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On the closed-form solution of the rotation matrix arising in computer vision problems [article]

Andriy Myronenko, Xubo Song
2009 arXiv   pre-print
This problem occurs in many computer vision tasks involving optimal rotation matrix estimation. The solution has been continuously reinvented in different fields as part of specific problems.  ...  We show the closed-form solution to the maximization of trace(A'R), where A is given and R is unknown rotation matrix.  ...  Introduction Many computer vision problems that require estimation of the optimal rotation matrix reduce to the maximization of tr(A T R) 1 for a given matrix A: max tr(A T R), s.t.  ... 
arXiv:0904.1613v1 fatcat:w5e2ycscsrbtpmi4svs6j37znu

Comparing two sets of corresponding six degree of freedom data

Mili Shah
2011 Computer Vision and Image Understanding  
Specifically, the best rotation and translation that aligns the position and orientation of one data set to the other is constructed by solving an optimization problem.  ...  In addition, a statistical method that identifies outliers in the data sets is proposed.  ...  This closed formed solution is similar to the closed formed solutions for the hand-eye calibration problem AX = ZB.  ... 
doi:10.1016/j.cviu.2011.05.007 fatcat:mskxgzapfzhahgmfdgan5v4w5y

Hand-Eye Calibration without Hand Orientation Measurement Using Minimal Solution [chapter]

Zuzana Kukelova, Jan Heller, Tomas Pajdla
2013 Lecture Notes in Computer Science  
In this paper we solve the problem of estimating the relative pose between a robot's gripper and a camera mounted rigidly on the gripper in situations where the rotation of the gripper w.r.t. the robot  ...  Further, we describe a method for selecting the geometrically correct solution among the algebraically correct ones computed by the solver.  ...  Acknowledgment The authors were supported by the EC under projects FP7-SME-2011-285839 De-Montes and FP7-288553 CloPeMa and by Grant Agency of the CTU Prague project SGS12/191/OHK3/3T/13.  ... 
doi:10.1007/978-3-642-37447-0_44 fatcat:lnv7ovcvkzbutinudp3ai5mbne

Complete Initial Solutions for Iterative Pose Estimation From Planar Objects

Kai Zhou, Xiangjun Wang, Zhong Wang, Hong Wei, Lei Yin
2018 IEEE Access  
Camera pose estimation from the image of a planar object has important applications in photogrammetry and computer vision.  ...  as the best state-of-the-art pose estimation algorithms, while with a significant decrease in computational cost.  ...  ACKNOWLEDGMENT The authors would like to thank Bo Lv and Yin Guan for designing the experimental platform. They also appreciate Yu Cao and Yu Feng's contribution on DSP programming.  ... 
doi:10.1109/access.2018.2827565 fatcat:ljqssdc34rhm3euppsontn3e2q

Robust Software for Computing Camera Motion Parameters

Robert Schreiber, Zeyu Li, Harlyn Baker
2008 Journal of Mathematical Imaging and Vision  
We revisit the method of Tsai, Huang, and Zhu for the computation of camera motion parameters in computer vision.  ...  We show how to correct for noise by finding the rank-one perturbation of a rotation closest to a give matrix.  ...  We call any matrix of the form (1) a rank-one perturbation of a rotation or ROPR.  ... 
doi:10.1007/s10851-008-0106-1 fatcat:qujsitgflzajnfj7ovvsxry67u

An Efficient Minimal Solution for Multi-camera Motion

Jonathan Ventura, Clemens Arth, Vincent Lepetit
2015 2015 IEEE International Conference on Computer Vision (ICCV)  
Existing methods for solving the multi-camera relative pose problem require extra correspondences, are slow to compute, and/or produce a multitude of solutions.  ...  Our solution uses a first-order approximation to relative pose in order to simplify the problem and produce an accurate estimate quickly.  ...  Acknowledgments This work was partially supported by NSF IIS-1464420 and the Christian Doppler Laboratory on Handheld AR.  ... 
doi:10.1109/iccv.2015.92 dblp:conf/iccv/VenturaAL15 fatcat:qdplqlcsgvh73eq6p3d2gyiz3i

Absolute pose for cameras under flat refractive interfaces

Sebastian Haner, Kalle Astrom
2015 2015 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)  
Closed-form solu- Computer Vision and Pattern Recognition, pages 125–132.  ...  Polynomial eigen- motion on underwater images. In International Conference value solutions to minimal problems in computer vision.  ... 
doi:10.1109/cvpr.2015.7298749 dblp:conf/cvpr/HanerA15 fatcat:wsoqph7yhzbnno76tsxqfdcqqy

A Closed-Form Solution to Non-Rigid Shape and Motion Recovery

Jing Xiao, Jinxiang Chai, Takeo Kanade
2006 International Journal of Computer Vision  
This paper proves that, under the weak-perspective projection model, once both the basis and the rotation constraints are imposed, we achieve a closed-form solution to the problem of non-rigid shape and  ...  The accuracy and robustness of our closed-form solution is evaluated quantitatively on synthetic data and qualitatively on real video sequences.  ...  Now the question is: is every solution in the space a valid solution of Q? If so, even if the ambiguity exists, one can compute an arbitrary solution in the space to solve the problem.  ... 
doi:10.1007/s11263-005-3962-9 fatcat:wzmefzcw5nbtbcd6u24oqn3gke

