Quaternion Fourier-Mellin moments for color images

The quaternion Fourier-Mellin moments for describing color images are introduced, which can be seen as the generalization of traditional Fourier-Mellin moments for gray-level images. Then, the quaternion Fourier-Mellin moment invariants are derived, which could be a useful tool in color object recognition tasks that require the similarity invariance. In addition, the problem of color image registration using quaternion Fourier-Mellin moments is discussed. The registration method can match color images differing in rotation and scaling. The advantage of our method is that it can process color image directly, without losing color information. Experimental results validate the effectiveness of the method we proposed.     

陀螺体动力学的四元数分析法

本文以四元数作为陀螺体的主刚体的定位参数，并以主刚体上转子的相对转角作为其转子的相对定位参数，导出了陀螺体对其质心的动量矩的矩阵表达式，在此基础上，利用动量矩定理进一步推导出了四元数形式的陀螺体动力学方程组。     

Hermitian tridiagonal solution with the least norm to quaternionic least squares problem

Quaternionic least squares (QLS) is an efficient method for solving approximate problems in quaternionic quantum theory. In view of the extensive applications of Hermitian tridiagonal matrices in physics, in this paper we list some properties of basis matrices and subvectors related to tridiagonal matrices, and give an iterative algorithm for finding Hermitian tridiagonal solution with the least norm to the quaternionic least squares problem by making the best use of structure of real representation matrices, we also propose a preconditioning strategy for the Algorithm LSQR-Q in Wang, Wei and Feng (2008) [14] and our algorithm. Numerical experiments are provided to verify the effectiveness of our method.     

基于并联机构的六维加速度传感器的方案设计及建模研究

提出一种新的基于并联机构的压电式六维加速度传感器的设计方案,即用并联机构充当传感器的弹性体结构,压电陶瓷同时充当传感器的敏感元件和并联机构的移动副,弹性球铰链代替传统的球面副.分别在质量块、外壳及地面上固结坐标系,基于多体系统理论推导两两之间位姿关系的解析表达式.运用牛顿-欧拉法建立系统的动力学方程,通过引入辅助角速度并用四元数来描述旋转矩阵和角速度矢量,将其转化成两个一阶常微分方程组的初值问题,并运用改进的欧拉算法进行求解,实现了六维加速度的完全解耦.针对四元数的违约问题,运用矩阵广义逆理论提出了一种有效的可重复运行的修正算法.利用建立的解耦模型及其算法对实例进行了求解,数据处理总时间小于采样点时间跨度,且理论计算值与ADAMS仿真数据吻合得很好;另外,通过试验进一步验证了设计方案的合理性以及数学模型的可靠性.     

Quaternion switching filter for impulse noise reduction in color image

A novel approach to impulse noise reduction in color image is introduced in this paper. By applying the quaternion unit transform theory, the difference between two color pixels can be represented in the quaternion form. Based on the difference mentioned above, an efficient filter that can switch between the vector median filter (VMF) and the identity filter (no filtering operation) is proposed. Extensive simulation result indicates that the proposed filter achieves a trade-off between noise suppression and detail preservation in both correlated and uncorrelated impulse noise scenarios when compared with other widely used filters. Furthermore, the computational complexity analysis shows that the proposed filter is quite efficient.     

Algorithm Q-LSQR for the least squares problem in quaternionic quantum theory

In this paper, an iterative algorithm for the standard quaternionic least squares problem is proposed without using the real (complex) representation. Our algorithm is implemented in the quaternion field and by means of direct quaternion arithmetic and is a natural generalization of the LSQR algorithm for the real least squares problem.     

转动角位移矢量及其应用

通过引入描述刚体转动位置的转动角位置矢量，定义了描述刚体转动的角位移矢量，得出了两次绕相交轴转动的转动角位移矢量的合成公式，否定了有限转动角位移不能定义为矢量的结论。     

基于四元数显著图和PCNN空洞滤波的足球检测

注意力选择和先验知识可有效的用于目标检测与跟踪。在基于注意力选择目标跟踪模型的基础上,引入了PCNN（Pulse Coupled Neural Network）空洞滤波及足球颜色的先验知识。一方面,针对有些情况下足球模糊不清,采用PCNN空洞滤波检测足球的连通性;另一方面,在注意力选择模型中引入了足球颜色的先验知识,进一步提高检测性能。首先提取球场区域,然后对由足球颜色先验知识、色差和亮度产生的四元数显著图进行PCNN空洞滤波,很多情况下可由此直接检测到足球。如果至此未检测到足球,继续利用四元数显著图生成感兴趣区域,并用足球的面积、圆形度和离心率等特征进一步检测目标,同时采用卡尔曼滤波器预测足球的位置作为补充检测。仿真结果显示,与Dynamic Kalman Filter with Velocity Control^[4]和Real Time Ball Detection Framework^[5]两种方法相比,检测成功率分别提高了11．5％和15．8％。     

基于视觉和扩展卡尔曼滤波的位姿和运动估计新方法

估计两参考坐标系之间的相对三维位姿和相对运动 ,对机器人导航、机器人装配、测量、跟踪、目标识别和摄像机定标来说是一个非常重要的问题。用八元数来表示摄像机和运动目标两坐标系之间相对平移和旋转 ,在假设运动目标的三维几何尺寸已知 ,且摄像机和运动目标之间的相对运动为匀速运动的情况下 ,由单个针孔摄像机获取运动目标的图像并测量其图像中的线特征点。由于旋转部分用四元数表示 ,状态转移函数是非线性的 ,测量函数由三维坐标变换和针孔摄像机模型所决定 ,存在严重的非线性 ,常规的卡尔曼滤波方法不适合 ,这里以扩展卡尔曼滤波方法作为数学模型 ,对状态转移函数和测量函数进行线性化后 ,对摄像机和运动目标之间的位姿和相对运动进行了估计 ,仿真结果表明 :该位姿和运动估计算法具有良好的收敛性     

Marginalized particle filter for spacecraft attitude estimation from vector measurements

An algorithm based on the marginalized particle filters （MPF） is given in details in this paper to solve the spacecraft attitude estimation problem： attitude and gyro bias estimation using the biased gyro and vector observations. In this algorithm, by marginalizing out the state appearing linearly in the spacecraft model, the Kalman filter is associated with each particle in order to reduce the size of the state space and computational burden. The distribution of attitude vector is approximated by a set of particles and estimated using particle filter, while the estimation of gyro bias is obtained for each one of the attitude particles by applying the Kalman filter. The efficiency of this modified MPF estimator is verified through numerical simulation of a fully actuated rigid body. For comparison, unscented Kalman filter （UKF） is also used to gauge the performance of MPE The results presented in this paper clearly derfionstrate that the MPF is superior to UKF in coping with the nonlinear model.