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A Novel Perceptual Hashing for Color Images Using a Full Quaternion Representation
( Xiaomei Xing ),( Yuesheng Zhu ),( Zhiwei Mo ),( Ziqiang Sun ),( Zhen Liu ) 한국인터넷정보학회 2015 KSII Transactions on Internet and Information Syst Vol.9 No.12
Quaternions have been commonly employed in color image processing, but when the existing pure quaternion representation for color images is used in perceptual hashing, it would degrade the robustness performance since it is sensitive to image manipulations. To improve the robustness in color image perceptual hashing, in this paper a full quaternion representation for color images is proposed by introducing the local image luminance variances. Based on this new representation, a novel Full Quaternion Discrete Cosine Transform (FQDCT)-based hashing is proposed, in which the Quaternion Discrete Cosine Transform (QDCT) is applied to the pseudo-randomly selected regions of the novel full quaternion image to construct two feature matrices. A new hash value in binary is generated from these two matrices. Our experimental results have validated the robustness improvement brought by the proposed full quaternion representation and demonstrated that better performance can be achieved in the proposed FQDCT-based hashing than that in other notable quaternion-based hashing schemes in terms of robustness and discriminability.
Vision-Based Relative Navigation Using Dual Quaternion for Spacecraft Proximity Operations
나윤주,방효충,목성훈 한국항공우주학회 2019 International Journal of Aeronautical and Space Sc Vol.20 No.4
Dual quaternion is the parameter that can describe position and attitude in a unified form. It is extension of dual number and quaternion; so, mathematical and parameter characteristics of those are holding. The attitude and orbital kinematics model can be concurrently integrated in a simplified and intuitive formulation with dual quaternion. From these merits, dual quaternion-based relative navigation for spacecraft proximity operation is investigated in this paper. Especially, the case is considered which interested points are not coincident with center of mass of spacecraft. At this time, it is obvious that position is affected by rotational motion of rigid body. With conventional decoupled relative kinematics, this attitude–position coupling effect cannot be described at once. However, the new dual quaternion-based relative kinematics can represent coupled orbital motion in a simple form. Motivated by these backgrounds, in this paper, to estimate relative position and attitude states using vision sensor, dual quaternion-based relative kinematics is formulated. To reduce the number of state variables, error dual quaternion is applied, which makes the number of state variable be six instead of eight, by using parameter constraints of dual quaternion. Extended Kalman filter and unscented Kalman filter are adopted to realize relative navigation. Since the necessity of velocity information in dual quaternion kinematics, two types system models are constructed—velocity propagation and velocity measurement model. In addition, the six line-of-sight measurements are used to update the dual quaternion parameter. Simulation results show that the kinematics model is accurately derived, states are well estimated, and statistics of estimation errors are consistent with estimated error covariance.
Characterization of a regular function with values in dual quaternions
김지은,손광호 한국수학교육학회 2015 純粹 및 應用數學 Vol.22 No.1
In this paper, we provide the notions of dual quaternions and their algebraic properties based on matrices. From quaternion analysis, we give the concept of a derivative of functions and and obtain a dual quaternion Cauchy-Riemann system that are equivalent. Also, we research properties of a regular function with values in dual quaternions and relations derivative with a regular function in dual quaternions.
The derivative of a dual quaternionic function with values in dual quaternions
김지은,손광호 호남수학회 2015 호남수학학술지 Vol.37 No.4
This paper gives the expression of dual quaternions and provides differential operators in dual quaternions. The paper also represents the derivative of dual quaternion-valued functions by using a corresponding Cauchy-Riemann system in dual quaternions.
THE DERIVATIVE OF A DUAL QUATERNIONIC FUNCTION WITH VALUES IN DUAL QUATERNIONS
KIM, JI EUN,SHON, KWANG HO The Honam Mathematical Society 2015 호남수학학술지 Vol.37 No.4
This paper gives the expression of dual quaternions and provides differential operators in dual quaternions. The paper also represents the derivative of dual quaternion-valued functions by using a corresponding Cauchy-Riemann system in dual quaternions.
CR-Submanifolds of HP^(m) and Hypersurfaces of the Cayley Plane whose Chen-type is 1
Ivko Dimitrić KYUNGPOOK UNIVERSITY 2000 Kyungpook mathematical journal Vol.40 No.2
We consider submanifolds of the quaternion projective space HP^(m) which are of Chentype 1 in the Euclidean space of quaternion-Hermitian matrices H(m+1) via the imbedding of HP^(m) which identifies a quaternion line with the projection operator onto it. The immersion vector of each of these submanifolds, which are equivalently characterized as being minimal in hyperspheres of H(m+1), is an eigenvector of the Laplacian when translated into a suitable center. We classify totally complex, quaternion CR and anti-CR submanifolds of HP^(m) which have type 1. These include the largest stable geodesic hypersphere and minimal quaternion Lagrangian and anti-Lagrangian submanifolds. We also study 1-type submanifolds of the Cayley projective plane OP²; characterizing a hypersurface of 1-type as the one that has two constant principal curvatures with respective multiplicities 7 and 8 along two natural distributions. Such hypersurface is then shown to be a geodesic hypersphere of radius cot^(-1) √7/17 which too is maximal stable. As a byproduct of our study we obtain some new sharp upper bounds on λ₁
A polar representation of a regularity of a dual quaternionic function in Clifford analysis
김지은,손광호 대한수학회 2017 대한수학회보 Vol.54 No.2
The paper gives the regularity of dual quaternionic functions and the dual Cauchy-Riemann system in dual quaternions. Also, the paper researches the polar representation and properties of a dual quaternionic function and their regular quaternionic functions.
A POLAR REPRESENTATION OF A REGULARITY OF A DUAL QUATERNIONIC FUNCTION IN CLIFFORD ANALYSIS
Kim, Ji Eun,Shon, Kwang Ho Korean Mathematical Society 2017 대한수학회보 Vol.54 No.2
The paper gives the regularity of dual quaternionic functions and the dual Cauchy-Riemann system in dual quaternions. Also, the paper researches the polar representation and properties of a dual quaternionic function and their regular quaternionic functions.
Hypermeromorphy of functions on split quaternions in Clifford analysis
김지은,손광호 영남수학회 2015 East Asian mathematical journal Vol.31 No.5
In this paper, we consider split quaternionic functions defined on an open set of split quaternions and give the split quaternionic functions whose each inverse function is sp-hyperholomorphic almost everywhere on Ω. Also, we describe the definitions and notions of pseudoholomorphic functions for split quaternions.
A TYPE OF THE EXPONENTIAL OF A MATRIX OVER DUAL QUATERNION IN CLIFFORD ANALYSIS
Ji Eun Kim 경남대학교 수학교육과 2018 Nonlinear Functional Analysis and Applications Vol.23 No.3
This paper proposes a form and use of exponential of a matrix over dual quaternions. Due to the property of the product for dual quaternions, we give the way of computing the exponential of a matrix with the exponential map from their Lie algebras into the dual quaternionic matrices and a form of an eigenvalue of the dual quaternionic exponential of a matrix.