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The field of mathematical morphology offers well-studied techniques for image processing. In this work, we view morphological operations through the lens of persistent homology, a tool at the heart of the field of topological data analysis.…
Homology features of spaces which appear in applications, for instance 3D meshes, are among the most important topological properties of these objects. Given a non-trivial cycle in a homology class, we consider the problem of computing a…
Multiply connected freeform surface features are widely encountered in industrial components, where toolpath generation often suffers from discontinuities, sharp turns, non-uniform scallop heights, and incomplete boundary coverage. This…
Much work has been done in topology optimization of multiscale structures for maximum stiffness or minimum compliance design. Such approaches date back to the original homogenization-based work by Bends{\o}e and Kikuchi from 1988, which…
An optimization-based strategy is proposed for coupling three-dimensional and one-dimensional problems (3D-1D coupling) in the context of soil-root interaction simulations. This strategy, originally designed to tackle generic 3D-1D coupled…
A fundamental problem in the texturing of 3D meshes using pre-trained text-to-image models is to ensure multi-view consistency. State-of-the-art approaches typically use diffusion models to aggregate multi-view inputs, where common issues…
In this article, a novel approach for merging 3D point cloud maps in the context of egocentric multi-robot exploration is presented. Unlike traditional methods, the proposed approach leverages state-of-the-art place recognition and learned…
State-of-the-art image segmentation algorithms generally consist of at least two successive and distinct computations: a boundary detection process that uses local image information to classify image locations as boundaries between objects,…
Lane segment topology reasoning constructs a comprehensive road network by capturing the topological relationships between lane segments and their semantic types. This enables end-to-end autonomous driving systems to perform road-dependent…
A computationally efficient method is presented for approximate optimization of cutting pattern of frame-supported and pneumatic membrane structures. The plane cutting sheet is generated by minimizing the error from the shape obtained by…
We present a single-image head mesh reconstruction framework that addresses the longstanding challenge of simultaneously preserving facial identity and producing industry-grade topology. Our framework adopts a coarse-to-fine optimization…
This work develops a nonlinear multigrid method for diffusion problems discretized by cell-centered finite volume methods on general unstructured grids. The multigrid hierarchy is constructed algebraically using aggregation of degrees of…
3D point cloud segmentation remains challenging for structureless and textureless regions. We present a new unified point-based framework for 3D point cloud segmentation that effectively optimizes pixel-level features, geometrical…
The Numerical Assembly Technique is extended to investigate arbitrary planar frame structures with the focus on the computation of natural frequencies. This allows us to obtain highly accurate results without resorting to spatial…
A new homogenization approach for the simulation of multi-phase flows in heterogeneous porous media is presented. It is based on the lattice Boltzmann method and combines the grayscale with the multi-component Shan-Chen method. Thus, it…
Homogenisation empowers the efficient macroscale system level prediction of physical scenarios with intricate microscale structures. Here we develop an innovative powerful, rigorous and flexible framework for asymptotic homogenisation of…
A variational coarse-graining framework for heterogeneous media is developed that allows for a seamless transition from the traditional static scenario to a arbitrary loading conditions, including inertia effects and body forces. The…
The Heterogeneous Multiscale Finite Element Method (FE-HMM) is a two-scale FEM based on asymptotic homogenization for solving multiscale partial differential equations. It was introduced in [W. E and B. Engquist, \emph{Commun. Math. Sci.},…
In this paper, we proposed and validated a fully automatic pipeline for hippocampal surface generation via 3D U-net coupled with active shape modeling (ASM). Principally, the proposed pipeline consisted of three steps. In the beginning, for…
Topology optimization methods face serious challenges when applied to structural design with fluid-structure interaction (FSI) loads, specially for high Reynolds fluid flow. This paper devises an explicit boundary method that employs…