Neural network design using Voronoi diagrams

A novel approach is proposed which determines the number of layers, the number of neurons in each layer, and their connection weights for a particular implementation of a neural network, with the multilayer feedforward topology, designed to classify patterns in the multidimensional feature space. The approach is based on construction of a Voronoi diagram over the set of points representing patterns in feature space and this finds added usefulness in deriving alternate neural network structures for realizing the desired pattern classification.     

Data structures and algorithms to support interactive spatial analysis using dynamic Voronoi diagrams

To support the need for interactive spatial analysis, it is often necessary to rethink the data structures and algorithms underpinning applications. This paper describes the development of an interactive environment in which a number of different Voronoi models of space can be manipulated together in real time to: (1) study their behaviour; (2) select appropriate models for specific analysis tasks; and (3) to examine how choice of one model over another will affect the interpretation of data. The paper studies six specific Voronoi diagram variants: the Ordinary Voronoi Diagram, the Farthest-point Voronoi Diagram, the Order-k Voronoi Diagram, the Ordered Order-k Voronoi Diagram, the kth Nearest-point Voronoi Diagram and the Multiplicatively Weighted Voronoi Diagram, and develops algorithms and data structures to store, rebuild and query these variants. From this, a generalised Voronoi data structure is proposed, from which specific Voronoi variants can be reconstructed dynamically as required. Algorithms for diagram reconstruction and for querying neighbourhood (topology or adjacency relations) of generator points and Voronoi regions are presented. An application program, developed on these ideas, is used to generate example results as proof of concept. It may be downloaded from a supporting website.     

Tracking a maneuvering target using neural fuzzy network

A fast target maneuver detecting and highly accurate tracking technique using a neural fuzzy network based on Kalman filter is proposed in this paper. In the automatic target tracking system, there exists an important and difficult problem: how to detect the target maneuvers and fast response to avoid miss-tracking? The traditional maneuver detection algorithms, such as variable dimension filter (VDF) and input estimation (IE) etc., are computation intensive and difficult to implement in real time. To solve this problem, neural network algorithms have been issued recently. However, the normal neural networks such as backpropagation networks usually produce the extra problems of low convergence speed and/or large network size. Furthermore, the way to decide the network structure is heuristic. To overcome these defects and to make use of neural learning ability, a developed standard Kalman filter with a self-constructing neural fuzzy inference network (KF-SONFIN) algorithm for target tracking is presented in this paper. By generating possible target trajectories including maneuver information to train the SONFIN, the trained SONFIN can detect when the maneuver occurred, the magnitude of maneuver values and when the maneuver disappeared. Without having to change the structure of Kalman filter nor modeling the maneuvering target, this new algorithm, SONFIN, can always find itself an economic network size with a fast learning process. Simulation results show that the KF-SONFIN is superior to the traditional IE and VDF methods in estimation accuracy.     

Restricting Voronoi diagrams to meshes using corner validation

Restricted Voronoi diagrams are a fundamental geometric structure used in many applications such as surface reconstruction from point sets or optimal transport. Given a set of sites V = { v _k}ⁿ_k=1 ? ?^d and a mesh X with vertices in ?^d connected by triangles, the restricted Voronoi diagram partitions X by computing for each site the portion of X for which the site is the nearest. The restricted Voronoi diagram is the intersection between the regular Voronoi diagram and the mesh. Depending on the site distribution or the ambient space dimension computing the regular Voronoi diagram may not be feasible using classical algorithms. In this paper, we extend Lévy and Bonneel's approach [ LB12 ] based on nearest neighbor queries. We show that their method is limited when the sites are not located on X . We propose a new algorithm for computing restricted Voronoi which reduces the number of sites considered for each triangle of the mesh and scales smoothly when the sites are far from the surface.     

Approximation of fruit skin patterns using spherical Voronoi diagrams

In nature, there are many tessellation patterns on curved surfaces that look like Voronoi diagrams. Typical examples are the patterns found on fruit skins. Verifying that a given tessellation is a Voronoi diagram will be useful for constructing mathematical models of polygonal patterns. However, the data are usually obtained as a 2D projected image, and hence it is not easy to compare it with a Voronoi diagram on a curved surfaces. We propose a framework for using a photograph of a fruit to measure the difference between the pattern on its skin and a spherical Voronoi diagram. The problem of finding the spherical Voronoi diagram that best fits the fruit skin pattern is reduced to an optimization problem. The validity of this formulation is evaluated using jackfruit and lychee. We also propose generalizations of our problem for further research.     

