Related papers: Diffeomorphic density registration
This study proposes an end-to-end unsupervised diffeomorphic deformable registration framework based on moving mesh parameterization. Using this parameterization, a deformation field can be modeled with its transformation Jacobian…
Modern machine learning increasingly leverages the insight that high-dimensional data often lie near low-dimensional, non-linear manifolds, an idea known as the manifold hypothesis. By explicitly modeling the geometric structure of data…
Registration is a fundamental task in medical robotics and is often a crucial step for many downstream tasks such as motion analysis, intra-operative tracking and image segmentation. Popular registration methods such as ANTs and NiftyReg…
Purpose: This study aims to explore training strategies to improve convolutional neural network-based image-to-image deformable registration for abdominal imaging. Methods: Different training strategies, loss functions, and transfer…
The simulation of physical phenomena with computer models relies on the estimation of physical and/or numerical parameters calibrated to fit experimental data. The approximations within the computer model and the errors in the measurements…
We introduce a compactification of the space of simple positive divisors on a Riemann surface, as well as a compactification of the universal family of punctured surfaces above this space. These are real manifolds with corners. We then…
Conventional deformable registration methods aim at solving an optimization model carefully designed on image pairs and their computational costs are exceptionally high. In contrast, recent deep learning based approaches can provide fast…
Physical reasons suggested in \cite{Ha-Ha} for the \emph{Quantum Gravity Problem} lead us to study \emph{type-changing metrics} on a manifold. The most interesting cases are \emph{Transverse Riemann-Lorentz Manifolds}. Here we study the…
Generalised diffeomorphisms in double field theory rely on an O(d,d) structure defined on tangent space. We show that any (pseudo-)Riemannian metric on the doubled space defines such a structure, in the sense that the generalised…
We provide a full characterization of geodesic completeness for spaces of configurations of landmarks with smooth Riemannian metrics that satisfy a rotational and translation invariance and which are induced from metrics on subgroups of the…
This study proposes a systematic image registration approach to align 2D optical thin-section images within a 3D digital rock volume. Using template image matching with differential evolution optimization, we identify the most similar 2D…
Shape optimization is commonly applied in engineering to optimize shapes with respect to an objective functional relying on PDE solutions. In this paper, we view shape optimization as optimization on Riemannian shape manifolds. We consider…
Under the fluctuation of the electric charge and atomic mass, this paper considers the theory of the thin film depletion layer formation of an ensemble of finitely excited, non-empty $d/f$-orbital heavy materials, from the thermodynamic…
We study the persistent homology of both functional data on compact topological spaces and structural data presented as compact metric measure spaces. One of our goals is to define persistent homology so as to capture primarily properties…
Classical deformable registration techniques achieve impressive results and offer a rigorous theoretical treatment, but are computationally intensive since they solve an optimization problem for each image pair. Recently, learning-based…
Purpose: Electron density is the most important tissue property influencing photon and ion dose distributions in radiotherapy patients. Dual-energy computed tomography (DECT) enables the determination of electron density by combining the…
We study a gradient flow on Sobolev diffeomorphisms for the problem of image registration. The energy functional quantifies the effect of transforming a template to a target, while also penalizing deformation of the metric tensor. The main…
We show that certain right-invariant metrics endow the infinite-dimensional Lie group of all smooth orientation-preserving diffeomorphisms of the circle with a Riemannian structure. The study of the Riemannian exponential map allows us to…
We analyze a variational time discretization of geodesic calculus on finite- and certain classes of infinite-dimensional Riemannian manifolds. We investigate the fundamental properties of discrete geodesics, the associated discrete…
We first introduce a class of divergence measures between power spectral density matrices. These are derived by comparing the suitability of different models in the context of optimal prediction. Distances between "infinitesimally close"…