Related papers: A Diffeomorphism Groupoid and Algebroid Framework …

Deformation field estimation is an important and challenging issue in many medical image registration applications. In recent years, deep learning technique has become a promising approach for simplifying registration problems, and has been…

Large displacement optical flow is an integral part of many computer vision tasks. Variational optical flow techniques based on a coarse-to-fine scheme interpolate sparse matches and locally optimize an energy model conditioned on colour,…

We present VoxelMorph, a fast learning-based framework for deformable, pairwise medical image registration. Traditional registration methods optimize an objective function for each pair of images, which can be time-consuming for large…

We propose Parallelised Diffeomorphic Sampling-based Motion Planning (PDMP). PDMP is a novel parallelised framework that uses bijective and differentiable mappings, or diffeomorphisms, to transform sampling distributions of sampling-based…

Registration of diffusion MRI tractography is an essential step for analyzing group similarities and variations in the brain's white matter (WM). Streamline-based registration approaches can leverage the 3D geometric information of fiber…

Recently, deep-learning-based approaches have been widely studied for deformable image registration task. However, most efforts directly map the composite image representation to spatial transformation through the convolutional neural…

In the last decades, some literature appeared using the Lie groups theory to solve problems in computer vision. On the other hand, Lie algebraic representations of the transformations therein were introduced to overcome the difficulties…

LiDAR odometry is a fundamental task for various areas such as robotics, autonomous driving. This problem is difficult since it requires the systems to be highly robust running in noisy real-world data. Existing methods are mostly local…

Limbless organisms of all sizes use undulating patterns of self-deformation to locomote. Geometric mechanics, which maps deformations to motions, provides a powerful framework to formalize and investigate the theoretical properties and…

Deformable image registration is crucial for aligning medical images in a nonlinear fashion across different modalities, allowing for precise spatial correspondence between varying anatomical structures. This paper presents NestedMorph, a…

Cortical surface registration is a fundamental tool for neuroimaging analysis that has been shown to improve the alignment of functional regions relative to volumetric approaches. Classically, image registration is performed by optimizing a…

A generalization of non-Abelian gauge theories of compact Lie groups is developed by gauging the non-compact group of volume-preserving diffeomorphisms of a $D$-dimensional space R^D. This group is represented on the space of fields defined…

We develop the diffeomorphism invariant Colombeau-type algebra of nonlinear generalized functions in a modern and compact way. Using a unifying formalism for the local setting and on manifolds, the construction becomes simpler and more…

We present an accurate, robust and fast method for registration of 3D scans. Our motion estimation optimizes a robust cost function on the intrinsic representation of rigid motions, i.e., the Special Euclidean group $\mathbb{SE}(3)$. We…

We study the problem of registration for medical CT images from a novel perspective -- the sensitivity to degree of deformations in CT images. Although some learning-based methods have shown success in terms of average accuracy, their…

Lagrangian multiform theory is a variational framework for integrable systems. In this article we introduce a new formulation which is based on symplectic geometry and which treats position, momentum and time coordinates of a…

The anelastic and pseudo-incompressible equations are two well-known soundproof approximations of compressible flows useful for both theoretical and numerical analysis in meteorology, atmospheric science, and ocean studies. In this paper,…

The study of diffeomorphism groups and their applications to problems in analysis and geometry has a long history. In geometric hydrodynamics, pioneered by V.~Arnold in the 1960s, one considers an ideal fluid flow as the geodesic motion on…

Data sets tend to live in low-dimensional non-linear subspaces. Ideal data analysis tools for such data sets should therefore account for such non-linear geometry. The symmetric Riemannian geometry setting can be suitable for a variety of…

Image registration is a fundamental step in medical image analysis. Ideally, the transformation that registers one image to another should be a diffeomorphism that is both invertible and smooth. Traditional methods like geodesic shooting…