The problem of integrating rotations and angular velocity from a known timeand space-dependent curvature is met in the dynamic analysis of non-linear spatial beams, if the numerical formulation is based on curvature, as in [1]. To avoid singularities and make the formulation more convenient, rotational quaternions q̂ are used for the parametrization of rotations. The relation between the curvatu...

Abstract The quaternion is a powerful and common tool to avoid singularity in rotational dynamics three-dimensional (3D) space. Here it has been particularly used as an alternative Euler angles rotation matrix. application of the exercised quadrotor modeling control. It changes represents singularity-free attitude model. for first time (for best knowledge authors), state-dependent differential ...

Scene Background Initialization (SBI) is one of the challenging problems in computer vision. Dynamic mode decomposition (DMD) a recently proposed method to robustly decompose video sequence into background model and corresponding foreground part. However, this needs convert color image grayscale for processing, which leads neglect coupling information between three channels image. In study, we ...

We introduce a symplectic dual quaternion variational integrator(DQVI) for simulating single rigid body motion in all six degrees of freedom. Dual quaternion is used to represent rigid body kinematics and one-step Lie group variational integrator is used to conserve the geometric structure, energy and momentum of the system during the simulation. The combination of these two becomes the first L...

In recent years, quaternion matrix completion (QMC) based on low-rank regularization has been gradually used in image processing. Unlike (LRMC) which handles RGB images by recovering each color channel separately, QMC models retain the connection of three channels and process them as a whole. Most existing quaternion-based methods formulate (LRQMC) nuclear norm (a convex relaxation rank) minimi...

In this work, we address the problem of global attitude control using direct inertial measurements. When using direct inertial measurement to observe the rigid body attitude, it is shown that due to a geometrical obstruction, it is impossible to achieve global asymptotic stability. In fact, for a particular initial condition the tracking error quaternion converges to a pure imaginary quaternion...

Recently, quaternion collaborative representationbased classification (QCRC) and quaternion sparse representation-based classification (QSRC) have been proposed for color face recognition. They can obtain correlation information among different color channels. However, their performance is unstable in different conditions. For example, QSRC performs better than than QCRC on some situations but ...

In this paper the problem of estimating a covariance matrix parametrized by an irreducible symmetric cone in a decision-theoretic set-up is considered. By making use of some results developed in a theory of finite-dimensional Euclidean simple Jordan algebras, Bartlett’s decomposition and an unbiased risk estimate formula for a general family of Wishart distributions on the irreducible symmetric...