Robust regression and outlier detection
Robust regression and outlier detection
A Crame´r-Rao–type lower bound for estimators with values in a manifold
Journal of Multivariate Analysis
A Framework for Uncertainty and Validation of 3-D RegistrationMethods Based on Points and Frames
International Journal of Computer Vision
Hilbert-Schmidt Lower Bounds for Estimators on Matrix Lie Groups for ATR
IEEE Transactions on Pattern Analysis and Machine Intelligence
Uniform Distribution, Distance and Expectation Problems for Geometric Features Processing
Journal of Mathematical Imaging and Vision
The Geometry of Algorithms with Orthogonality Constraints
SIAM Journal on Matrix Analysis and Applications
Landmark-based registration using features identified through differential geometry
Handbook of medical imaging
International Journal of Computer Vision - Joint special issue on image analysis
Means and Averaging in the Group of Rotations
SIAM Journal on Matrix Analysis and Applications
Feature-Based Registration of Medical Images: Estimation and Validation of the Pose Accuracy
MICCAI '98 Proceedings of the First International Conference on Medical Image Computing and Computer-Assisted Intervention
Rigid Point-Surface Registration Using an EM Variant of ICP for Computer Guided Oral Implantology
MICCAI '01 Proceedings of the 4th International Conference on Medical Image Computing and Computer-Assisted Intervention
A Riemannian Framework for Tensor Computing
International Journal of Computer Vision
Journal of Mathematical Imaging and Vision
IS4TM'03 Proceedings of the 2003 international conference on Surgery simulation and soft tissue modeling
Extrapolation of sparse tensor fields: application to the modeling of brain variability
IPMI'05 Proceedings of the 19th international conference on Information Processing in Medical Imaging
Journal of Mathematical Imaging and Vision
A Riemannian approach to anisotropic filtering of tensor fields
Signal Processing
An Intrinsic Framework for Analysis of Facial Surfaces
International Journal of Computer Vision
Regularizing Flows over Lie Groups
Journal of Mathematical Imaging and Vision
Statistical Computing on Manifolds: From Riemannian Geometry to Computational Anatomy
Emerging Trends in Visual Computing
On the Topology and Geometry of Spaces of Affine Shapes
Journal of Mathematical Imaging and Vision
Kernel Density Estimation on Riemannian Manifolds: Asymptotic Results
Journal of Mathematical Imaging and Vision
Statistical M-Estimation and Consistency in Large Deformable Models for Image Warping
Journal of Mathematical Imaging and Vision
Pre-image as Karcher Mean Using Diffusion Maps: Application to Shape and Image Denoising
SSVM '09 Proceedings of the Second International Conference on Scale Space and Variational Methods in Computer Vision
Probabilistic models for shapes as continuous curves
Journal of Mathematical Imaging and Vision
Intrinsic Regression Models for Manifold-Valued Data
MICCAI '09 Proceedings of the 12th International Conference on Medical Image Computing and Computer-Assisted Intervention: Part II
New Riemannian techniques for directional and tensorial image data
Pattern Recognition
Intrinsic mean for semi-metrical shape retrieval via graph cuts
Proceedings of the 29th DAGM conference on Pattern recognition
Contributions to 3D diffeomorphic atlas estimation: application to brain images
MICCAI'07 Proceedings of the 10th international conference on Medical image computing and computer-assisted intervention - Volume Part I
Population Shape Regression from Random Design Data
International Journal of Computer Vision
ECCV'10 Proceedings of the 11th European conference on Computer vision: Part VI
Endowing canonical geometries to cardiac structures
STACOM'10/CESC'10 Proceedings of the First international conference on Statistical atlases and computational models of the heart, and international conference on Cardiac electrophysiological simulation challenge
Riemannian Metric and Geometric Mean for Positive Semidefinite Matrices of Fixed Rank
SIAM Journal on Matrix Analysis and Applications
Differential feedback of MIMO channel gram matrices based on geodesic curves
IEEE Transactions on Wireless Communications
Geodesic Methods in Computer Vision and Graphics
Foundations and Trends® in Computer Graphics and Vision
Nearest-neighbor search algorithms on non-Euclidean manifolds for computer vision applications
Proceedings of the Seventh Indian Conference on Computer Vision, Graphics and Image Processing
Diffusion maps as a framework for shape modeling
Computer Vision and Image Understanding
A Bayesian generative model for surface template estimation
Journal of Biomedical Imaging
Detection of 3D spinal geometry using iterated marginal space learning
MCV'10 Proceedings of the 2010 international MICCAI conference on Medical computer vision: recognition techniques and applications in medical imaging
Principal spine shape deformation modes using riemannian geometry and articulated models
AMDO'06 Proceedings of the 4th international conference on Articulated Motion and Deformable Objects
Performance evaluation of grid-enabled registration algorithms using bronze-standards
MICCAI'06 Proceedings of the 9th international conference on Medical Image Computing and Computer-Assisted Intervention - Volume Part II
Geodesic Polar Coordinates on Polygonal Meshes
Computer Graphics Forum
Sparse coding and dictionary learning for symmetric positive definite matrices: a kernel approach
ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part II
Manifold statistics for essential matrices
ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part II
EUROSCA'12 Proceedings of the 11th ACM SIGGRAPH / Eurographics conference on Computer Animation
Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation
International Journal of Computer Vision
Unscented Kalman Filtering on Riemannian Manifolds
Journal of Mathematical Imaging and Vision
Full Length Article: Information geometry of target tracking sensor networks
Information Fusion
Bayesian epipolar geometry estimation from tomographic projections
ACCV'12 Proceedings of the 11th Asian conference on Computer Vision - Volume Part IV
Statistical analysis of manual segmentations of structures in medical images
Computer Vision and Image Understanding
Geodesic Regression and the Theory of Least Squares on Riemannian Manifolds
International Journal of Computer Vision
A robust algorithm for template curve estimation based on manifold embedding
Computational Statistics & Data Analysis
International Journal of Computer Vision
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In medical image analysis and high level computer vision, there is an intensive use of geometric features like orientations, lines, and geometric transformations ranging from simple ones (orientations, lines, rigid body or affine transformations, etc.) to very complex ones like curves, surfaces, or general diffeomorphic transformations. The measurement of such geometric primitives is generally noisy in real applications and we need to use statistics either to reduce the uncertainty (estimation), to compare observations, or to test hypotheses. Unfortunately, even simple geometric primitives often belong to manifolds that are not vector spaces. In previous works [1, 2], we investigated invariance requirements to build some statistical tools on transformation groups and homogeneous manifolds that avoids paradoxes. In this paper, we consider finite dimensional manifolds with a Riemannian metric as the basic structure. Based on this metric, we develop the notions of mean value and covariance matrix of a random element, normal law, Mahalanobis distance and 驴2 law. We provide a new proof of the characterization of Riemannian centers of mass and an original gradient descent algorithm to efficiently compute them. The notion of Normal law we propose is based on the maximization of the entropy knowing the mean and covariance of the distribution. The resulting family of pdfs spans the whole range from uniform (on compact manifolds) to the point mass distribution. Moreover, we were able to provide tractable approximations (with their limits) for small variances which show that we can effectively implement and work with these definitions.