ACM SIGGRAPH 2005 Papers
ISMAR '05 Proceedings of the 4th IEEE/ACM International Symposium on Mixed and Augmented Reality
Intrinsic Statistics on Riemannian Manifolds: Basic Tools for Geometric Measurements
Journal of Mathematical Imaging and Vision
Journal of Mathematical Imaging and Vision
Skinning with dual quaternions
Proceedings of the 2007 symposium on Interactive 3D graphics and games
Geometric skinning with approximate dual quaternion blending
ACM Transactions on Graphics (TOG)
Statistical Computing on Manifolds: From Riemannian Geometry to Computational Anatomy
Emerging Trends in Visual Computing
An algorithm to compute averages on matrix Lie groups
IEEE Transactions on Signal Processing
Vision-based estimation of three-dimensional position and pose of multiple underwater vehicles
IROS'09 Proceedings of the 2009 IEEE/RSJ international conference on Intelligent robots and systems
Distributed collaborative localization of multiple vehicles from relative pose measurements
Allerton'09 Proceedings of the 47th annual Allerton conference on Communication, control, and computing
Distributed consensus on camera pose
IEEE Transactions on Image Processing
Distributed consensus algorithms for merging feature-based maps with limited communication
Robotics and Autonomous Systems
Statistics of shape via principal geodesic analysis on lie groups
CVPR'03 Proceedings of the 2003 IEEE computer society conference on Computer vision and pattern recognition
ICEC'06 Proceedings of the 5th international conference on Entertainment Computing
On averaging in clifford groups
IWMM'04/GIAE'04 Proceedings of the 6th international conference on Computer Algebra and Geometric Algebra with Applications
Applications of conformal geometric algebra in computer vision and graphics
IWMM'04/GIAE'04 Proceedings of the 6th international conference on Computer Algebra and Geometric Algebra with Applications
A closed-form solution to the problem of averaging over the lie group of special orthogonal matrices
ISNN'10 Proceedings of the 7th international conference on Advances in Neural Networks - Volume Part I
Rotation averaging with application to camera-rig calibration
ACCV'09 Proceedings of the 9th Asian conference on Computer Vision - Volume Part II
International Journal of Robotics Research
Iterative Estimation of Rigid-Body Transformations
Journal of Mathematical Imaging and Vision
Image and Vision Computing
Conjugate gradient on Grassmann manifolds for robust subspace estimation
Image and Vision Computing
Fitting smoothing splines to time-indexed, noisy points on nonlinear manifolds
Image and Vision Computing
Advances in matrix manifolds for computer vision
Image and Vision Computing
Consensus algorithms in a multi-agent framework to solve PTZ camera reconfiguration in UAVs
ICIRA'12 Proceedings of the 5th international conference on Intelligent Robotics and Applications - Volume Part I
EUROSCA'12 Proceedings of the 11th ACM SIGGRAPH / Eurographics conference on Computer Animation
Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation
SMI 2013: Morphological shape generation through user-controlled group metamorphosis
Computers and Graphics
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In this paper we give precise definitions of different, properly invariant notions of mean or average rotation. Each mean is associated with a metric in SO(3). The metric induced from the Frobenius inner product gives rise to a mean rotation that is given by the closest special orthogonal matrix to the usual arithmetic mean of the given rotation matrices. The mean rotation associated with the intrinsic metric on SO(3) is the Riemannian center of mass of the given rotation matrices. We show that the Riemannian mean rotation shares many common features with the geometric mean of positive numbers and the geometric mean of positive Hermitian operators. We give some examples with closed-form solutions of both notions of mean.