Understanding people motion in video sequences using Voronoi diagrams

This work describes a model for understanding people motion in video sequences using Voronoi diagrams, focusing on group detection and classification. We use the position of each individual as a site for the Voronoi diagram at each frame, and determine the temporal evolution of some sociological and psychological parameters, such as distance to neighbors and personal spaces. These parameters are used to compute individual characteristics (such as perceived personal space and comfort levels), that are analyzed to detect the formation of groups and their classification as voluntary or involuntary. Experimental results based on videos obtained from real life as well as from a crowd simulator were analyzed and discussed.     

Improvement of tracking performance using prediction-based algorithms for a maneuvering target

This paper presents a study involving prediction of a complicated maneuvering target, with the aim of improving the tracking performance of a fire control system (FCS). In this study, we predict the position of a complicated maneuvering target 5 s in advance using the information up to the current time. Because of the large error caused by the complicated maneuvers and the long prediction time interval, the mechanical system of the fire control system will take a heavy load. In order to cope with this problem, several approaches to decreasing the prediction error have been proposed including the prediction algorithms based on the multiple model(MM) filter, interacting multiple model (IMM) filter, and variable dimension with input estimation (VDIE) filter. Finally, comparative simulation results are presented to verify the performance of the filters.     

Landfill gas emission prediction using Voronoi diagrams and importance sampling

Municipal solid waste (MSW) landfills are among the nation's largest emitters of methane, a key greenhouse gas, and there is considerable interest in quantifying the surficial methane emissions from landfills. There are limitations in obtaining accurate emissions data by field measurements, and in characterizing an entire landfill with only a few such emissions measurements. This paper proposes an emissions prediction approach using numerous ambient air volatile organic compound (VOC) measurements above the surface of a landfill that are more easily obtained. Many large landfills are already collecting ambient air methane data based on existing regulations. The proposed method is based on the inverse solution of the standard Gaussian dispersion equations. However, only the VOC concentrations and locations are required. The locations of maximum likelihood of the point sources are predicted using Voronoi diagrams, and importance sampling is performed to further refine the locations. Point source strengths are calculated using non-negative least squares, and the point emission rates are then summed to give the total landfill emission rate. The proposed method is successfully demonstrated on a series of four landfill case studies. Three hypothetical landfills were selected for validation studies by forward and backward solution of the dispersion equations. The fourth case study is an active central Florida MSW landfill. The proposed method shows promise in accurately and robustly predicting landfill gas emissions, and requires only measured ambient VOC concentrations and locations.     

Voronoi diagrams of set-theoretic solid models

The definition of a Voronoi diagram is extended to arbitrary set-theoretic solid models. A method for approximating such diagrams using recursive subdivision is described. The method relies on octrees, which have been used for computing the distances between whole solid models. Two- and three-dimensional images generated using the algorithm are presented     

一种基于动态规划的机动目标检测前跟踪方法

针对传统动态规划检测前跟踪算法仅适用于匀速直线运动目标或慢机动目标的局限性,提出了一种将交互式多模型(IMM)滤波与基于动态规划的检测前跟踪算法相结合的机动目标处理算法。该算法应用于近程毫米波雷达探测环境下,根据被测目标的实际运动情况建立了匀加速运动、匀速转弯运动及匀速运动模型,在动态规划算法基础上考虑了多种运动模型以及模型之间的转换和预测,避免了因模型不匹配导致的跟踪效果变差的问题。仿真结果显示,相比于传统动态规划检测算法,该算法能够更加有效地实现对机动目标的检测和跟踪,适于工程应用。     

Discrete Voronoi diagrams and the SKIZ operator: a dynamicalgorithm

The Voronoi diagram (VD) is a popular tool for partitioning the support of an image. An algorithm is presented for constructing VD when the seed set, which determines the Voronoi regions, can be modified by adding and removing seeds. The number of pixels and seeds revisited for updating the diagram and the neighbor relationships among seeds is minimized. A result on cocircular seeds is presented. The adjacency, or dual, graph of the VD is readily obtained. The use of the algorithm for constructing skeletons by influence zones (SKIZ) is demonstrated     

Incremental reconstruction of generalized Voronoi diagrams on grids

We present an incremental algorithm for constructing and reconstructing Generalized Voronoi Diagrams (GVDs) on grids. Our algorithm, Dynamic Brushfire, uses techniques from the path planning community to efficiently update GVDs when the underlying environment changes or when new information concerning the environment is received. Dynamic Brushfire is an order of magnitude more efficient than current approaches. In this paper we present the algorithm, compare it to current approaches on several experimental domains involving both simulated and real data, and demonstrate its usefulness for multirobot path planning.     

