichannel Blind Deconvolution

In this paper we study geometrical structures of the manifold of Finite Impulse Response (FIR) filters, and develop a natural gradient learning algorithm for blind deconvolution. First, A Lie group structure is introduced to the FIR manifold and the Riemannian metric is then derived by using the isometric property of the Lie group. The natural gradient on the FIR manifold is obtained by introducing a nonholonomic transformation. The Kullback-Leibler divergence is introduced as the measure of mutual independence of the output signals of the demixing model and a feasible cost function is derived for blind deconvolution. An efficient learning algorithm is presented based on the natural gradient approach and its stability analysis is also provided. Finally, we give computer simulations to demonstrate the performance and effectiveness of the proposed natural gradient algorithm.     

基于自动秩估计的黎曼优化矩阵补全算法及其在图像补全中的应用

矩阵补全(MC)作为压缩感知(CS)的推广,已广泛应用于不同领域。近年来,基于黎曼优化的MC算法因重构精度高、计算速度快的特点,引起了广泛关注。针对基于黎曼优化的MC算法需假设原矩阵秩固定已知,且随机选择迭代起点的特点,该文提出一种基于自动秩估计的黎曼优化MC算法。该算法通过优化包含秩正则项的目标函数,迭代获取秩估计值和预重构矩阵。在估计所得秩对应的矩阵空间上以预重构矩阵为迭代起点,利用基于黎曼流形的共轭梯度法进行矩阵补全,从而提高重构精度。实验结果表明,与几种经典的图像补全方法相比,该文算法图像重构精度显著提高。     

基于黎曼流形监督降维的矩阵CFAR增强检测

矩阵CFAR检测是从几何流形角度处理雷达目标检测问题的新技术。为进一步提升其在复杂杂波背景下的检测性能,本文提出一种黎曼流形监督降维的矩阵CFAR增强检测方法。首先,将检测问题视为目标与杂波的分类问题,分别构建黎曼流形上目标单元与杂波单元的类内和类间权重矩阵;其次,为增强目标与杂波的可分性,采用保持类内几何距离最小,类间几何距离最大的准则建立降维目标函数,并基于Grassmann流形求解降维优化问题获得映射矩阵;最后,提出一种矩阵CFAR增强检测方法,实现目标增强检测。采用蒙特卡罗方法对仿真数据和实测海杂波数据进行实验分析,结果表明,所提出的方法能够进一步提升检测性能。      

Diffeomorphic metric mapping of high angular resolution diffusion imaging based on Riemannian structure of orientation distribution functions

In this paper, we propose a novel large deformation diffeomorphic registration algorithm to align high angular resolution diffusion images (HARDI) characterized by orientation distribution functions (ODFs). Our proposed algorithm seeks an optimal diffeomorphism of large deformation between two ODF fields in a spatial volume domain and at the same time, locally reorients an ODF in a manner such that it remains consistent with the surrounding anatomical structure. To this end, we first review the Riemannian manifold of ODFs. We then define the reorientation of an ODF when an affine transformation is applied and subsequently, define the diffeomorphic group action to be applied on the ODF based on this reorientation. We incorporate the Riemannian metric of ODFs for quantifying the similarity of two HARDI images into a variational problem defined under the large deformation diffeomorphic metric mapping framework. We finally derive the gradient of the cost function in both Riemannian spaces of diffeomorphisms and the ODFs, and present its numerical implementation. Both synthetic and real brain HARDI data are used to illustrate the performance of our registration algorithm.     

An ant colony optimisation algorithm for aggregated multicast based on minimum grouping model

The tree‐based delivery structure of the traditional Internet protocol multicast requires each on‐tree router to maintain a forwarding state for a group. This leads to a state scalability problem when large numbers of concurrent groups exist in a network. To address this state scalability problem, a novel scheme called aggregated multicast has recently been proposed, in which multiple groups are forced to share one delivery tree. In this paper, we define the aggregated multicast problem based on the minimum grouping model, and propose an ant colony optimisation algorithm. The relative fullness of the tree is defined according to the characteristics of the minimum grouping problem and is introduced as an important component in identifying the aggregation fitness function between two multicast groups. New pheromone update rules are designed based on the aggregation fitness function. To improve the convergence time of the algorithm, we use the changes (brought by each group) in the relative fullness of the current tree as the selection heuristic information. The impact of the relative fullness of the tree is analysed using the hypothesis test, and simulation results indicate that introducing relative fullness to the fitness function can significantly improve the optimisation performance of the algorithm. Compared with other heuristic algorithms, our algorithm has better optimisation performance and is more suitable for scenarios with larger bandwidth waste rates. Copyright © 2011 John Wiley & Sons, Ltd.     

