Related papers: Diffeomorphic density registration
Diffusion tensor cardiac magnetic resonance (DT-CMR) is a method capable of providing non-invasive measurements of myocardial microstructure. Image registration is essential to correct image shifts due to intra and inter breath-hold motion…
We discuss hypersurface motions in Riemannian manifolds whose normal velocity is a function of the induced hypersurface volume element and derive a second order partial differential equation for the corresponding time function $\tau(x)$ at…
We describe a method for recovering the irradiance underlying a collection of images corrupted by atmospheric turbulence. Since supervised data is often technically impossible to obtain, assumptions and biases have to be imposed to solve…
Deformable medical image registration is an essential task in computer-assisted interventions. This problem is particularly relevant to oncological treatments, where precise image alignment is necessary for tracking tumor growth, assessing…
In this paper, we propose a novel large deformation diffeomorphic registration algorithm to align high angular resolution diffusion images (HARDI) characterized by orientation distribution functions (ODFs). Our proposed algorithm seeks an…
In this paper, I shall demonstrate that sufficiently high-dimensional closed positively-curved Riemannian manifolds are either diffeomorphic to a spherical space form, or isometric to a locally compact rank one symmetric space. This…
Our results concern geometry of a manifold endowed with a pair of complementary orthogonal distributions (plane fields) and a time-dependent Riemannian metric. The work begins with formulae concerning deformations of geometric quantities as…
Registration, which aims to find an optimal one-to-one correspondence between different data, is an important problem in various fields. This problem is especially challenging when large deformations occur. In this paper, we present a novel…
This paper introduces and studies a metamorphosis framework for geometric measures known as varifolds, which extends the diffeomorphic registration model for objects such as curves, surfaces and measures by complementing diffeomorphic…
Whole-body Positron Emission Tomography (PET) registration is essential for multi-parametric tumor characterization and assessment of metastatic disease progression. In deep learning-based deformable registration, the dense displacement…
We survey the role of symmetry in diffeomorphic registration of landmarks, curves, surfaces, images and higher-order data. The infinite dimensional problem of finding correspondences between objects can for a range of concrete data types be…
Medical image registration is a challenging task involving the estimation of spatial transformations to establish anatomical correspondence between pairs or groups of images. Recently, deep learning-based image registration methods have…
The diffeomorphic registration framework enables to define an optimal matching function between two probability measures with respect to a data-fidelity loss function. The non convexity of the optimization problem renders the choice of this…
Image registration is a fundamental task in medical image analysis. Recently, deep learning based image registration methods have been extensively investigated due to their excellent performance despite the ultra-fast computational time.…
This work proposes a multimodal diffeomorphic registration method using Neural Ordinary Differential Equations (Neural ODEs). Nonrigid registration algorithms exhibit tradeoffs between their accuracy, the computational complexity of their…
The geometrical diffraction theory, in the sense of Keller,is here reconsidered as an obstacle problem in the Riemannian geometry. The first result is the proof of the existence and the analysis of the main properties of the diffracted…
Deep learning based methods provide efficient solutions to medical image registration, including the challenging problem of diffeomorphic image registration. However, most methods register normal image pairs, facing difficulty handling…
We survey some results on travel time tomography. The question is whether we can determine the anisotropic index of refraction of a medium by measuring the travel times of waves going through the medium. This can be recast as geometry…
Deep-learning-based registration methods emerged as a fast alternative to conventional registration methods. However, these methods often still cannot achieve the same performance as conventional registration methods because they are either…
Diffusion tensor based cardiovascular magnetic resonance (DT-CMR) offers a non-invasive method to visualize the myocardial microstructure. With the assumption that the heart is stationary, frames are acquired with multiple repetitions for…