Tracking of Lines in Spherical Images via Sub-Riemannian Geodesics in $${\text {}}$$

Algorithms for automatically selecting a scalar or locally varying regularization parameter for total variation models with an \(L^{\tau }\)-data fidelity term, \(\tau \in \{1,2\}\), are presented. The automated selection of the regularization parameter is based on the discrepancy principle, whereby in each iteration a total variation model has to be minimized. In the case of a locally varying parameter, this amounts to solve a multiscale total variation minimization problem. For solving the constituted multiscale total variation model, convergent first- and second-order methods are introduced and analyzed. Numerical experiments for image denoising and image deblurring show the efficiency, the competitiveness, and the performance of the proposed fully automated scalar and locally varying parameter selection algorithms.     

Logarithmic control,trajectory tracking,and formation for nonholonomic vehicles on Lie group SE(2)

This paper studies the problem of set-point stabilisation, trajectory tracking, and formation tracking for unicycle-type vehicles by taking advantage of the exponential coordinates and the other mathematical tools provided by the Lie group setting of the special Euclidean group SE(2). Motivated by recent developments in geometric control approaches for holonomic systems, we first study the stabilisation problem for nonholonomic constrained kinematic systems by improving the logarithmic stabilising control laws in such a way that they can satisfy nonholonomic constraints too. We then extend the control design to the problem of trajectory tracking by proposing auxiliary systems and investigating the conditions for which the adjoint map in the Lie algebra preserves the velocity constraint. This leads to a global control law which is valid for general time-varying as well as non-smooth trajectories. The tracking control law is also applied to the problem of leader-follower formation tracking by constructing nonholonomic virtual leaders in the desired formation. Finally, the kinematic control law is translated to a differential drive robot using the backstepping technique. To demonstrate the effectiveness of the controllers, the numerical results are presented and the performances are compared with the other three controllers in the literature.     

Partition Algorithm For Parallel Processing Of Array Multiplication In Gf(2m) Fields

The multiplication operations in GF(2m) fields are widely used in cryptosystems. However, the multiplication operations for public-key cryptosystems require very large operands with 512 bits or more, and then existing multipliers are not available for such multiplications. In this paper, we will present a partition algorithm to divide large operands into small operands such as 32 bits or 64 bits, and then existing multipliers can be employed. We also present a parallel version of the partition algorithm by employing an important natural property of the multiplication operations in GF(2m) fields.     

Integrated Guidance and Feedback Control of Underactuated Robotics System in SE(3)

An integrated guidance and feedback control scheme for steering an underactuated vehicle through desired waypoints in three-dimensional space, is developed here. The underactuated vehicle is modeled as a rigid body with four control inputs. These control inputs actuate the three degrees of freedom of rotational motion and one degree of freedom of translational motion in a vehicle body-fixed coordinate frame. This actuation model is appropriate for a wide range of underactuated vehicles including spacecraft with internal attitude actuators, vertical take-off and landing (VTOL) aircraft, fixed-wing multirotor unmanned aerial vehicles (UAVs), maneuverable robotic vehicles, etc. The guidance problem is developed on the special Euclidean group of rigid body motions, SE(3), in the framework ofgeometric mechanics, which represents the vehicle dynamics globally on this configuration manifold. The integrated guidance and control algorithm selects the desired trajectory for the translational motion that passes through the given waypoints, and the desired trajectory for the attitude based on the desired thrust direction to achieve the translational motion trajectory. A feedback control law is then obtained to steer the underactuated vehicle towards the desired trajectories in translation and rotation. This integrated guidance and control scheme takes into account known bounds on control inputs and generates a trajectory that is continuous and at least twice differentiable, which can be implemented with continuous and bounded control inputs. The integrated guidance and feedback control scheme is applied to an underactuated quadcopter UAV to autonomously generate a trajectory through a series of given waypoints in SE(3) and track the desired trajectory in finite time. The overall stability analysis of the feedback system is addressed. Discrete time models for the dynamics and control schemes of the UAV are obtained in the form of Lie group variational integrators using the discrete Lagrange-d’Alembert principle. Almost global asymptotic stability of the feedback system over its state space is shown analytically and verified through numerical simulations.     

射频识别技术(RFID)及其在图书馆领域的应用

该文介绍了RFID系统的组成、工作原理及特点,着重阐述了RFID技术在图书馆的应用和在推广应用中存在的问题,最后论述了RFID在图书馆的应用前景。     

A nonlinear position and attitude observer on SE(3) using landmark measurements

This paper addresses the problem of position and attitude estimation, based on landmark readings and velocity measurements. A derivation of a nonlinear observer on SE(3) is presented, using a Lyapunov function conveniently expressed as a function of the difference between the estimated and the measured landmark coordinates. The resulting feedback laws are explicit functions of the landmark measurements and velocity readings, exploiting the sensor information directly in the observer. The proposed observer yields almost global asymptotic stabilization of the position and attitude errors and exponential convergence in any closed ball inside the region of attraction. Also, it is shown that the asymptotic convergence of the estimation error trajectories is shaped by the landmark geometry and observer design parameters. The problem of non-ideal velocity readings is also considered, and the observer is augmented to compensate for bias in the angular and linear velocity measurements. The resulting position, attitude, and bias estimation errors are shown to converge exponentially fast to the desired equilibrium points, for bounded initial estimation errors. Simulation results are presented to illustrate the stability and convergence properties of the observer.     

