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Fingerprint authentication systems have become ubiquitous with the event of smart devices and cheap sensors. Because of its use in a wide range of devices, it is important that the biometric authentication systems are computationally cheap, and at the same time robust to distortions and noises. Most of the existing fingerprint authentication systems are based on conventional mathematics or complex filter and consequently features extracted are computationally expensive or gross approximate with a large margin of errors leading to drops in the accuracy of the system. In this paper, we propose a fingerprint template based on translation and rotation invariant features of the delaunay triangulation of minutiae. However existing methods of comparison of delaunay triangles features do not always result in an optimum match because of the distortion in the different prints of the same finger. In the proposed method, features extracted from the delaunay triangulation are augmented with the information of local ridges based on discrete curvature and digital straightness. Experimentation with FVC2000 shows that the proposed method has better performances compared to the latest techniques. [ABSTRACT FROM AUTHOR]

The matching area selection algorithm is one of the key technologies for underwater gravity-aided inertial navigation system. Positioning accuracy and matching rate of gravity matching can be improved in high quality matching area. The traditional matching area selection algorithms usually use the statistical characteristic parameters of gravity field, which is difficult to reflect the spatial characteristics of gravity field. In order to explore more vector characteristics and spatial relation characteristics of gravity field and find more potential matching areas, the matching area selection algorithm based on Delaunay triangulation is proposed in this article. The proposed algorithm establishes the three-dimensional model and extracts spatial feature parameters to analysis gravity field. The comprehensive characteristics matrix is used to select matching area by feature extraction and cluster analysis. The experimental results show that the proposed algorithm can extract more characteristics of gravity field, and select more effective matching areas than the traditional algorithms. [ABSTRACT FROM AUTHOR]

Objectives:Face swapping technology has important application value in entertainment, virtual reality, film and so on. However, existing methods are limited by face pose consistency and can not over- come the influence of occlusion. Methods:We proposes a method of face swapping using convolutional neu-ral network and tiny facet primitive. Firstly,detect the face using the cascade convolutional neural network and segment the face to determine the replacement region using fully convolutional network.Then,the Wal- lis transform is applied to adjust the skin color of the source image to make it consistent with the skin color of the face in the target image.After that, using facial key points detection method based on an ensemble of regression trees and Delaunay triangulation to construct the face triangulation network,then replacing faces based on tiny facet primitive. Finally, applying Poisson fusion to eliminate splicing traces between different images. Results: We evaluate the performance of the proposed method compared with existing method through qualitative and quantitative experiments. Experimental results show that face segment can well solve the problem of occlusion such as cap,glasses,and hair.Moreover,when source image and target image have different face poses,replacing face area using tiny facet primitive separately performs better than using the whole face area. Conclusions:Our method can well solve the problem of face pose consistency limita- tion and occlusion,which has certain practical application value. [ABSTRACT FROM AUTHOR]

The security of wireless sensor networks is a significant concern and can be achieved by the application of cryptographic algorithms. The symmetric key encryption techniques are widely used cryptographic mechanisms for the security of sensor networks due to its low computational complexity. A symmetric key encryption technique requires a secret key to be shared between both parties for confidential communication. In a wireless sensor network, it is difficult to know which node is going to be in its communication range at the deployment phase. If prior knowledge of sensor location exists, it is an added advantage and helps in the distribution of secret keys among nodes. Even if with the expected location information, distributing the keys properly among the nodes is a challenging task. A proper algorithm must be used so that it gives the adequate utilization of the distributed keys with a minimal number of keys per sensor node. In this paper, we propose a location-dependent key distribution scheme. We use Delaunay Triangulation for the efficient distribution of keys among sensor nodes. The method gives a high probability of secure communication links among nodes with high resilience to the network. [ABSTRACT FROM AUTHOR]

