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We extend our work for compression of currents and varifolds to a compression algorithm for the embedded normal cycles representation of shape, restricted to the constant normal kernel case, using the Nystrom approximation in Reproducing…
Recent developments in mechanical, aerospace, and structural engineering have driven a growing need for efficient ways to model and analyse structures at much larger and more complex scales than before. While established numerical methods…
Modelling deformation of anatomical objects observed in medical images can help describe disease progression patterns and variations in anatomy across populations. We apply a stochastic generalisation of the Large Deformation Diffeomorphic…
Registration is an essential tool in image analysis. Deep learning based alternatives have recently become popular, achieving competitive performance at a faster speed. However, many contemporary techniques are limited to volumetric…
Recent progress in PDE constrained optimization on shape manifolds is based on the Hadamard form of shape derivatives, i.e., in the form of integrals at the boundary of the shape under investigation, as well as on intrinsic shape metrics.…
We propose a novel weakly supervised discriminative algorithm for learning context specific registration metrics as a linear combination of conventional similarity measures. Conventional metrics have been extensively used over the past two…
We introduce a deep encoder-decoder architecture for image deformation prediction from multimodal images. Specifically, we design an image-patch-based deep network that jointly (i) learns an image similarity measure and (ii) the…
Accurate tracking of an anatomical landmark over time has been of high interests for disease assessment such as minimally invasive surgery and tumor radiation therapy. Ultrasound imaging is a promising modality benefiting from low-cost and…
Segmentation of microscopy images constitutes an ill-posed inverse problem due to measurement noise, weak object boundaries, and limited labeled data. Although deep neural networks provide flexible nonparametric estimators, unconstrained…
We address the challenge of parameter-efficient fine-tuning (PEFT) for three-dimensional (3D) U-Net-based denoising diffusion probabilistic models (DDPMs) in magnetic resonance imaging (MRI) image generation. Despite its practical…
Deep distance metric learning (DDML), which is proposed to learn image similarity metrics in an end-to-end manner based on the convolution neural network, has achieved encouraging results in many computer vision tasks.$L2$-normalization in…
Randomized block Krylov subspace methods form a powerful class of algorithms for computing the extreme eigenvalues of a symmetric matrix or the extreme singular values of a general matrix. The purpose of this paper is to develop new…
We propose a novel neural deformable model (NDM) targeting at the reconstruction and modeling of 3D bi-ventricular shape of the heart from 2D sparse cardiac magnetic resonance (CMR) imaging data. We model the bi-ventricular shape using…
Second-order optimization methods, such as cubic regularized Newton methods, are known for their rapid convergence rates; nevertheless, they become impractical in high-dimensional problems due to their substantial memory requirements and…
We present a parallel distributed-memory algorithm for large deformation diffeomorphic registration of volumetric images that produces large isochoric deformations (locally volume preserving). Image registration is a key technology in…
We present a new approach to discretizing shape optimization problems that generalizes standard moving mesh methods to higher-order mesh deformations and that is naturally compatible with higher-order finite element discretizations of…
Frequency-dependent correlations, such as the spectral function and the dynamical structure factor, help understand condensed matter experiments. Within the density matrix renormalization group (DMRG) framework, an accurate method for…
In this contribution we device and analyze improved variants of the non-conforming dual approach for trust-region reduced basis (TR-RB) approximation of PDE-constrained parameter optimization that has recently been introduced in [Keil et…
We present a method for metric optimization in the Large Deformation Diffeomorphic Metric Mapping (LDDMM) framework, by treating the induced Riemannian metric on the space of diffeomorphisms as a kernel in a machine learning context. For…
A standard approach to reduced-order modeling of higher-order linear dynamical systems is to rewrite the system as an equivalent first-order system and then employ Krylov-subspace techniques for reduced-order modeling of first-order…