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Noise smoothing for VR equipment in quaternions

1998 IIE Transactions  
The former is described by a space curve in 3-dimensional Euclidean space, while the latter is represented by a curve in the unit quaternion space.  ...  Smooth motion generation is an important issue in the computer animation and virtual reality (VR) area. In general, the motion of a rigid body consists of translation and orientation.  ...  The rest of this paper is organized as follows: Section 2 gives a review of the crucial properties of a unit quaternion, Section 3 presents our motion-fairing technique with experimental results, and Section  ... 
doi:10.1080/07408179808966503 fatcat:dz34ke2l3nhjbmy5uhikcdoeie

Pose Representations for Deep Skeletal Animation [article]

Nefeli Andreou, Andreas Aristidou, Yiorgos Chrysanthou
2022 arXiv   pre-print
Our representation is based on dual quaternions, the mathematical abstractions with well-defined operations, which simultaneously encode rotational and positional orientation, enabling a hierarchy-aware  ...  nuances correlated with skeletal characteristics.  ...  Acknowledgements The authors would like to thank Anastasios Yiannakidis for his help in rendering the results and helping with the implementation of the acRNN model, as well as Victoria Fernández Abrevaya  ... 
arXiv:2111.13907v2 fatcat:3osbcojzhzgwtkobu73qulnswe

Multiview registration via graph diffusion of dual quaternions

Andrea Torsello, Emanuele Rodola, Andrea Albarelli
2011 CVPR 2011  
The approach allows for a completely generic topology with which the pairwise motions are diffused.  ...  The projection is performed by representing the motions as dual quaternions, an algebraic structure that is related to the group of 3D rigid transformations, and by performing a diffusion along the graph  ...  Quaternions with unitary norm are called unit quaternions.  ... 
doi:10.1109/cvpr.2011.5995565 dblp:conf/cvpr/TorselloRA11 fatcat:4gceu44uvzesdjgo4zwnunm66q

On quaternion analyticity: Enabling quaternion-valued nonlinear adaptive filtering

Bukhari Che Ujang, Clive Cheong Took, Danilo P. Mandic
2012 2012 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)  
The introduced class of algorithms make full use of quaternion algebra and provide generic extensions of the corresponding real and complex solutions.  ...  The strict Cauchy-Riemann-Fueter (CRF) analyticity conditions establish that only linear quaternion-valued functions are analytic, prohibiting the development of quaternion-valued nonlinear adaptive filters  ...  For a fair comparison, we also considered the performance of three parallel real-valued RNNs trained with RTRL [10] .  ... 
doi:10.1109/icassp.2012.6288329 dblp:conf/icassp/UjangTM12 fatcat:une4zbg4svdmzn4z7g34fkukpu

General construction of time-domain filters for orientation data

Jehee Lee, Sung Yong Shin
2002 IEEE Transactions on Visualization and Computer Graphics  
His recent research interests include motion capture and retargeting, performance-based computer animation, real-time rendering, and collision detection.  ...  Capturing live motion has gained considerable attention in computer animation as an important motion generation technique. Canned motion data comprise both position and orientation components.  ...  A quaternion of unit length is called a unit quaternion, which can be considered a point on the unit hyper-sphere Ë ¿ .  ... 
doi:10.1109/2945.998665 fatcat:iey2yxslungpvb2qjchbge24di

Quaternion Space Sparse Decomposition for Motion Compression and Retrieval [article]

Mingyang Zhu, Huaijiang Sun, Zhigang Deng
2012 Proceedings of the 2004 ACM SIGGRAPH/Eurographics symposium on Computer animation - SCA '04  
) with the sparseness constraint on the weight part.  ...  on quaternion.  ...  A rotational transformation can be representated as a unit quaternion, and we denote the unit quaternion space as S 3 .  ... 
doi:10.2312/sca/sca12/183-192 fatcat:zqej6y74ajakpnepfcgulokjje

Fusing Inertial Sensor Data in an Extended Kalman Filter for 3D Camera Tracking

Arif Tanju Erdem, Ali Ozer Ercan
2015 IEEE Transactions on Image Processing  
We show using both simulated and real data that it is always better to fuse both sensors in the measurement stage and that in particular, accelerometer helps more with the 3D position tracking accuracy  ...  useful when the camera undergoes fast motion.  ...  + ⋅ = 1. (8) A unit quaternion represents a rotation by an angle around a unit axis , which are related to the quaternion components as = ! ! and = ! !  ... 
doi:10.1109/tip.2014.2380176 pmid:25531951 fatcat:dkqxyraleba4pgay32vtvdgd2a

Concurrent Validity of Accelerations Measured Using a Tri-Axial Inertial Measurement Unit while Walking on Firm, Compliant and Uneven Surfaces

Michael H. Cole, Wolbert van den Hoorn, Justin K. Kavanagh, Steven Morrison, Paul W. Hodges, James E. Smeathers, Graham K. Kerr, Friedemann Paul
2014 PLoS ONE  
a real-world setting (all differences ,0.16 m.s 22 ).  ...  The findings demonstrated excellent agreement between accelerations derived from the inertial measurement unit and motion analysis system, including while walking on uneven surfaces that better approximate  ...  Acknowledgments The authors thank Ms Jodi Rippey, Ms Cara Graepel and Dr Feng Qiu for assistance with data collection and the participants who gave so generously of their time. Author Contributions  ... 
doi:10.1371/journal.pone.0098395 pmid:24866262 pmcid:PMC4035289 fatcat:upabqf7csvdnlf6odywtmow27e

