# Statistics on diffeomorphisms via tangent space representations

@article{Vaillant2004StatisticsOD, title={Statistics on diffeomorphisms via tangent space representations}, author={Marc Vaillant and M. I. Miller and Laurent Younes and Alain Trouv{\'e}}, journal={NeuroImage}, year={2004}, volume={23}, pages={S161-S169} }

## 238 Citations

A Log-Euclidean Framework for Statistics on Diffeomorphisms

- Mathematics, Computer ScienceMICCAI
- 2006

This article focuses on the computation of statistics of invertible geometrical deformations (i.e., diffeomorphisms), based on the generalization to this type of data of the notion of principal logarithm, which is a simple 3D vector field and well-defined for diffe morphisms close enough to the identity.

Robust Diffeomorphic Mapping via Geodesically Controlled Active Shapes

- Computer ScienceInt. J. Biomed. Imaging
- 2013

The robustness of this algorithm as applied to the workflow of a large neuroanatomical study is demonstrated by comparing to an existing diffeomorphic landmark matching algorithm.

Evolution Equations with Anisotropic Distributions and Diffusion PCA

- MathematicsGSI
- 2015

This paper presents derivations of evolution equations for the family of paths that in the Diffusion PCA framework are used for approximating data likelihood and shows how rank-deficient metrics can be mixed with an underlying Riemannian metric.

Locally Linear Diffeomorphic Metric Embedding (LLDME) for surface-based anatomical shape modeling

- MathematicsNeuroImage
- 2011

Diffeomorphic 3D Image Registration via Geodesic Shooting Using an Efficient Adjoint Calculation

- Computer Science, MathematicsInternational Journal of Computer Vision
- 2011

The key contribution of this work is to provide an accurate estimation of the so-called initial momentum, which is a scalar function encoding the optimal deformation between two images through the Hamiltonian equations of geodesics.

Multi-manifold diffeomorphic metric mapping for aligning cortical hemispheric surfaces

- PhysicsNeuroImage
- 2010

Principal Component Based Diffeomorphic Surface Mapping

- MathematicsIEEE Transactions on Medical Imaging
- 2012

This new algorithm reduces the complexity of the estimation of diffeomorphic transformations by incorporating a shape prior in which a nonlinear diffeomorph shape space is represented by a linear space of initial momenta of Diffeomorphic geodesic flows from a fixed template.

A Sub-Riemannian Modular Framework for Diffeomorphism-Based Analysis of Shape Ensembles

- MathematicsSIAM J. Imaging Sci.
- 2018

This work proposes a new mathematical and computational framework, in which velocity fields are constrained to be built through a combination of local deformation modules with few degrees of freedom, and derives a method to estimate a Frechet mean from a series of observat...

Transport of Relational Structures in Groups of Diffeomorphisms

- MathematicsJournal of Mathematical Imaging and Vision
- 2008

This paper discusses two main options for translating the relative variation of one shape with respect to another in a template centered representation, based on the Riemannian metric and the coadjoint transport.

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