Related papers: GPU Based Detection of Topological Changes in Voro…
Voronoi tessellations have been used to model the geometric arrangement of cells in morphogenetic or cancerous tissues, however so far only with flat hypersurfaces as cell-cell contact borders. In order to reproduce the experimentally…
The dynamics of glassy materials slows down upon cooling, typically showing either Arrhenius or super-Arrhenius behavior. However, it was recently shown that 2D cell-based models for biological tissues can be continuously tuned between…
Extraction of a high-fidelity 3D medial axis is a crucial operation in CAD. When dealing with a polygonal model as input, ensuring accuracy and tidiness becomes challenging due to discretization errors inherent in the mesh surface.…
In type-II superconductors, the dynamics of superconducting vortices determine their transport properties. In the Ginzburg-Landau theory, vortices correspond to topological defects in the complex order parameter. Extracting their precise…
Voronoi diagrams naturally produce convex, watertight, and topologically consistent cells, making them an appealing representation for 3D shape reconstruction. However, standard differentiable Voronoi approaches typically optimize generator…
We describe a technique for improving the performance of hydrodynamics codes which employ a moving Voronoi mesh. Currently, such codes are susceptible to high-frequency noise produced by rapid adjustments in the grid topology on the…
In stark contrast to the case of images, finding a concise, learnable discrete representation of 3D surfaces remains a challenge. In particular, while polygon meshes are arguably the most common surface representation used in geometry…
Machine learning techniques have been used to quantify the relationship between local structural features and variations in local dynamical activity in disordered glass-forming materials. To date these methods have been applied to an array…
Topology optimization is able to maximally leverage the high DOFs and mechanical potentiality of porous foams but faces three fundamental challenges: conforming to free-form outer shapes, maintaining geometric connectivity between adjacent…
We point out that interesting features in high energy physics data can be determined from properties of Voronoi tessellations of the relevant phase space. For illustration, we focus on the detection of kinematic "edges" in two dimensions,…
Voronoi diagrams are a fundamental geometric data structure for obtaining proximity relations. We consider collections of axis-aligned orthogonal polyhedra in two and three-dimensional space under the max-norm, which is a particularly…
Quasi-continuous structural transformation from the crystalline to amorphous state takes place in graphite during ball-milling. The quantitative characteristics of a short- and a medium-range orders in carbon nanomaterials structure are…
Let $P$ be a set of $n$ points and $Q$ a convex $k$-gon in ${\mathbb R}^2$. We analyze in detail the topological (or discrete) changes in the structure of the Voronoi diagram and the Delaunay triangulation of $P$, under the convex distance…
Histograms are widely used in medical imaging, network intrusion detection, packet analysis and other stream-based high throughput applications. However, while porting such software stacks to the GPU, the computation of the histogram is a…
Deep learning has been used as a powerful tool for various tasks in computer vision, such as image segmentation, object recognition and data generation. A key part of end-to-end training is designing the appropriate encoder to extract…
Minimization diagrams encompass a large class of diagrams of interest in the literature, such as generalized Voronoi diagrams. We develop an abstract perturbation theory and perform a sensitivity analysis for functions depending on sets…
Classical topological concepts are applied to understand high performance computing simulations of molecules writhing in three dimensional space. These simulations produce peta-bytes of floating point data, to describe 3 dimensional changes…
The Voronoi diagram-based dual-front active contour models are known as a powerful and efficient way for addressing the image segmentation and domain partitioning problems. In the basic formulation of the dual-front models, the evolving…
Topological data analysis is an emerging area in exploratory data analysis and data mining. Its main tool, persistent homology, has become a popular technique to study the structure of complex, high-dimensional data. In this paper, we…
We present a general framework for computing two-dimensional Voronoi diagrams of different classes of sites under various distance functions. The framework is sufficiently general to support diagrams embedded on a family of two-dimensional…