Optimal least-squares solution to the hand-eye calibration problem

Amit Dekel, Linus Harenstam-Nielsen, Sergio Caccamo
2020 2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)  
We propose a least-squares formulation to the noisy handeye calibration problem using dual-quaternions, and introduce efficient algorithms to find the exact optimal solution, based on analytic properties  ...  SE(3) can be represented by unit DQ, Q = q + ǫq ′ with Q ⊗ Q * = 1, where q, q ′ ∈ H, ⊗ is the quaternionic product, and * is the usual quaternion conjugation.  ...  Lower table: Algorithm's timing averaged over 24500 real data runs.  ... 
doi:10.1109/cvpr42600.2020.01361 dblp:conf/cvpr/DekelHC20 fatcat:3zhb7oyo3jcpvco442wzu3y664

Egomotion using assorted features

Vivek Pradeep, Jongwoo Lim
2010 2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition  
Utilizing trifocal tensor geometry and quaternion representation of rotation matrices, we develop a polynomial system from which camera motion parameters can be robustly extracted in the presence of noise  ...  We describe a novel and robust minimal solver for performing online visual odometry with a stereo rig.  ...  Introduction Real-time estimation of camera motion using only sparse sets of features from visual input is an active research topic in the computer vision and robotics communities.  ... 
doi:10.1109/cvpr.2010.5539792 dblp:conf/cvpr/PradeepL10 fatcat:h44bt7vlergxhk3vw77htxewre

Double NURBS trajectory generation and synchronous interpolation for five-axis machining based on dual quaternion algorithm

Jun Zhang, Liqiang Zhang, Kai Zhang, Jian Mao
2015 The International Journal of Advanced Manufacturing Technology  
By utilizing dual-quaternion to describe five-axis tool posture, the linear tool path in WCS is fitted with dualquaternion B-spline vector function in order to obtain the equidistant double NURBS curves  ...  An equidistant double NURBS tool paths (EDNTP) fairing method satisfying the given fitting accuracy is proposed for the linear tool path in work coordinate system (WCS).  ...  If P is one point of the rigid body with the following relations: p ¼ Ap þ d ð5Þ The above spatial displacement of rigid body can be described with dual quaternion as follows: Z ¼ Z þ εR ð6Þ The real part  ... 
doi:10.1007/s00170-015-7723-9 fatcat:oomhmpunozcbziikjoby6mwju4

Compressing deep quaternion neural networks with targeted regularization

Riccardo Vecchi, Simone Scardapane, Danilo Comminiello, Aurelio Uncini
2020 CAAI Transactions on Intelligence Technology  
In addition, for many real-world applications and embedded implementations, there is the need of designing sufficiently compact networks, with few weights and neurons.  ...  Similar to their real-valued counterparts, quaternion neural networks require custom regularisation strategies to avoid overfitting.  ...  For fairness, we also compared two additional baselines, where we add the BN layers, but regularise only with the R Q or R QL strategies.  ... 
doi:10.1049/trit.2020.0020 fatcat:aqwj6xzfqvcsbkhzauku7j26e4

Quaternion correlation for tracking crystal motions

Qiwei Shi, Félix Latourte, François Hild, Stéphane Roux
2016 Measurement science and technology  
Both synthetic and real experimental cases are considered to illustrate the method.  ...  Introducing a quaternion-based formalism reveals very convenient to handle crystal symmetry and orientation extraction.  ...  Acknowledgments The authors acknowledge the financial support of EDF with R&D MAP and PERFORM projects.  ... 
doi:10.1088/0957-0233/27/9/095006 fatcat:n525dwolsff3jiffg3btkq4jpq

Dual Quaternion Based Close Proximity Operation for In-Orbit Assembly via Model Predictive Control

Chuqi Sun, Yan Xiao, Zhaowei Sun, Dong Ye, Jiafu Liu
2021 International Journal of Aerospace Engineering  
A six-degree-of-freedom (6-DOF) motion control for in-orbit assembly close proximity operation between a service satellite and a target satellite is addressed in detail.  ...  The dynamics based on dual quaternion are introduced to dispose the coupling effect between translation and rotation in a succinct frame, in which relevant perturbation and disturbance are involved.  ...  Similar to complex numbers, dual numbers consist of real and dual parts denoted as: z = a + εb, where ε 2 = 0, ε ≠ 0: ð11Þ In terms of Clifford algebra, dual quaternion fills the real and dual part with  ... 
doi:10.1155/2021/1305095 fatcat:7qijhe527jgqpptzg5qoip5r4a

Robust H-infinity kinematic control of manipulator robots using dual quaternion algebra [article]

Luis Felipe Cruz Figueredo, Bruno Vilhena Adorno, João Yoshiyuki Ishihara
2021 arXiv   pre-print
requirements with minimum instantaneous control effort.  ...  dual quaternions.  ...  such as homogeneous transformation matrices (HTM) and unit dual quaternions.  ... 
arXiv:1811.05436v3 fatcat:rhbujumpbbdozlpj3rqqbtm62u
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