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We develop and assess an optimization-based approach to parametric geometry reduction. Given a family of parametric domains, we aim to determine a parametric diffeomorphism $\Phi$ that maps a fixed reference domain $\Omega$ into each…

We introduce a meshfree exterior calculus (MEEC) for learning structure-preserving descriptions of physics on point clouds, and use it to build MEEC-Net, a data-efficient surrogate that transfers across resolutions, geometries, and physical…

The Earth mover's distance (EMD) is a useful metric for image recognition and classification, but its usual implementations are not differentiable or too slow to be used as a loss function for training other algorithms via gradient descent.…

The recent improvements in cryo-electron microscopy (cryo-EM) in the past few years are now allowing to observe molecular complexes at atomic resolution. As a consequence, numerous structures derived from cryo-EM are now available in the…

We introduce a projective Riesz $s$-kernel for the unit sphere $\mathbb{S}^{d-1}$ and investigate properties of $N$-point energy minimizing configurations for such a kernel. We show that these configurations, for $s$ and $N$ sufficiently…

Perhaps surprisingly, the total electron microscopy (EM) data collected to date is less than a cubic millimeter. Consequently, there is an enormous demand in the materials and biological sciences to image at greater speed and lower dosage,…

In neural networks, developing regularization algorithms to settle overfitting is one of the major study areas. We propose a new approach for the regularization of neural networks by the local Rademacher complexity called LocalDrop. A new…

In this paper, we argue that the problem of registering two sets of functional data, where the underlying mean function has sharp features, is not properly addressed by methods designed to align a bunch of growth curves data. We provide a…

A recent paper (Neural Networks, {\bf 132} (2020), 253-268) introduces a straightforward and simple kernel based approximation for manifold learning that does not require the knowledge of anything about the manifold, except for its…

Standard convolutions are prevalent in image processing and deep learning, but their fixed kernels limits adaptability. Several deformation strategies of the reference kernel grid have been proposed. Yet, they lack a unified theoretical…

Kernel methods provide a principled approach to nonparametric learning. While their basic implementations scale poorly to large problems, recent advances showed that approximate solvers can efficiently handle massive datasets. A shortcoming…

Single particle cryo-electron microscopy has become a critical tool in structural biology over the last decade, able to achieve atomic scale resolution in three dimensional models from hundreds of thousands of (noisy) two-dimensional…

Deep learning-based methods have recently demonstrated promising results in deformable image registration for a wide range of medical image analysis tasks. However, existing deep learning-based methods are usually limited to small…

Deformable registration continues to be one of the key challenges in medical image analysis. While iconic registration methods have started to benefit from the recent advances in medical deep learning, the same does not yet apply for the…

This paper presents a novel non-rigid point set registration method that is inspired by unsupervised clustering analysis. Unlike previous approaches that treat the source and target point sets as separate entities, we develop a holistic…

This paper focuses on minimizing a smooth function combined with a nonsmooth regularization term on a compact Riemannian submanifold embedded in the Euclidean space under a decentralized setting. Typically, there are two types of approaches…

Identification of model parameters in computer simulations is an important topic in computer experiments. We propose a new method, called the projected kernel calibration method, to estimate these model parameters. The proposed method is…

We propose a framework for 2D shape analysis using positive definite kernels defined on Kendall's shape manifold. Different representations of 2D shapes are known to generate different nonlinear spaces. Due to the nonlinearity of these…

We present a novel kernel-based machine learning algorithm for identifying the low-dimensional geometry of the effective dynamics of high-dimensional multiscale stochastic systems. Recently, the authors developed a mathematical framework…

Most of the deep learning based medical image registration algorithms focus on brain image registration tasks.Compared with brain registration, the chest CT registration has larger deformation, more complex background and region over-lap.…