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This study proposes an innovative approach to analyze spatial patterns of behavior by integrating information in weighted Voronoi diagrams. The objective of the research is to analyze the temporal distribution of an experimental subject in…
Dense packing of hydrophobic residues in the cores of globular proteins determines their stability. Recently, we have shown that protein cores possess packing fraction $\phi \approx 0.56$, which is the same as dense, random packing of amino…
Studies of large-scale structures in the Universe, such as superstructures or cosmic voids, have been widely used to characterize the properties of the cosmic web through statistical analyses. On the other hand, the 2-point correlation…
Since the Voronoi diagram appears in many applications, the topic of improving its computational efficiency remains attractive. We propose a novel yet efficient method to compute Voronoi diagrams bounded by a given domain, i.e., the clipped…
Effective transport properties of heterogeneous structures are predicted by geometric microstructural parameters, but these can be difficult to calculate. Here, a boundary element code with a recurrent series method accurately and…
votess is a library for computing parallel 3D Voronoi tessellations on heterogeneous platforms, from CPUs and GPUs, to future accelerator architectures. To do so, it leverages the SYCL abstraction layer to achieve portability and…
Although coherent large-scale structures such as filaments and walls are apparent to the eye in galaxy redshift surveys, they have so far proven difficult to characterize with computer algorithms. This paper presents a procedure that uses…
Symmetry is an important composition feature by investigating similar sides inside an image plane. It has a crucial effect to recognize man-made or nature objects within the universe. Recent symmetry detection approaches used a smoothing…
We investigate Voronoi-like tessellations of bipartite quadrangulations on surfaces of arbitrary genus, by using a natural generalization of a bijection of Marcus and Schaeffer allowing to encode such structures into labeled maps with a…
We present a method to characterize the distribution of length-scales of finite, disordered patterns with, on average, radial symmetry. This method makes it possible to quantify the distribution of characteristic length scales in cases…
We investigate the application of volume statistics to probe the distribution of underdense regions in the large-scale structure of the Universe. This statistic measures the distortion of Eulerian volume elements relative to Lagrangian ones…
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…
We introduce a general, efficient method to completely describe the topology of individual grains, bubbles, and cells in three-dimensional polycrystals, foams, and other multicellular microstructures. This approach is applied to a pair of…
The large-scale structure of the universe is comprised of virialized blob-like clusters, linear filaments, sheet-like walls and huge near empty three-dimensional voids. Characterizing the large scale universe is essential to our…
A new method for analyzing the morphological features of point patterns is presented. The method is taken from the study of molecular liquids, where it has been introduced for making a statistical description of anisotropic distributions.…
Mimicking natural tessellation patterns is a fascinating multi-disciplinary problem. Geometric methods aiming at reproducing such partitions on surface meshes are commonly based on the Voronoi model and its variants, and are often faced…
A multiresolution technique on tessellation graphs for particle dynamics is proposed. This allows to split spatial field data given on millions of discrete particle positions into scale-dependent contributions. The Delaunay tessellation is…
The cosmic web that characterizes the large-scale structure of the Universe can be quantified by a variety of methods. For example, large redshift surveys can be used in combination with point process algorithms to extract long curvilinear…
Graph embedding provides a feasible methodology to conduct pattern classification for graph-structured data by mapping each data into the vectorial space. Various pioneering works are essentially coding method that concentrates on a…
Although Poisson-Voronoi diagrams have interesting mathematical properties, there is still much to discover about the geometrical properties of its grains. Through simulations, many authors were able to obtain numerical approximations of…