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In spite of its overall efficiency and robustness for capturing the interface in multiphase fluid dynamics simulations, the well-known shortcoming of the level-set method is associated with the lack of a systematic approach for preserving…

Topological data analysis (TDA) has emerged as one of the most promising techniques to reconstruct the unknown shapes of high-dimensional spaces from observed data samples. TDA, thus, yields key shape descriptors in the form of persistent…

We propose a novel approach for image segmentation that combines Neural Ordinary Differential Equations (NODEs) and the Level Set method. Our approach parametrizes the evolution of an initial contour with a NODE that implicitly learns from…

The goal of this paper is to achieve a computational model and corresponding efficient algorithm for obtaining a sparse representation of the fitting surface to the given scattered data. The basic idea of the model is to utilize the…

We present a new multi-fluid, multi-temperature plasma solver with adaptive Cartesian mesh (ACM) based on a full-Newton (non-linear, implicit) scheme for collisional low-temperature plasma. The particle transport is described using the…

This work presents a comprehensive framework for enhanced diffusion modeling in fluid-structure interactions by combining the Immersed Boundary Method (IBM) with stochastic trajectories and high-order spectral boundary conditions. Using…

Spectral-based subspace clustering methods have proved successful in many challenging applications such as gene sequencing, image recognition, and motion segmentation. In this work, we first propose a novel spectral-based subspace…

Embedded boundary methods alleviate many computational challenges, including those associated with meshing complex geometries and solving problems with evolving domains and interfaces. Developing model reduction methods for computational…

3D Gaussian Splatting (3DGS) has emerged as a leading technique for novel view synthesis, demonstrating exceptional rendering efficiency. \replaced[]{Well-reconstructed surfaces can be characterized by low configurational entropy, where…

Image segmentation is an essential component in many image processing and computer vision tasks. The primary goal of image segmentation is to simplify an image for easier analysis, and there are two broad approaches for achieving this: edge…

We process snapshots of trajectories of evolution equations with intrinsic symmetries, and demonstrate the use of recently developed eigenvector-based techniques to successfully quotient out the degrees of freedom associated with the…

This paper presents DENSER, an efficient and effective approach leveraging 3D Gaussian splatting (3DGS) for the reconstruction of dynamic urban environments. While several methods for photorealistic scene representations, both implicitly…

We analyze actual methods that generate smooth frame fields both in 2D and in 3D. We formalize the 2D problem by representing frames as functions (as it was done in 3D), and show that the derived optimization problem is the one that…

This paper presents a new monolithic free-surface formulation that exhibits correct kinetic and potential energy behavior. We focus in particular on the temporal energy behavior of two-fluids flow with varying densities. Correct energy…

Novel view synthesis from a sparse set of input images is a challenging problem of great practical interest, especially when camera poses are absent or inaccurate. Direct optimization of camera poses and usage of estimated depths in neural…

We propose a method that morphs high-orger meshes such that their boundaries and interfaces coincide/align with implicitly defined geometries. Our focus is particularly on the case when the target surface is prescribed as the zero…

We present a fully Lagrangian particle level-set method based on high-order polynomial regression. This enables closest-point redistancing without requiring a regular Cartesian mesh, relaxing the need for particle-mesh interpolation.…

This paper presents a variational based approach to fusing hyperspectral and multispectral images. The fusion process is formulated as an inverse problem whose solution is the target image assumed to live in a much lower dimensional…

Recent years have witnessed substantial advancements in the field of 3D reconstruction from 2D images, particularly following the introduction of the neural radiance field (NeRF) technique. However, reconstructing a 3D high dynamic range…

Novel view synthesis has been greatly enhanced by the development of radiance field methods. The introduction of 3D Gaussian Splatting (3DGS) has effectively addressed key challenges, such as long training times and slow rendering speeds,…