On Affine Invariant Clustering and Automatic Cast Listing in Movies [chapter]

Andrew Fitzgibbon, Andrew Zisserman
2002 Lecture Notes in Computer Science  
Such clustering requirements are generic to a number of problems in computer vision.  ...  For the particular special case of corresponding point sets we demonstrate that the affine invariant measure we introduced may be obtained in closed form.  ...  David Capel and Michael Black made a number of helpful comments. Funding was provided by the Royal Society and the EC CogViSys project.  ... 
doi:10.1007/3-540-47977-5_20 fatcat:e6cgfysjynerrhovm3at4tlg6m

Fast and Stable Algebraic Solution to L2 Three-View Triangulation

Zuzana Kukelova, Tomas Pajdla, Martin Bujnak
2013 2013 International Conference on 3D Vision  
In this paper we provide a new fast and stable algebraic solution to the problem of L 2 triangulation from three views.  ...  We evaluate the precision and speed of our solver on both synthetic and real datasets. 1  ...  Introduction The triangulation [13] is one of the fundamental problems in computer vision and it is an important part of all structurefrom-motion systems [23, 21] .  ... 
doi:10.1109/3dv.2013.50 dblp:conf/3dim/KukelovaPB13 fatcat:ru2vqe7n3zfcfg445kurpkviby

Simultaneous Multiple Rotation Averaging Using Lagrangian Duality [chapter]

Johan Fredriksson, Carl Olsson
2013 Lecture Notes in Computer Science  
Multiple rotation averaging is an important problem in computer vision. The problem is challenging because of the nonlinear constraints required to represent the set of rotations.  ...  To our knowledge no one has proposed any globally optimal solution for the case of simultaneous updates of the rotations.  ...  through the programme GlobalVision and the Swedish strategic research project ELLIIT.  ... 
doi:10.1007/978-3-642-37431-9_19 fatcat:46ookv23ordxvno7eukrjlqnzu

Making minimal solvers fast

M. Bujnak, Z. Kukelova, T. Pajdla
2012 2012 IEEE Conference on Computer Vision and Pattern Recognition  
We demonstrate them on three important minimal computer vision problems. 1  ...  In this paper we propose methods for speeding up minimal solvers based on Gröbner bases and action matrix eigenvalue computations.  ...  It is because in this solution almost all computations can be done in a closed form.  ... 
doi:10.1109/cvpr.2012.6247840 dblp:conf/cvpr/BujnakKP12 fatcat:lgm7b4mmqfhbjozpqpy7zzsz6i

Revisiting the PnP Problem: A Fast, General and Optimal Solution

Yinqiang Zheng, Yubin Kuang, Shigeki Sugimoto, Kalle Astrom, Masatoshi Okutomi
2013 2013 IEEE International Conference on Computer Vision  
The novelty lies in a non-unit quaternion representation to parameterize the rotation and a simple but elegant formulation of the PnP problem into an unconstrained optimization problem.  ...  In this paper, we revisit the classical perspective-n-point (PnP) problem, and propose the first non-iterative O(n) solution that is fast, generally applicable and globally optimal.  ...  This work was partially supported by the Grants-in-Aid for Scientific Research (no. 25240025) from the Japan Society for the Promotion of Science, and the strategic research projects ELLIIT and eSSENCE  ... 
doi:10.1109/iccv.2013.291 dblp:conf/iccv/ZhengKSAO13 fatcat:dokjqqvxsbhbzlkyjzlju54qum

Rotation Averaging and Strong Duality

Anders Eriksson, Carl Olsson, Fredrik Kahl, Tat-Jun Chin
2018 2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition  
In this paper we explore the role of duality principles within the problem of rotation averaging, a fundamental task in a wide range of computer vision applications.  ...  In its conventional form, rotation averaging is stated as a minimization over multiple rotation constraints.  ...  This work has been funded by the Australian Research Council through grants FT170100072 and DP160103490, the Swedish Research Council (no. 2016-04445), the Swedish Foundation for Strategic Research (Semantic  ... 
doi:10.1109/cvpr.2018.00021 dblp:conf/cvpr/ErikssonOKC18 fatcat:tar77vspuza6diblflix3b24ry

A semi-supervised framework for mapping data to the intrinsic manifold

Haifeng Gong, Chunhong Pan, Qing Yang, Hanqing Lu, Songde Ma
2005 Tenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1  
The experiments show that APD can recover the underlying intrinsic parameters of points on scattered data manifold successfully.  ...  Given a set of partially labeled points, the map to a specified parameter manifold is computed by an iterative neighborhood average method called Anchor Points Diffusion procedure (APD).  ...  Saul for providing the teapot and trefoil data. The first author would like to thank Jian Cheng and Gökhan H. Bakır for many helpful discussions.  ... 
doi:10.1109/iccv.2005.18 dblp:conf/iccv/GongPYLM05 fatcat:aobhe3dn3jb53hqibs7clrwy3a
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