Related papers: A Diffeomorphism Groupoid and Algebroid Framework …

Our anatomy is in constant motion. With modern MR imaging it is possible to record this motion in real-time during an ongoing radiation therapy session. In this paper we present an image registration method that exploits the sequential…

In many applications, one encounters signals that lie on manifolds rather than a Euclidean space. In particular, covariance matrices are examples of ubiquitous mathematical objects that have a non Euclidean structure. The application of…

We present a novel approach for the reconstruction of dynamic geometric shapes using a single hand-held consumer-grade RGB-D sensor at real-time rates. Our method does not require a pre-defined shape template to start with and builds up the…

We present a method for nonrigid registration of 2-D geometric shapes. Our contribution is twofold. First, we extend the classic chamfer-matching energy to a variational functional. Secondly, we introduce a meshless deformation model that…

In this paper, we propose SRIF, a novel Semantic shape Registration framework based on diffusion-based Image morphing and Flow estimation. More concretely, given a pair of extrinsically aligned shapes, we first render them from multi-views,…

With this work, we release CLAIRE, a distributed-memory implementation of an effective solver for constrained large deformation diffeomorphic image registration problems in three dimensions. We consider an optimal control formulation. We…

Current Structure-from-Motion (SfM) methods typically follow a two-stage pipeline, combining learned or geometric pairwise reasoning with a subsequent global optimization step. In contrast, we propose a data-driven multi-view reasoning…

Spatially varying regularization accommodates the deformation variations that may be necessary for different anatomical regions during deformable image registration. Historically, optimization-based registration models have harnessed…

In medical imaging, the diffusion models have shown great potential for synthetic image generation tasks. However, these approaches often lack the interpretable connections between the generated and real images and can create anatomically…

Unsupervised deep-learning (DL) models were recently proposed for deformable image registration tasks. In such models, a neural-network is trained to predict the best deformation field by minimizing some dissimilarity function between the…

We prove that the Riemannian exponential map of the right-invariant $L^2$ metric on the group of volume-preserving diffeomorphisms of a two-dimensional manifold with a nonempty boundary is a nonlinear Fredholm map of index zero.

Deformable image registration plays a fundamental role in medical image analysis by enabling spatial alignment of anatomical structures across subjects. While recent deep learning-based approaches have significantly improved computational…

We present a postprocessing layer for deformable image registration to make a registration field more diffeomorphic by encouraging Jacobians of the transformation to be positive. Diffeomorphic image registration is important for medical…

This paper introduces a description of Endomorphisms of the translation group in an affine plane, will define the addition and composition of the set of endomorphisms and specify the neutral elements associated with these two actions and…

Previous deep image registration methods that employ single homography, multi-grid homography, or thin-plate spline often struggle with real scenes containing depth disparities due to their inherent limitations. To address this, we propose…

This paper introduces VPreg, a novel diffeomorphic image registration method. This work provides several improvements to our past work on mesh generation and diffeomorphic image registration. VPreg aims to achieve excellent registration…

We present a geometric framework for discrete classical field theories, where fields are modeled as "morphisms" defined on a discrete grid in the base space, and take values in a Lie groupoid. We describe the basic geometric setup and…

The purpose of this paper is to describe geometrically discrete Lagrangian and Hamiltonian Mechanics on Lie groupoids. From a variational principle we derive the discrete Euler-Lagrange equations and we introduce a symplectic 2-section,…

Let $\mathcal{D}$ be a dataset of smooth 3D-surfaces, partitioned into disjoint classes $\mathit{CL}_j$, $j= 1, \ldots, k$. We show how optimized diffeomorphic registration applied to large numbers of pairs $S,S' \in \mathcal{D}$ can…

In this paper we propose a (non-linear) smoothing algorithm for group-affine observation systems, a recently introduced class of estimation problems on Lie groups that bear a particular structure. As most non-linear smoothing methods, the…