Robust regression and outlier detection
Robust regression and outlier detection
Scale-Space and Edge Detection Using Anisotropic Diffusion
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Crame´r-Rao–type lower bound for estimators with values in a manifold
Journal of Multivariate Analysis
Delaunay mesh generation governed by metric specifications. Part II. applications
Finite Elements in Analysis and Design
Estimating 3-D rigid body transformations: a comparison of four major algorithms
Machine Vision and Applications - Special issue on performance evaluation
Computable elastic distances between shapes
SIAM Journal on Applied Mathematics
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
Diffeomorphisms Groups and Pattern Matching in Image Analysis
International Journal of Computer Vision
The Geometry of Algorithms with Orthogonality Constraints
SIAM Journal on Matrix Analysis and Applications
Multivariate normal distributions parametrized as a Riemannian symmetric space
Journal of Multivariate Analysis
International Journal of Computer Vision - Joint special issue on image analysis
Computational Framework for Segmentation and Grouping
Computational Framework for Segmentation and Grouping
Means and Averaging in the Group of Rotations
SIAM Journal on Matrix Analysis and Applications
The Geometry of the Newton Method on Non-Compact Lie Groups
Journal of Global Optimization
Group Actions, Homeomorphisms, and Matching: A General Framework
International Journal of Computer Vision - Special issue on statistical and computational theories of vision: Part II
Constrained Flows of Matrix-Valued Functions: Application to Diffusion Tensor Regularization
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part I
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
MICCAI '98 Proceedings of the First International Conference on Medical Image Computing and Computer-Assisted Intervention
Restricted delaunay triangulations and normal cycle
Proceedings of the nineteenth annual symposium on Computational geometry
Regularizing Flows for Constrained Matrix-Valued Images
Journal of Mathematical Imaging and Vision
Analysis of Planar Shapes Using Geodesic Paths on Shape Spaces
IEEE Transactions on Pattern Analysis and Machine Intelligence
Computing Large Deformation Metric Mappings via Geodesic Flows of Diffeomorphisms
International Journal of Computer Vision
A Differential Geometric Approach to the Geometric Mean of Symmetric Positive-Definite Matrices
SIAM Journal on Matrix Analysis and Applications
A Riemannian Framework for Tensor Computing
International Journal of Computer Vision
Geodesic Shooting for Computational Anatomy
Journal of Mathematical Imaging and Vision
Intrinsic Statistics on Riemannian Manifolds: Basic Tools for Geometric Measurements
Journal of Mathematical Imaging and Vision
Journal of Mathematical Imaging and Vision
Visualization and Processing of Tensor Fields (Mathematics and Visualization)
Visualization and Processing of Tensor Fields (Mathematics and Visualization)
Sparse Approximation of Currents for Statistics on Curves and Surfaces
MICCAI '08 Proceedings of the 11th International Conference on Medical Image Computing and Computer-Assisted Intervention, Part II
Image and Vision Computing
Riemannian elasticity: a statistical regularization framework for non-linear registration
MICCAI'05 Proceedings of the 8th international conference on Medical image computing and computer-assisted intervention - Volume Part II
A log-euclidean framework for statistics on diffeomorphisms
MICCAI'06 Proceedings of the 9th international conference on Medical Image Computing and Computer-Assisted Intervention - Volume Part I
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
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
IPMI'05 Proceedings of the 19th international conference on Information Processing in Medical Imaging
A riemannian framework for the processing of tensor-valued images
DSSCV'05 Proceedings of the First international conference on Deep Structure, Singularities, and Computer Vision
Geodesic shooting and diffeomorphic matching via textured meshes
EMMCVPR'05 Proceedings of the 5th international conference on Energy Minimization Methods in Computer Vision and Pattern Recognition
A log-euclidean polyaffine framework for locally rigid or affine registration
WBIR'06 Proceedings of the Third international conference on Biomedical Image Registration
Landmark matching via large deformation diffeomorphisms
IEEE Transactions on Image Processing
Log-domain diffeomorphic registration of diffusion tensor images
WBIR'10 Proceedings of the 4th international conference on Biomedical image registration
Diffeomorphic 3D Image Registration via Geodesic Shooting Using an Efficient Adjoint Calculation
International Journal of Computer Vision
Pattern learning and recognition on statistical manifolds: an information-geometric review
SIMBAD'13 Proceedings of the Second international conference on Similarity-Based Pattern Recognition
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Computational anatomy is an emerging discipline that aims at analyzing and modeling the individual anatomy of organs and their biological variability across a population. The goal is not only to model the normal variations among a population, but also discover morphological differences between normal and pathological populations, and possibly to detect, model and classify the pathologies from structural abnormalities. Applications are very important both in neuroscience, to minimize the influence of the anatomical variability in functional group analysis, and in medical imaging, to better drive the adaptation of generic models of the anatomy (atlas) into patient-specific data (personalization). However, understanding and modeling the shape of organs is made difficult by the absence of physical models for comparing different subjects, the complexity of shapes, and the high number of degrees of freedom implied. Moreover, the geometric nature of the anatomical features usually extracted raises the need for statistics and computational methods on objects that do not belong to standard Euclidean spaces. We investigate in this chapter the Riemannian metric as a basis for developing generic algorithms to compute on manifolds. We show that few computational tools derived from this structure can be used in practice as the atoms to build more complex generic algorithms such as mean computation, Mahalanobis distance, interpolation, filtering and anisotropic diffusion on fields of geometric features. This computational framework is illustrated with the joint estimation and anisotropic smoothing of diffusion tensor images and with the modeling of the brain variability from sulcal lines.