A colored traveling salesman problem (CTSP) is a generalization of the well-known multiple traveling salesman problem. It utilizes colors to differentiate the accessibility of its cities to its salesmen. In our prior work, CTSPs are formulated over graphs associated with a city-color matrix. This work redefines a general colored traveling salesman problem (GCTSP) in the framework of hypergraphs and reveals several important properties of GCTSP. In GCTSP, the setting of city colors is richer than that in CTSPs. As results, it can be used to model and address various complex scheduling problems. Then, a Delaunay-triangulation-based Variable Neighborhood Search (DVNS) algorithm is developed to solve large-scale GCTSPs. At the beginning stage of DVNS, a divide and conquer algorithm is exploited to prepare a Delaunay candidate set for lean insertion. Next, the incumbent solution is perturbed by utilizing greedy multi-insertion and exchange mutation to obtain a variety of neighborhoods. Subsequently, 2-opt and 3-opt are used for local search in turn. Extensive experiments are conducted for many large scale GCTSP cases among which two maximal ones are up to 33000+ cities for 4 salesmen and 240 salesmen given 11000+ cities, respectively. The results show that the proposed method outperforms the existing four genetic algorithms and two VNS methods in terms of search ability and convergence rate. [ABSTRACT FROM AUTHOR]

In this paper, we address the problem of minimum number of Steiner points of constrained 1-line-fixed Steiner tree (abbreviated to the MNSP-C1LF-ST problem), which is defined as follows. Given n terminals located at the same side of a fixed line l in the Euclidean plane R 2 and a constant L, we are asked to find a Steiner tree T to interconnect these n terminals in R 2 such that the Steiner points of the tree T, which has at least one Steiner point, are all located on the fixed line l and that the weight w (T) = ∑ e ∈ T w (e) ≤ L , the objective is to minimize the number s(T) of Steiner points of the tree T, where the weight w (e) = 0 if the two endpoints of that edge e ∈ T are located on the line l and otherwise the weight w(e) is the Euclidean distance between the two endpoints of that edge e ∈ T . In addition, when L is the minimum weight of all possible constrained 1-line-fixed Steiner trees as mentioned above, we refer to this version as the problem of minimum number of Steiner points of constrained 1-line-fixed minimum Steiner tree (abbreviated to the MNSP-C1LF-MST problem). We obtain two main results. (1) Using strategies of finding a minimum spanning tree with a degree constraint, we can design a 3-approximation algorithm in time O (n 2 log n) to solve the MNSP-C1LF-ST problem. (2) Combining Delaunay triangulation properties and strategies of finding a minimum spanning tree with a degree constraint, we can provide a simple exact algorithm in time O (n log n log β (n)) to solve the MNSP-C1LF-MST problem, where β (n) = min { i | log (i) n ≤ 4 - 6 / n } . [ABSTRACT FROM AUTHOR]

Residential areas is one of the basic geographical elements on the map and an important content of the map representation. Multi-scale residential areas matching refers to the process of identifying and associating entities with the same name in different data sources, which can be widely used in map compilation, data fusion, change detection and update. A matching method considering spatial neighborhood features is proposed to solve the complex matching problem of multi-scale residential areas. The method uses Delaunay triangulation to divide complex matching entities in different scales into closed domains through spatial neighborhood clusters, which can obtain many-to-many matching candidate feature sets. At the same time, the geometric features and topological features of the residential areas are fully considered, and the Relief-F algorithm is used to determine the weight values of different similarity features. Then the similarity and spatial neighborhood similarity of the polygon residential areas are calculated, after which the final matching results are obtained. The experimental results show that the accuracy rate, recall rate and F value of the matching method are all above 90%, which has a high matching accuracy. It can identify a variety of matching relationships and overcome the influence of certain positional deviations on matching results. The proposed method can not only take account of the spatial neighborhood characteristics of residential areas, but also identify complex matching relationships in multi-scale residential areas accurately with a good matching effect.

