Related papers: Registration-based model reduction in complex two-…

Multimodal image registration is a very challenging problem for deep learning approaches. Most current work focuses on either supervised learning that requires labelled training scans and may yield models that bias towards annotated…

We provide a unifying framework for $\mathcal{L}_2$-optimal reduced-order modeling for linear time-invariant dynamical systems and stationary parametric problems. Using parameter-separable forms of the reduced-model quantities, we derive…

Objective: Evaluate and compare multiple mechanics-based and traditional regularization strategies within a variational image registration framework for quasi-static ultrasound elastography. Methods:We reformulate a previously proposed…

Solving and optimising Partial Differential Equations (PDEs) in geometrically parameterised domains often requires iterative methods, leading to high computational and time complexities. One potential solution is to learn a direct mapping…

Reduced-order models are essential tools to deal with parametric problems in the context of optimization, uncertainty quantification, or control and inverse problems. The set of parametric solutions lies in a low-dimensional manifold (with…

This paper focuses on the mathematical framework for reducing the complexity of models using path signatures. The structure of these signatures, which can be interpreted as collections of iterated integrals along paths, is discussed and…

This paper deals with non-Lipschitz nonlinear systems. Such systems can be approximated by a linear map of so-called signatures, which play a crucial role in the theory of rough paths and can be interpreted as collections of iterated…

An efficient computational approach for optimal reconstruction of binary-type images suitable for models in various applications including biomedical imaging is developed and validated. The methodology includes derivative-free optimization…

Dimension reduction is often the first step in statistical modeling or prediction of multivariate spatial data. However, most existing dimension reduction techniques do not account for the spatial correlation between observations and do not…

We introduce HyperMorph, a framework that facilitates efficient hyperparameter tuning in learning-based deformable image registration. Classical registration algorithms perform an iterative pair-wise optimization to compute a deformation…

Deep learning models incorporating linear SSMs have gained attention for capturing long-range dependencies in sequential data. However, their large parameter sizes pose challenges for deployment on resource-constrained devices. In this…

This paper presents a novel predictive model, MetaMorph, for metamorphic registration of images with appearance changes (i.e., caused by brain tumors). In contrast to previous learning-based registration methods that have little or no…

This work studies the problem of unsupervised RGB-D point cloud registration, which aims at training a robust registration model without ground-truth pose supervision. Existing methods usually leverages unposed RGB-D sequences and adopt a…

Dissipative partial differential equations that exhibit chaotic dynamics tend to evolve to attractors that exist on finite-dimensional manifolds. We present a data-driven reduced order modeling method that capitalizes on this fact by…

We investigate a projection-based reduced-order model of the steady incompressible Navier-Stokes equations for moderate Reynolds numbers. In particular, we construct an "embedded" reduced basis space, by applying proper orthogonal…

Chemical kinetic models in terms of ordinary differential equations correspond to finite dimensional dissipative dynamical systems involving a multiple time scale structure. Most dimension reduction approaches aimed at a slow…

In this paper, a parametric model order reduction (pMOR) technique is proposed to find a simplified system representation of a large-scale and complex thermal system. The main principle behind this technique is that any change of the…

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…

Let $\Omega\subset\mathbb{R}^n$, $n\ge 2$, be a bounded connected $C^2$ domain. For any unit vector $\nu\in\mathbb{R}^n$, let $T_{\lambda}^{\nu}=\{x\in\mathbb{R}^n:x\cdot\nu=\lambda\}$,…

We discuss a method of parameter reduction in complex models known as the Manifold Boundary Approximation Method (MBAM). This approach, based on a geometric interpretation of statistics, maps the model reduction problem to a geometric…