Journal of Mathematical Imaging and Vision
A Riemannian approach to anisotropic filtering of tensor fields
Signal Processing
Statistical Computing on Manifolds: From Riemannian Geometry to Computational Anatomy
Emerging Trends in Visual Computing
Fast GL(n)-Invariant Framework for Tensors Regularization
International Journal of Computer Vision
Learning averages over the lie group of symmetric positive-definite matrices
IJCNN'09 Proceedings of the 2009 international joint conference on Neural Networks
New Riemannian techniques for directional and tensorial image data
Pattern Recognition
Higher-order smoothing splines versus least squares problems on Riemannian manifolds
Journal of Dynamical and Control Systems
An algorithm to compute averages on matrix Lie groups
IEEE Transactions on Signal Processing
Riemannian Metric and Geometric Mean for Positive Semidefinite Matrices of Fixed Rank
SIAM Journal on Matrix Analysis and Applications
Riemannian geometry applied to BCI classification
LVA/ICA'10 Proceedings of the 9th international conference on Latent variable analysis and signal separation
Convergence and smoothness analysis of subdivision rules in Riemannian and symmetric spaces
Advances in Computational Mathematics
A differential-geometrical framework for color image quality measures
ISVC'10 Proceedings of the 6th international conference on Advances in visual computing - Volume Part III
Journal of Mathematical Imaging and Vision
Horoball hulls and extents in positive definite space
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
A note on computing matrix geometric means
Advances in Computational Mathematics
Smoothing tensor-valued images using anisotropic geodesic diffusion
SSPR'06/SPR'06 Proceedings of the 2006 joint IAPR international conference on Structural, Syntactic, and Statistical Pattern Recognition
Fast and simple calculus on tensors in the log-euclidean framework
MICCAI'05 Proceedings of the 8th international conference on Medical Image Computing and Computer-Assisted Intervention - Volume Part I
A riemannian approach to diffusion tensor images segmentation
IPMI'05 Proceedings of the 19th international conference on Information Processing in Medical Imaging
Riemannian graph diffusion for DT-MRI regularization
MICCAI'06 Proceedings of the 9th international conference on Medical Image Computing and Computer-Assisted Intervention - Volume Part II
Image and Vision Computing
Fitting smoothing splines to time-indexed, noisy points on nonlinear manifolds
Image and Vision Computing
Sampling-free linear Bayesian update of polynomial chaos representations
Journal of Computational Physics
Anisotropy Preserving DTI Processing
International Journal of Computer Vision
Fitting polynomial volumes to surface meshes with Voronoï squared distance minimization
SGP '13 Proceedings of the Eleventh Eurographics/ACMSIGGRAPH Symposium on Geometry Processing
Hi-index | 0.01 |
In this paper we introduce metric-based means for the space of positive-definite matrices. The mean associated with the Euclidean metric of the ambient space is the usual arithmetic mean. The mean associated with the Riemannian metric corresponds to the geometric mean. We discuss some invariance properties of the Riemannian mean and we use differential geometric tools to give a characterization of this mean.