Aiming at the infeasibility of using quadrilateral-prisms to describe sharp shapes, an improved vertical stretch algorithm was proposed to generate three-dimensional (3D) hybrid meshes based on the quadrilateral mesh converted from triangles to discretize the geometric models with pinch-out features. A robust and automatic mesh generator was developed, which served as a preprocessing tool for simulating metal forming, water flows and transports. An initial mixed mesh composed of cuspate hexahedra, quadrilateral- and triangular-prisms was constructed to capture the sharp features of pinch-out regions effectively. Five splitting templates were established to divide the 3D elements derived from pinch-out sub-domains into tetrahedra and triangular-prisms. The concept of splitting points was defined, based on which the appropriate implementation mode of each splitting template could be determined, so as to achieve the conformity and consistency of common faces and edges between different kinds of elements. Two topological optimization templates were established to improve the quality of degenerated triangular-prisms and tetrahedra. A new pinch-out boundary quadrilateral insertion method was proposed to avoid the generation of cuspate hexahedra, which simplified the conformity treatment strategies and improved the quality of the resulting mesh to a certain extent. Practical applications confirmed that the hybrid mesh generation methods proposed in this paper could discretize the geometric models with pinch-out features precisely. The requirements on mesh conformity and refinement were also able to be fully satisfied. [ABSTRACT FROM AUTHOR]

In wireless sensor networks (WSNs), the sensor nodes collect data from the target area and send it to the base station through a multi-hop connection. As a result, high energy dissipation of the sensor node may occur. Some times failure of nodes on large scale create partitions in the network. Also, the presence of obstacles is the reason for the coverage gap in networks. The introduction of mobile nodes has been measured to be a worthy approach to significantly decrease the energy dissipation of the static sensor nodes. This job is realized by considering the route through which the mobile collectors move to collect data from the sensor nodes. Another challenging job is to find the path of the mobile collector in an area with obstacles. In this work, an obstacle aware connectivity establishment (OACE) using mobile nodes in wireless sensor networks is proposed. The mobile robot collects data from each partition and carries forward to other partitions so data finally reaches to sink. To achieve this, a Delaunay triangulation based obstacle avoidance clustering has been performed. The performance of the proposed algorithm has been shown by varying the sensor nodes to a single mobile node and multiple mobile nodes. The number of partitions in the network also plays an important role in network performance. Simulation results show that the proposed method with multiple mobile collectors is more energy-efficient with less latency as compared to the single mobile collector for data collection. [ABSTRACT FROM AUTHOR]

Amongst clustering algorithms, density-based clustering has many advantages, including simplicity and the ability to detect clusters of different shapes and discover outliers. Nevertheless, all current density-based clustering algorithms need input parameters. These are difficult to determine and have a substantial impact on the clustering results. DBSCAN is a density-based clustering algorithm that has been widely used in different scientific fields for many years. In this study, a hybrid algorithm named MOGA-DBSCAN, which combines the DBSCAN algorithm with the multi-objective genetic algorithm (MOGA), has been proposed. In this algorithm, the clustering problem is regarded as a multi-objective optimization problem to optimize certain cluster validity indices, which indicate the goodness of the clustering solutions. In this way, the appropriate values of the DBSCAN parameters could be determined automatically. NSGA-II is used to solve this optimization problem, and a new cluster validity index based on detected outliers is used as a fitness function to increase the quality of solutions. The use of such a multi-objective algorithm optimizes several indices simultaneously and yields high-quality results. Moreover, the Delaunay triangulation algorithm, which needs no input parameters, is used to determine the initial bounds of the DBSCAN parameters to reduce the number of generations. The results indicate that the proposed algorithm has an acceptable level of accuracy in determining the DBSCAN parameters. [ABSTRACT FROM AUTHOR]

Detecting the intangible continuous object (ICO) is a significant task, especially when the ICO is harmful as a toxic gas. Many studies used steady sensors to sketch the contour and find the area of the ICO. Applying the mobile sensors can further improve the precision of the detected ICO by efficiently adjusting the positions of a subset of the deployed sensors. This paper proposed two methods to figure out the area of the ICO, named Delaunay triangulation with moving sensors (MDT) and convex hull with moving sensors (MCH). First, the proposed methods divide the sensors into ICO-covered and ICO-uncovered sensors. Next, the convex hull algorithm and the Delaunay triangulation geometric architecture are applied to figure out the rough boundary of the ICO. Then, the area of the ICO is further refined by the proposed sensor moving algorithm. Simulation results show that the figured out area sizes of MDT and MCH are 135% and 102% of the actual ICO. The results are better than the planarization algorithms Gabriel Graph (GG) and Delaunay triangulation without moving sensors, that amount to 137% and 145% of the actual ICO. The simulation also evaluates the impact of the sensors’ moving step size to find the compromise between the accuracy of the area and the convergence time of area refinement.

