• Publications
  • Influence
Sparse Multi-Scale Diffeomorphic Registration: The Kernel Bundle Framework
TLDR
The kernel bundle extension of the LDDMM framework that allows multiple kernels at multiple scales to be incorporated in the registration is presented and the mathematical foundation of the framework is presented with derivation of the KB-EPDiff evolution equations.
Manifold Valued Statistics, Exact Principal Geodesic Analysis and the Effect of Linear Approximations
TLDR
A comparison between the non-linear analog of Principal Component Analysis, Principal Geodesic Analysis, in its linearized form and its exact counterpart that uses true intrinsic distances is presented.
Anisotropic Distributions on Manifolds: Template Estimation and Most Probable Paths
TLDR
This work uses anisotropic diffusion processes to generalize normal distributions to manifolds and to construct a framework for likelihood estimation of template and covariance structure from manifold valued data, and derives flow equations for the most probable paths reaching sampled data points.
A Geometric Framework for Stochastic Shape Analysis
TLDR
This work derives two approaches for inferring parameters of the stochastic model from landmark configurations observed at discrete time points and employs an expectation-maximization based algorithm using a Monte Carlo bridge sampling scheme to optimise the data likelihood.
Optimization over geodesics for exact principal geodesic analysis
TLDR
This paper develops methods for numerically solving optimization problems over spaces of geodesics using numerical integration of Jacobi fields and second order derivatives of geodeic families and exemplifies the differences between the linearized and exact algorithms caused by the non-linear geometry.
Latent Space Non-Linear Statistics
TLDR
This paper develops new techniques for maximum likelihood inference in latent space, and adress the computational complexity of using geometric algorithms with high-dimensional data by training a separate neural network to approximate the Riemannian metric and cometric tensor capturing the shape of the learned data manifold.
Diffusion bridges for stochastic Hamiltonian systems with applications to shape analysis
TLDR
This work develops a general scheme for bridge sampling in the case of finite dimensional systems of shape landmarks and singular solutions in fluid dynamics, that covers stochastic landmark models for which no suitable simulation method has been proposed in the literature.
Kernel Bundle Diffeomorphic Image Registration Using Stationary Velocity Fields and Wendland Basis Functions
TLDR
Experimental results show that wKB-SVF is a robust, flexible registration framework that allows theoretically well-founded and computationally efficient multi-scale representation of deformations and is equally well-suited for both inter- and intra-subject image registration.
Horizontal Dimensionality Reduction and Iterated Frame Bundle Development
TLDR
A dimensionality reduction procedure for data in Riemannian manifolds that moves the analysis from a center point to local distance measurements, providing a natural view of data generated by multimodal distributions and stochastic processes.
...
1
2
3
4
5
...