Nilpotent Approximations of Sub-Riemannian Distances for Fast Perceptual Grouping of Blood Vessels in 2D and 3D

We propose an efficient approach for the grouping of local orientations (points on vessels) via nilpotent approximations of sub-Riemannian distances in the 2D and 3D roto-translation groups SE(2) and SE(3). In our distance approximations we consider homogeneous norms on nilpotent groups that locally approximate SE(n), and which are obtained via the exponential and logarithmic map on SE(n). In a qualitative validation we show that the norms provide accurate approximations of the true sub-Riemannian distances, and we discuss their relations to the fundamental solution of the sub-Laplacian on SE(n). The quantitative experiments further confirm the accuracy of the approximations. Quantitative results are obtained by evaluating perceptual grouping performance of retinal blood vessels in 2D images and curves in challenging 3D synthetic volumes. The results show that (1) sub-Riemannian geometry is essential in achieving top performance and (2) grouping via the fast analytic approximations performs almost equally, or better, than data-adaptive fast marching approaches on \(\mathbb {R}^n\) and SE(n).     

Visualization of Equivalence in 2D Bivariate Fields

In this paper, we show how the equivalence property leads to the novel concept of equivalent regions in mappings from ?ⁿ to ?ⁿ. We present a technique for obtaining these regions both in the domain and the codomain of such a mapping, and determine their correspondence. This enables effective investigation of variation equivalence within mappings, and between mappings in terms of comparative visualization. We implement our approach for n = 2, and demonstrate its utility using different examples.     

Finite-time optimal formation control of multi-agent systems on the Lie group SE(3)

This paper investigates the finite-time optimal formation problem of multi-agent systems on the Lie group SE(3), for the situation when the formation time and/or the cost function need to be considered. Under the condition that the formation time is given according to the task requirement, a finite-time optimal formation controller is proposed for the two-agent case to guarantee that the desired formation is achieved at the given time and the corresponding cost function is optimal. For the systems with multiple agents, the obtained finite-time optimal formation control law has second-order approximation accuracy. Finally, some numerical simulations are provided to illustrate the effectiveness of the theoretical results.     

有限域与Ramsey数Rn(k)的下界

研究有限域GF(p')上的循环图的结构性质,给出一些图的团数的解析表达式,并给出计算Rarnsey数Rn(k)下界的一种算法,得到一个Ramsey数的新下界：R3(8)≥4111。     

The geometric convexity on SE(3) and its application to the formation tracking in multi-vehicle systems

This paper considers the problem of geometric convexity on special Euclidean group SE(3) and its application to the formation tracking in multi-vehicle systems. Motivated by the convex hull on Euclidean space, the specific expression of geodesic connecting two points on SE(3) is obtained based on the Pontryagin's Minimum Principle. Then it is extended to the geometric convex combination for multiple points, based on which the virtual systems on SE(3) is given to be used in the application of formation tracking problem. In light of the geometric convex combination and virtual systems on SE(3), a consensus-based tracking protocol is proposed to guarantee that the formation is achieved under the directed acyclic graphs. Finally, two numerical examples are provided to demonstrate the validity of the theoretical results.     

Hierarchical Correlation Clustering in Multiple 2D Scalar Fields

Sets of multiple scalar fields can be used to model many types of variation in data, such as uncertainty in measurements and simulations or time‐dependent behavior of scalar quantities. Many structural properties of such fields can be explained by dependencies between different points in the scalar field. Although these dependencies can be of arbitrary complexity, correlation, i.e., the linear dependency, already provides significant structural information. Existing methods for correlation analysis are usually limited to positive correlation, handle only local dependencies, or use combinatorial approximations to this continuous problem. We present a new approach for computing and visualizing correlated regions in sets of 2‐dimensional scalar fields. This paper describes the following three main contributions: (i) An algorithm for hierarchical correlation clustering resulting in a dendrogram, (ii) a generalization of topological landscapes for dendrogram visualization, and (iii) a new method for incorporating negative correlation values in the clustering and visualization. All steps are designed to preserve the special properties of correlation coefficients. The results are visualized in two linked views, one showing the cluster hierarchy as 2D landscape and the other providing a spatial context in the scalar field's domain. Different coloring and texturing schemes coupled with interactive selection support an exploratory data analysis.     

International Association for Multibody System Dynamics (IMSD)

Multibody System Dynamics -     

基于聚类的快速时域关联规则发现算法

时域数据的挖掘是数据挖掘领域经常遇到的问题。而时域关联规则的发现研究是关联规则的一个重要研究课题。该文在对周期关联规则进行深入研究的基础上,形式化定义了基本的时域关联规则概念,并提出了基于Apriori的发现周期关联规则的CCAR算法。CCAR的核心思想是首先把各项目按照周期时间分布进行聚类,根据聚类结果把每个项目分成几个动态的有效时间区域。在应用Apriori算法时,用项目的各个时间区域扩展项目集Ⅰ,然后根据作者提出的带时间属性的JOIN操作由Lk-1生成Ck,并由约简操作删除Ck中不满足条件的候选频繁项目集以提高算法的效率。算法理论分析和实验都表明CCAR是有效的。     

Saliency detection via outlier pursuit in compress domain (SDOPCD)

Microsystem Technologies - A saliency detection technique has been proposed in this article. The two major constituents, proximal gradient pursuit and compress sensing techniques, are the important...     

Bilinear modeling via augmented Lagrange multipliers (BALM)

This paper presents a unified approach to solve different bilinear factorization problems in computer vision in the presence of missing data in the measurements. The problem is formulated as a constrained optimization where one of the factors must lie on a specific manifold. To achieve this, we introduce an equivalent reformulation of the bilinear factorization problem that decouples the core bilinear aspect from the manifold specificity. We then tackle the resulting constrained optimization problem via Augmented Lagrange Multipliers. The strength and the novelty of our approach is that this framework can seamlessly handle different computer vision problems. The algorithm is such that only a projector onto the manifold constraint is needed. We present experiments and results for some popular factorization problems in computer vision such as rigid, non-rigid, and articulated Structure from Motion, photometric stereo, and 2D-3D non-rigid registration.