The deployment of wireless sensor nodes affects the WSN performance, such as the sensing coverage, the connectivity between sensor nodes, and the network lifetime. The deployment is much more complicated when the sensor nodes are heterogeneous and there are some environmental obstacles in an area of interest. The deployment of heterogeneous sensor nodes in an area of interest with obstacles is a challenging problem and also proven to be an NP-complete problem. This paper proposes and evaluates a wireless sensor node deployment algorithm, called DeVForce-AP. The proposed algorithm combines the benefits of the two well-known deployment algorithms, Delaunay triangulation method (D) and extended virtual force algorithm (eVForce), with the adaptive parameter (AP) tuning mechanism. The DeVForce-AP attempts to improve the sensing coverage and network lifetime of the heterogeneous wireless sensor node. The practical deployment problems, such as the environmental obstacles, the network connectivity, and the sensing coverage area, have also been addressed. The DeVForce-AP consists of two steps. In the first step, the DeVForce-AP applies the Delaunay triangulation method to find and eliminate the largest coverage hole in the area of interest. In the second step, the DeVForce-AP applies eVForce method to avoid the existence of environmental obstacles and maintain the network connectivity. Moreover, the proposed DeVForce-AP automatically adjusts its parameters to the environmental scenario. Thus, there is no need to configure the parameters of the DeVForce-AP. The simulation results show that the proposed DeVForce-AP outperforms the random deployment, the traditional Delaunay triangulation deployment, and the traditional virtual force deployment methods.

Physical oceanography models rely heavily on grid discretization. It is known that unstructured grids perform well in dealing with boundary fitting problems in complex nearshore regions. However, it is time-consuming to find a set of unstructured grids in specific ocean areas, particularly in the case of land areas that are frequently changed by human construction. In this work, an attempt was made to use machine learning for the optimization of the unstructured triangular meshes formed with Delaunay triangulation in the global ocean field, so that the triangles in the triangular mesh were closer to equilateral triangles, the long, narrow triangles in the triangular mesh were reduced, and the mesh quality was improved. Specifically, we used Delaunay triangulation to generate the unstructured grid, and then developed a K-means clustering-based algorithm to optimize the unstructured grid. With the proposed method, unstructured meshes were generated and optimized for global oceans, small sea areas, and the South China Sea estuary to carry out data experiments. The results suggested that the proportion of triangles with a triangle shape factor greater than 0.7 amounted to 77.80%, 79.78%, and 79.78%, respectively, in the unstructured mesh. Meanwhile, the proportion of long, narrow triangles in the unstructured mesh was decreased to 8.99%, 3.46%, and 4.12%, respectively.

DELAUNAYSPARSE contains both serial and parallel codes written in Fortran 2003 (with OpenMP) for performing medium- to high-dimensional interpolation via the Delaunay triangulation. To accommodate the exponential growth in the size of the Delaunay triangulation in high dimensions, DELAUNAYSPARSE computes only a sparse subset of the complete Delaunay triangulation, as necessary for performing interpolation at the user specified points. This article includes algorithm and implementation details, complexity and sensitivity analyses, usage information, and a brief performance study. [ABSTRACT FROM AUTHOR]

