UV-Diagram: A Voronoi Diagram for Uncertain Spatial Databases

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Safe Adaptive Multi-Agent Coverage Control

This paper presents a safe adaptive coverage controller for multi-agent systems with actuator faults and time-varying uncertainties. The centroidal Voronoi tessellation (CVT) is applied to generate an optimal configuration of multi-agent systems for covering an area of interest. As a conventional CVT-based controller cannot prevent collisions between agents with non-zero size, a control barrier function (CBF) based controller is developed to ensure collision avoidance with a function approximation technique (FAT) based design to deal with system uncertainties. The proposed controller is verified under simulations

Representation of Imprecise Digital Objects

International audienceIn this paper, we investigate a new framework to handle noisy digital objects. We consider digital closed simple 4-connected curves that are the result of an imperfect digital conversion (scan, picture, etc), and call digital imprecise contours such curves for which an imprecision value is known at each point. This imprecision value stands for the radius of a ball around each point, such that the result of a perfect digitization lies in the union of all the balls. In the first part, we show how to define an imprecise digital object from such an imprecise digital contour. To do so, we define three classes of pixels : inside, outside and uncertain pixels. In the second part of the paper, we build on this definition for a volumetric analysis (as opposed to contour analysis) of imprecise digital objects. From so-called toleranced balls, a filtration of objects, called λ-objects is defined. We show how to define a set of sites to encode this filtration of objects

A Method to Construct Approximate Fuzzy Voronoi Diagram for Fuzzy Numbers of Dimension Two

In this paper, we propose an approximate "fuzzy Voronoi" diagram(FVD)for fuzzy numbers of dimension two (FNDT) by designing an extension ofcrisp Voronoi diagram for fuzzy numbers. The fuzzy Voronoi sites are defined asfuzzy numbers of dimension two. In this approach, the fuzzy numbers have a convexcontinuous differentiable shape. The proposed algorithm has two stages: in the firststage we use the Fortune’s algorithm in order to construct a "fuzzy Voronoi" diagramfor membership values of FNDTs that are equal to 1. In the second stage, we proposea new algorithm based on the Euclidean distance between two fuzzy numbers in orderto construct the approximate "fuzzy Voronoi" diagram for values of the membershipof FNDTs that are smaller than 1. The experimental results are presented for aparticular shape, the fuzzy ellipse numbers

Image-Guided Voronoi Aesthetic Patterns with an Uncertainty Algorithm Based on Cloud Model

Tessellation-based art is an important technique for computer aided aesthetic patterns generation, and Voronoi diagram plays a key role in the preprocessing, whose uncertainty mechanism is still a challenge. However, the existing techniques handle the uncertainty incompletely and unevenly, and the corresponding algorithms are not of high efficiency; thus it is impossible for users to obtain the results in real time. For a reference image, a Voronoi aesthetic pattern generation algorithm with uncertainty based on cloud model is proposed, including uncertain line representation using an extended cloud model and Voronoi polygon approximation filling with uncertainty. In view of the different parameters, seven groups of experiments and various experimental analyses are conducted. Compared with the related algorithms, the proposed technique performs better on running time, and its time complexity is approximatively linear related to the size of the input image. The experimental results show that it can produce visually similar effect with the frayed or cracked soil and has three advantages, that is, uncertainty, simplicity, and efficiency. The proposal can be a powerful alternative to the traditional methods and has a prospect of applications in the digital entertainment, home decoration, clothing design, and various fields

UV-diagram: A voronoi diagram for uncertain data (technical report),” 2009

Abstract — The Voronoi diagram is an important technique for answering nearest-neighbor queries for spatial databases. In this paper, we study how the Voronoi diagram can be used on uncertain data, which are inherent in scientific and business applications. In particular, we propose the Uncertain-Voronoi Diagram (or UV-diagram in short). Conceptually, the data space is divided into distinct “UV-partitions”, where each UV-partition P is associated with a set S of objects; any point q located in P has the set S as its nearest neighbor with non-zero probabilities. The UV-diagram facilitates queries that inquire objects for having non-zero chances of being the nearest neighbor of a given query point. It also allows analysis of nearest neighbor information, e.g., finding out how many objects are the nearest neighbors in a given area. However, a UV-diagram requires exponential construction and storage costs. To tackle these problems, we devise an alternative representation for UV-partitions, and develop an adaptive index for the UV-diagram. This index can be constructed in polynomial time. We examine how it can be extended to support other related queries. We also perform extensive experiments to validate the effectiveness of our approach. I

UV-Diagram: A Voronoi Diagram for Uncertain Spatial Databases

The Voronoi diagram is an important technique for answering nearest-neighbor queries for spatial databases. We study how the Voronoi diagram can be used for uncertain spatial data, which are inherent in scientific and business applications. Specifically, we propose the Uncertain-Voronoi diagram (or UV-diagram), which divides the data space into disjoint "UV-partitions". Each UV-partition P is associated with a set S of objects, such that any point q located in P has the set S as its nearest neighbor with nonzero probabilities. The UV-diagram enables queries that return objects with nonzero chances of being the nearest neighbor (NN) of a given point q. It supports "continuous nearest-neighbor search", which refreshes the set of NN objects of q, as the position of q changes. It also allows the analysis of nearest-neighbor information, for example, to find out the number of objects that are the nearest neighbors of any point in a given area. A UV-diagram requires exponential construction and storage costs. To tackle these problems, we devise an alternative representation of a UV-diagram, by using a set of UV-cells. A UV-cell of an object o is the extent e for which o can be the nearest neighbor of any point q ∈ e. We study how to speed up the derivation of UV-cells by considering its nearby objects. We also use the UV-cells to design the UV-index, which supports different queries, and can be constructed in polynomial time. We have performed extensive experiments on both real and synthetic data to validate the efficiency of our approaches.Department of Computin