Results 31 to 40 of about 994 (259)
Robust Dual-Color Watermarking Based on Quaternion Singular Value Decomposition
IEEE Access, 2020 This paper proposes a robust dual-color watermarking based on quaternion singular value decomposition (QSVD), which can embed large payloads into color images with low distortion, and can obtain strong robustness to process color image in a holistic ...
Yong Chen +3 more
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Construction of dual-generalized complex Fibonacci and Lucas quaternions
Karpatsʹkì Matematičnì Publìkacìï, 2022 The aim of this paper is to construct dual-generalized complex Fibonacci and Lucas quaternions. It examines the properties both as dual-generalized complex number and as quaternion. Additionally, general recurrence relations, Binet's formulas, Tagiuri's (
G.Y. Şentürk, N. Gürses, S. Yüce
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Functional Calculus for Dual Quaternions
Advances in Applied Clifford Algebras, 2023 We give a formula for $f(η)$, where $f :\mathbb C \to \mathbb C$ is a continuously differentiable function satisfying $f(\bar z) = \overline{f(z)}$, and $η$ is a dual quaternion. Note this formula is straightforward or well known if $η$ is merely a dual number or a quaternion.
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A new proof of the generalized Hamiltonian–Real calculus [PDF]
Royal Society Open Science, 2016 The recently introduced generalized Hamiltonian–Real (GHR) calculus comprises, for the first time, the product and chain rules that makes it a powerful tool for quaternion-based optimization and adaptive signal processing.
Dongpo Xu, Hua Gao, Danilo P. Mandic
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A dual quaternion algorithm of the Helmert transformation problem
Earth, Planets and Space, 2018 Rigid transformation including rotation and translation can be elegantly represented by a unit dual quaternion. Thus, a non-differential model of the Helmert transformation (3D seven-parameter similarity transformation) is established based on unit dual ...
Huaien Zeng +3 more
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On Rayleigh Quotient Iteration for the Dual Quaternion Hermitian Eigenvalue Problem
MathematicsThe application of eigenvalue theory to dual quaternion Hermitian matrices holds significance in the realm of multi-agent formation control. In this paper, we study the use of Rayleigh quotient iteration (RQI) for solving the right eigenpairs of dual ...
Shan-Qi Duan +2 more
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A Novel Distribution for Representation of 6D Pose Uncertainty
Micromachines, 2022 The 6D Pose estimation is a crux in many applications, such as visual perception, autonomous navigation, and spacecraft motion. For robotic grasping, the cluttered and self-occlusion scenarios bring new challenges to the this field.
Lei Zhang, Huiliang Shang, Yandan Lin
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Dual-Quaternion Fourier Transform
CoRR, 2023 Fourier transform (FT) plays a crucial role in a broad range of applications, from enhancement, restoration and analysis through to security, compression and manipulation. The Fourier transform (FT) is a process that converts a function into a form that describes the frequencies.
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On tertions and dual numbers [PDF]
Notes on Number Theory and Discrete MathematicsIn a previous author's paper [1], the mathematical object called "tertion" was discussed. Some operations over tertions were introduced and their properties were studied. There, it was showed that the complex numbers and quaternions can be represented by
Krassimir T. Atanassov
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A Closed-Form Solution to Linear Feature-Based Registration of LiDAR Point Clouds
Remote Sensing, 2021 Due to the high complexity of geo-spatial entities and the limited field of view of LiDAR equipment, pairwise registration is a necessary step for integrating point clouds from neighbouring LiDAR stations.
Yongbo Wang +3 more
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