To perform numerical analyses, such as bio-mechanical analyses, on bones, it is necessary to construct the mesh model of the shape of the bone. In previous studies, the mesh has been generated by assuming that bones are homogeneous in terms of material distribution. However, bones are inherently heterogeneous. Therefore, the mesh has to be generated by considering the variation of the properties of bones. In this study, we propose a method for automatically generating a bone mesh by considering its heterogeneity. However, only two-dimensional triangular meshes are considered. In the proposed method, the boundary polylines of a bone are extracted from its computed tomography (CT) image using the marching squares method. Nodes are randomly generated on and inside the boundary polylines, and triangles are generated from the nodes by Delaunay triangulation. When the nodes are generated on and inside the boundary polylines, the density of the nodes is controlled by threshold functions defined by the magnitude of the gradient vector of the Hounsfield unit values of the CT image. The proposed method was implemented using C++ and visualization toolkit, and experiments were performed using CT images on the right femur, hip bones, and vertebra. We also verified that the proposed method can generate meshes reflecting the variation of the properties of bones. [ABSTRACT FROM AUTHOR]

We present a mixed reality-based assistive system for shading paper sketches. Given a paper sketch made by an artist, our interface helps inexperienced users to shade it appropriately. Initially, using a simple Delaunay-triangulation based inflation algorithm, an approximate depth map is computed. The system then highlights areas (to assist shading) based on a rendering of the 2.5-dimensional inflated model of the input contour. With the help of a mixed reality system, we project the highlighted areas back to aid users. The hints given by the system are used for shading and are smudged appropriately to apply an artistic shading to the sketch. The user is given flexibility at various levels to simulate conditions such as height and light position. Experiments show that the proposed system aids novice users in creating sketches with impressive shading. [ABSTRACT FROM AUTHOR]

A spatial colocation pattern is a group of spatial features whose instances frequently appear together in close proximity to each other. The proximity of instances is generally measured by the distance between them. If the distance is smaller than a distance threshold that is specified by users, they have a neighbor relationship. However, it is difficult for users to give a suitable distance threshold and mining results also vary widely with different distance thresholds. In addition, using distance thresholds are hard to accurately obtain neighborhoods of instances in heterogeneous distribution density data sets. In this study, we propose a new method for determining the neighbor relationship of instances in space without the distance threshold based on Delaunay triangulation (DT). We design three filtering strategies, such as a feature invalid edge, a global positive edge, and a local positive edge, to constrain the original DT to accurately extract the neighborhoods of instances in space. Then, a miner called DT‐based colocation (DTC) pattern mining is developed. Different from the traditional algorithms which adopt the time‐consuming generate‐test candidate model, DTC directly collects the table instances of colocation patterns from the constrained DT by building neighboring polygons and filters prevalent patterns. We compare the results mined by DTC with by the traditional algorithms at macrolevel and microlevel on both real and synthetic data sets to prove that the DTC algorithm improves the effectiveness and fineness of mining results. [ABSTRACT FROM AUTHOR]

This paper considers the efficient minimization of the infinite time average of a stationary ergodic process in the space of a handful of design parameters which affect it. Problems of this class, derived from physical or numerical experiments which are sometimes expensive to perform, are ubiquitous in engineering applications. In such problems, any given function evaluation, determined with finite sampling, is associated with a quantifiable amount of uncertainty, which may be reduced via additional sampling. The present paper proposes a new optimization algorithm to adjust the amount of sampling associated with each function evaluation, making function evaluations more accurate (and, thus, more expensive), as required, as convergence is approached. The work builds on our algorithm for Delaunay-based Derivative-free Optimization via Global Surrogates (Δ -DOGS, see JOGO 10.1007/s10898-015-0384-2). The new algorithm, dubbed α -DOGS, substantially reduces the overall cost of the optimization process for problems of this important class. Further, under certain well-defined conditions, rigorous proof of convergence to the global minimum of the problem considered is established. [ABSTRACT FROM AUTHOR]

This paper addresses reliable and efficient calculation of the mode of a multivariate sample, which is a classical fusion function. In particular, we focus on the inputs given on the unit simplex, when aggregating elements of Atanassov intuitionistic fuzzy sets, interval‐valued fuzzy sets and their extensions, as well as compositional data. We outline the use of a specially designed 2‐additive fuzzy measures and the Choquet integral for the purposes of reducing computational complexity in higher dimensions. We present computational analysis and benchmark four different methods of density‐based mode estimation. [ABSTRACT FROM AUTHOR]