Randomized incremental construction of Delaunay and Voronoi diagrams

In this paper we give a new randomized incremental algorithm for the construction of planar Voronoi diagrams and Delaunay triangulations. The new algorithm is more on-line than earlier similar methods, takes expected timeO(ngn) and spaceO(n), and is eminently practical to implement. The analysis of the algorithm is also interesting in its own right and can serve as a model for many similar questions in both two and three dimensions. Finally we demonstrate how this approach for constructing Voronoi diagrams obviates the need for building a separate point-location structure for nearest-neighbor queries.Leonidas Guibas and Micha Sharir wish to acknowledge the generous support of the DEC Systems Research Center in Palo Alto, California, where some of this work was carried out. Donald Knuth has been supported by NSF Grant CCR-86-10181. Micha Sharir has been supported by NSF Grant CCR-89-01484, ONR Grant N00014-K-87-0129, the U.S.-Israeli Binational Science Foundation, and the Fund for Basic Research administered by the Israeli Academy of Sciences.     

Randomized incremental construction of Delaunay and Voronoi diagrams

In this paper we give a new randomized incremental algorithm for the construction of planar Voronoi diagrams and Delaunay triangulations. The new algorithm is more “on-line” than earlier similar methods, takes expected timeO(n?gn) and spaceO(n), and is eminently practical to implement. The analysis of the algorithm is also interesting in its own right and can serve as a model for many similar questions in both two and three dimensions. Finally we demonstrate how this approach for constructing Voronoi diagrams obviates the need for building a separate point-location structure for nearest-neighbor queries.     

Duality of constrained Voronoi diagrams and Delaunay triangulations

We introduce theconstrained Voronoi diagram of a planar straight-line graph containingn vertices or sites where the line segments of the graph are regarded as obstacles, and show that an extended version of this diagram is the dual of theconstrained Delaunay triangulation. We briefly discussO(n logn) algorithms for constructing the extended constrained Voronoi diagram.This work was partially supported by a grant from the Natural Sciences and Engineering Research Council of Canada.     

Minimax particle filtering for tracking a highly maneuvering target

In this paper, we propose a new framework of particle filtering that adopts the minimax strategy. In the approach, we minimize a maximized risk, and the process of the risk maximization is reflected when computing the weights of particles. This scheme results in the significantly reduced variance of the weights of particles that enables the robustness against the degeneracy problem, and we can obtain improved quality of particles. The proposed approach is robust against environmentally adverse scenarios, particularly when the state of a target is highly maneuvering. Furthermore, we can reduce the computational complexity by avoiding the computation of a complex joint probability density function. We investigate the new method by comparing its performance to that of standard particle filtering and verify its effectiveness through experiments. The employed strategy can be adopted for any other variants of particle filtering to enhance tracking performance.     

移动点Voronoi图拓扑维护策略的研究

移动环境下基于Voronoi图的最近邻查询必须要解决随时间不断改变的移动点Voronoi图的拓扑结构的维护问题。通过一组离散的,有限的事件序列对其对偶图Delaunay图拓扑改变过程的模拟来实现对移动点Voronoi图拓扑结构的维护。把带有事件驱动机制的移动数据结构（Kinetic Data Structure,KDS）模型作为移动点的运动模型,给出了KDS模型对其对偶图Delaunay图拓扑结构改变维护的具体策略,并对移动环境下动态插入或删除移动点时Voronoi图的拓扑维护问题进行了研究。最后给出了移动环境下基于Voronoi图的近邻查询的数据库实现模型。     

Fast implementation of ground maneuvering target focusing

Ground maneuvering target detection is a hot topic in the applications of synthetic aperture radar (SAR), whereas its focusing performance is severely deteriorated by range migration and Doppler frequency migration during a long integration time. This paper proposes a novel method to image the target and estimate its parameters via performing two independent 2-dimensional (2-D) searches after a parameter separation operation. In order to improve the search speed, we set the limited search ranges and propose local mapping sparse Fourier transform (LMSFT) to replace fast Fourier transform (FFT). Compared with the traditional algorithms, the proposed method can realize fast coherent integration of multiple maneuvering targets via compensating the high-order range migration and Doppler frequency migration. In addition, the proposed method is stable under noise. Several simulation results have validated the effectiveness of the proposed method.