Related papers: Constructing Two-Dimensional Voronoi Diagrams via …
This paper presents a novel method for real-time 3D navigation in large-scale, complex environments using a hierarchical 3D visibility graph (V-graph). The proposed algorithm addresses the computational challenges of V-graph construction…
Overlaid oriented Voronoi diagrams (OOVDs) are known to provide useful data for the construction of optimal Euclidean $1$-Steiner trees. The theoretical time complexity of construction methods exploiting the OOVD is $O(n^2)$, but a…
We present medial parametrization, a new approach to parameterizing any compact planar domain bounded by simple closed curves. The basic premise behind our proposed approach is to use two close Voronoi sites, which we call dipoles, to…
A set S of n points in general position in R^d defines the unique Voronoi diagram of S. Its dual tessellation is the Delaunay triangulation (DT) of S. In this paper we consider the parabolic functional on the set of triangulations of S and…
This work concerns adaptive refinement procedures for meshes of polygonal virtual elements. Specifically, refinement procedures previously proposed by the authors for structured meshes are generalized for the challenging case of arbitrary…
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…
How to divide floor plans or navigation maps into semantic representations, such as rooms and corridors, is an important research question in fields such as human-robot interaction, place categorization, or semantic mapping. While most…
Representing a scanned map of the real environment as a topological structure is an important research in robotics. %is currently an important research. Since topological representations of maps save a huge amount of map storage space and…
Given two sets of training samples, general method is to estimate the density function and classify the test sample according to higher values of estimated densities. Natural way to estimate the density should be histogram tending to…
We present Deformable Voxel Grids (DVGs) for 3D shapes comparison and processing. It consists of a voxel grid which is deformed to approximate the silhouette of a shape, via energy-minimization. By interpreting the DVG as a local…
Micro-Aerial Vehicles (MAVs) have the advantage of moving freely in 3D space. However, creating compact and sparse map representations that can be efficiently used for planning for such robots is still an open problem. In this paper, we…
Modeling microstructures is an interesting problem not just in Materials Science but also in Mathematics and Statistics. The most basic model for steel microstructure is the Poisson-Voronoi diagram. It has mathematically attractive…
We present a simple yet effective general-purpose framework for modeling 3D shapes by leveraging recent advances in 2D image generation using CNNs. Using just a single depth image of the object, we can output a dense multi-view depth map…
Voronoi mosaics inspired by the seed points placed on the Archimedes Spirals are reported. Voronoi entropy was calculated for these patterns. Equidistant and non-equidistant patterns are treated. Voronoi mosaics built from cells of equal…
Although deep neural networks have been a dominant method for many 2D vision tasks, it is still challenging to apply them to 3D tasks, such as medical image segmentation, due to the limited amount of annotated 3D data and limited…
We show how to preprocess a weighted undirected $n$-vertex planar graph in $\tilde O(n^{4/3})$ time, such that the distance between any pair of vertices can then be reported in $\tilde O(1)$ time. This improves the previous $\tilde…
Color image segmentation is a crucial step in many computer vision and pattern recognition applications. This article introduces an adaptive and unsupervised clustering approach based on Voronoi regions, which can be applied to solve the…
A new approach to the generation of random sequences and two dimensional random patterns is proposed in this paper in which random sequences are generated by making use of either Delaunay triangulation or Voronoi diagrams drawn from random…
Divide and conquer is an established algorithm design paradigm that has proven itself to solve a variety of problems efficiently. However, it is yet to be fully explored in solving problems with a neural network, particularly the problem of…
Computing the diameter of the intersection graphs of objects is a basic problem in computational geometry. Previous works showed that the complexity of computing the diameter mainly depends on the object types: for unit disks and squares in…