We introduce Delaunay Point Processes, a framework for the extraction of geometric structures from images. Our approach simultaneously locates and groups geometric primitives (line segments, triangles) to form extended structures (line networks, polygons) for a variety of image analysis tasks. Similarly to traditional point processes, our approach uses Markov Chain Monte Carlo to minimize an energy that balances fidelity to the input image data with geometric priors on the output structures. However, while existing point processes struggle to model structures composed of inter-connected components, we propose to embed the point process into a Delaunay triangulation, which provides high-quality connectivity by construction. We further leverage key properties of the Delaunay triangulation to devise a fast Markov Chain Monte Carlo sampler. We demonstrate the flexibility of our approach on a variety of applications, including line network extraction, object contouring, and mesh-based image compression. [ABSTRACT FROM AUTHOR]

Kinetic data structures represent an extension to ordinary data structures, where the underlying data become time dependent (e.g. moving points). In this paper, we define the kinetic locally minimal triangulation (KLMT) as a kinetic data structure extension to the locally minimal triangulation in the Euclidean plane. We explore the general properties of this data structure in order to show what types of events need to be considered during its life cycle; we also describe the predicates associated with these events. To describe the general kinetic features, we prove that KLMT is responsive, compact, efficient and non-local. In the combinatorial analysis of KLMT, we briefly describe the mathematical apparatus commonly used to investigate computational complexity properties of kinetic data structures and use it to establish the bounds on the number of events processed during the life cycle of this data structure. Finally, the obtained results are compared to the kinetic Delaunay triangulation showing that KLMT may provide some benefits over kinetic Delaunay triangulation, namely simplifying the mathematical equations that need to be computed in order to obtain the times of events. [ABSTRACT FROM AUTHOR]

Aiming at that complex topological structure and various feature details of tree point cloud, this paper proposed an algorithm for extract the curve skeleton based on point clou d contraction. Firstly, in order to directly apply the mesh shrinkage algorithm on the surface of the point cloud, it performed local cloud p rincipal component analysis and Delaunay triangulation on the point cloud . Secondly,for the problem th at the tree point cloud's complex topology and the details of the last branch, it used the curvature normal operator to shrink the point cloud . In view of the slenderness of the branches of the trees and the gentle curvature, it used the modified Q EM mesh simplification method to fold the triangular mesh into a one-dimensional curve skeleton. Finally, it connected and centered the resulting curve skeleton. The algorithm operated directly on the point cloud and did not require additional information and pre-processing operations. It had good robustness to noise and residual fault clouds. Experiments show that compared with other classical algorithms such as Ll-medial and Rosa, the tree point cloud skeleton extracted by the algorithm has a good topological structure, which fully expresses the biological structure and cha racteristics of trees in the natural environment. The skeleton extraction speed of the tree point cloud is increased by more than 3 times, and the branch reconstruction degree is increased by 25% . [ABSTRACT FROM AUTHOR]

Coxeter triangulations are triangulations of Euclidean space based on a single simplex. By this we mean that given an individual simplex we can recover the entire triangulation of Euclidean space by inductively reflecting in the faces of the simplex. In this paper we establish that the quality of the simplices in all Coxeter triangulations is O (1 / d) of the quality of regular simplex. We further investigate the Delaunay property for these triangulations. Moreover, we consider an extension of the Delaunay property, namely protection, which is a measure of non-degeneracy of a Delaunay triangulation. In particular, one family of Coxeter triangulations achieves the protection O (1 / d 2) . We conjecture that both bounds are optimal for triangulations in Euclidean space. [ABSTRACT FROM AUTHOR]