Joint interference alignment precoding based on the optimization algorithm on the Grassmannian manifold

To solve the interference problem between users of the multiuser MIMO system, we first transform the system sum rate maximization problem into joint optimization of interference signal power and useful signal power. On this basis, we propose a weighted interference alignment objective function, causing the system to obtain a higher sum rate by adjusting the weight with different signal-to-noise ratios. Then, we model the transmit subspace and the interference subspace on the Grassmannian manifold and propose joint interference alignment precoding based on the Grassmannian conjugacy gradient algorithm (GCGA-JIAP algorithm). In contrast to conventional interference alignment algorithms, our proposed algorithm can reduce the computational cost by transforming the constrained optimization of the complex Euclidean space into unconstrained optimization with the degenerate dimension on the Grassmannian manifold. Computer simulation shows that the proposed algorithm improves the convergence of the iterative optimization of the transmitter precoding matrix and the receiver postprocessing matrix and also improves the sum rate performance of the multiuser MIMO interference system.     

Nichtlineare Trajektorienfolgeregelung für einen Laborhelikopter

This contribution is devoted to the nonlinear tracking control problem of the laboratory experiment helicopter 3DOF distributed by Quanser. The laboratory experiment belongs to the class of mechanical systems with three degrees-of-freedom and two control inputs. It is well known that the systematic design of nonlinear controllers for underactuated mechanical systems is a challenge compared to fully actuated systems. On certain simplifying assumptions, which very well apply to the operating range of practical interest, we can show that the mathematical model is configuration flat. Thereby, a mechanical system is said to be configuration flat if it is differential flat and the flat outputs solely depend on the generalized coordinates of the mechanical system. The controller design is based on a formulation of the mechanical system on a Riemannian manifold where the kinetic energy serves as a natural Riemannian metric. In a first step a nonlinear tracking controller including an integral part in the linear error system is designed by means of a quasi-static state feedback. In a second step the design of the tracking controller is based on the theory of exact linearization utilizing the so-called dynamic extension algorithm. The experimental results of both controllers are compared and discussed in detail. In particular, the quasi-static state feedback controller shows an excellent tracking behavior. The performance as being obtained by the nonlinear controlled cannot be achieved by conventional linear control strategies.     

Distance based kernels for video tensors on product of Riemannian matrix manifolds

In this paper, we explore the inherent geometry of video tensors by modeling them as points in product of Riemannian matrix manifolds. A video tensor is decomposed into three modes (factors) using matrix unfolding operation and each mode is represented as a point in a product space of Grassmannian and symmetric positive definite (SPD) matrix manifold. Hence a video is represented as a point in the Cartesian product of three such product spaces. Being a manifold valued (non-Euclidean) representation, application of several state-of-the-art Euclidean machine learning algorithms lead to inferior results. To overcome this, we propose positive definite kernels which map the points from product manifold space to Hilbert space. The proposed kernel functions implicitly make use of geodesic distance on product manifold to obtain a similarity measure and generate a kernel-gram matrix. In addition, we generate a discriminative feature representation for each manifold valued point using kernel-gram matrix diagonalization. Classification is performed in a sparse framework. The proposed methodology is tested over three publicly available datasets for hand gesture, traffic signal and sign language recognition. Experimentation performed over these datasets show that the proposed methodology is powerful in terms of classification accuracy in comparison with the state-of-the-art methods.     

基于Grassmann流形几何深度网络的图像集识别方法

近年来,深度学习以其强大的非线性计算能力在目标检测和识别任务中取得了巨大的突破。现有的深度学习网络几乎都是以数据的欧氏结构为前提,而在计算机视觉中许多数据都具有严格的流形结构,如图像集可表示为Grassmann流形。基于数据的流形几何结构来设计深度学习网络,将微分几何理论与深度学习理论相结合,提出一种基于Grassmann流形的深度图像集识别网络。同时在模型训练过程中,使用基于矩阵链式法则的反向传播算法来更新模型,并将权值的优化过程转换为Grassmann流形上的黎曼优化问题。实验结果表明:该方法不仅在结果上识别准确率得到了提高,同时在训练和测试速度上也有一个数量级的提升。     

Oblique Projections for Direction-of-Arrival Estimation With Prior Knowledge

Estimation of directions-of-arrival (DOA) is an important problem in various applications and a priori knowledge on the source location is sometimes available. To exploit this information, standard methods are based on the orthogonal projection of the steering manifold onto the noise subspace associated with the a priori known DOA. In this paper, we derive and analyze the Cramer-Rao bound associated with this model and in particular we point out the limitations of this approach when the known and unknown DOA are closely spaced and the associated sources are uncorrelated (block-diagonal source covariance). To fill this need, we propose to integrate a priori known locations of several sources into the MUSIC algorithm based on oblique projection of the steering manifold. Finally, we show that the proposed approach is able to almost completely cancel the influence of the known DOA on the unknown ones for block-diagonal source covariance and for sufficient signal-to-noise ratio (SNR).     

A joint swarm intelligence algorithm for multi-user detection in MIMO-OFDM system

In the multi-input multi-output orthogonal frequency division multiplexing (MIMO-OFDM) system, traditional multi-user detection (MUD) algorithms that usually used to suppress multiple access interference are difficult to balance system detection performance and the complexity of the algorithm. To solve this problem, this paper proposes a joint swarm intelligence algorithm called Ant Colony and Particle Swarm Optimisation (AC-PSO) by integrating particle swarm optimisation (PSO) and ant colony optimisation (ACO) algorithms. According to simulation results, it has been shown that, with low computational complexity, the MUD for the MIMO-OFDM system based on AC-PSO algorithm gains comparable MUD performance with maximum likelihood algorithm. Thus, the proposed AC-PSO algorithm provides a satisfactory trade-off between computational complexity and detection performance.     

Mutual information–based LPI optimisation for radar network

Radar network can offer significant performance improvement for target detection and information extraction employing spatial diversity. For a fixed number of radars, the achievable mutual information (MI) for estimating the target parameters may extend beyond a predefined threshold with full power transmission. In this paper, an effective low probability of intercept (LPI) optimisation algorithm is presented to improve LPI performance for radar network. Based on radar network system model, we first provide Schleher intercept factor for radar network as an optimisation metric for LPI performance. Then, a novel LPI optimisation algorithm is presented, where for a predefined MI threshold, Schleher intercept factor for radar network is minimised by optimising the transmission power allocation among radars in the network such that the enhanced LPI performance for radar network can be achieved. The genetic algorithm based on nonlinear programming (GA-NP) is employed to solve the resulting nonconvex and nonlinear optimisation problem. Some simulations demonstrate that the proposed algorithm is valuable and effective to improve the LPI performance for radar network.     

智能反射表面辅助的无线携能通信网络资源分配算法

为了解决终端设备能量受限、网络覆盖范围有限等问题,实现绿色万物高效互联,引入了一种新的智能反射表面技术,构建智能反射表面辅助的无线携能通信网络.为了进一步提升该网络的总吞吐量,提出了一种以速率和最大化为目标的资源分配方案.考虑基站的发射功率限制、所有物联网设备最低能量需求限制和智能反射表面的相移约束,建立联合发射波束设...     

Riemannian Drums,Anisotropic Curve Evolution,and Segmentation

The method of curve evolution is a popular method for recovering shape boundaries. However, isotropic metrics have always been used to induce the flow of the curve and potential steady states tend to be difficult to determine numerically, especially in noisy or low-contrast situations. Initial curves shrink past the steady state and soon vanish. In this paper, anisotropic metrics are considered to remedy the situation by taking the orientation of the feature gradient into account. The problem of shape recovery or segmentation is formulated as the problem of finding minimum cuts of a Riemannian manifold. Approximate methods, namely anisotropic geodesic flows and the solution of an eigenvalue problem, are discussed.     

Active contour evolved by joint probability classification on Riemannian manifold

In this paper, we present an active contour model for image segmentation based on a nonparametric distribution metric without any intensity a priori of the image. A novel nonparametric distance metric, which is called joint probability classification, is established to drive the active contour avoiding the instability induced by multimodal intensity distribution. Considering an image as a Riemannian manifold with spatial and intensity information, the contour evolution is performed on the image manifold by embedding geometric image feature into the active contour model. The experimental results on medical and texture images demonstrate the advantages of the proposed method.     

大规模MIMO系统中基于牛顿迭代和超松弛迭代的WWSE预编码算法

在大规模 MIMO 系统中,将牛顿迭代法用于传统的 WWSE 预编码算法求逆运算,但是其迭代初始值计算复杂。针对这一问题,提出WWSESOR-NT算法。在SOR算法的基础上提出中间算法,然后与牛顿迭代算法相结合,利用中间算法直接对高阶矩阵的逆进行估算,将得到的结果作为牛顿迭代法的迭代初始值以加快收敛速度。仿真结果显示,与传统牛顿迭代法比较,WWSESOR-NT 算法能够以更少的迭代次数和近似相同的复杂度逼近WWSE算法的性能。