In this paper we present an edge swapping approach for incorporating line segments into triangulation. If the initial triangulation is Delaunay, the algorithm tends to produce optimal Constrained Delaunay triangulation by improving the triangles' aspect ratios from the local area being constrained. There are two types of methods for constructing Constrained Delaunay Triangulation: straight-forward ones which take both points and line segments as source data and produce constrained triangulation from them at once; and post-processing ones which take an already constructed triangulation and incorporate line segments into it. While most of the existing post-processing approaches clear the triangle's edges intersected by the line segment being incorporated and fill the opened hole (cavity) by re-triangulating it, the only processing that our algorithm does is to change the triangulation connectivity and to improve the triangles' aspect ratios through edge swapping. Hereof, it is less expensive in terms of both operating and memory costs. The motivation behind our approach is that most of the existing straight-forward triangulators are too slow and not stable enough. The idea is to use pure Delaunay triangulator to produce an initial Delaunay triangulation and later on to constrain it to the line segments (in other words, to split the processing into two steps, each of which is stable enough and the combination of them works much faster). The algorithm also minimizes the number of the newly introduced triangulation points - new points are added only if any of the line segment's endpoints does not match an existing triangulation point. [ABSTRACT FROM AUTHOR]

A novel method for automatic triangular grid generation on a free-form surface based on Coulomb's law is proposed in this paper, which we refer to as the particle self-organizing system (PSOS). The self-organizing of particles is realized by the interaction between charged particles, which brings about an even layout of particles. After connecting the optimized particles, a uniform triangular grid is generated. First, a moderate number of grid points are randomly arranged on the surface. Second, the grid points are regarded as charged particles with the same charge in the electric field and free to move driven by the Coulomb force. Third, the equilibrium state of the particle system is acquired according to the equivalent electric field intensity of each particle. Finally, the triangular grid is generated by the Delaunay method. According to the different motion space of particles, the particle self-organizing system can be divided into an indirect method and a direct method. The particle motion space of the indirect method is the parameter domain; the grid layout is obtained first and then mapped back to the space surface. The particle motion space of the direct method is the physical space of the surface; a grid is generated directly on the physical domain, and no mapping process is needed. The case studies indicate that both methods can generate a uniform triangular grid quickly, with the direct method having a higher grid quality. [ABSTRACT FROM AUTHOR]

The article publishes archaeological materials found on the surface of a settlement with the “ash lenses” of the Noua culture discovered during the investigation of the nearby large Cucuteni-Trypillia settlement by the village of Stolniceni in the Edinet District. The finds are represented both by characteristic pottery and by various crafts made of clay, stone, flint and horn, among which there is a fragment of the mold or part of the mace head. Along with the introduction of findings from the Stolniceni II site into scientific use, an attempt is made to illustrate its local and regional context by mapping the settlements of the Noua culture from the territory of Moldova and the subsequent GIS processing of data on their distribution. The use of some algorithms of spatial analysis made it possible to allocate about 20 clusters of sites, each of which includes 5-9 settlements and is located on an area of 25-70 sq. km. It seems that such a distribution of sites marks the presence of clearly delineated territorial entities that served as an arena for cyclical movements of specific cattle-breeding communities, and a consistent change in the grazing area.

Cell-based fluorescence imaging assays have the potential to generate massive amount of data, which requires detailed quantitative analysis. Often, as a result of fixation, labeled nuclei overlap and create a clump of cells. However, it is important to quantify phenotypic read out on a cell-by-cell basis. In this paper, we propose a novel method for decomposing clumps of nuclei using high-level geometric constraints that are derived from low-level features of maximum curvature computed along the contour of each clump. Points of maximum curvature are used as vertices for Delaunay triangulation (DT), which provides a set of edge hypotheses for decomposing a clump of nuclei. Each hypothesis is subsequently tested against a constraint satisfaction network for a near optimum decomposition. The proposed method is compared with other traditional techniques such as the watershed method with/without markers. The experimental results show that our approach can overcome the deficiencies of the traditional methods and is very effective in separating severely touching nuclei.

This paper considers the problem of improving the routing performance of hierarchical Delaunay networks. Delaunay network is a network topology for peer-to-peer systems based on the Delaunay triangulation of a set of points associated with a set of peers. It is known that Delaunay networks have a favorable property as a topology for peer-to-peer systems such that a greedy routing scheme always delivers a given message to its destination without encountering a dead-end. The key idea used in the proposed method is to apply a hash function to the address of participant peers. More concretely, by applying a hash function to the coordinate point of the peers and by associating several points to each peer, we could realize an overlay so that the number of hops to the destination in the original network could be significantly reduced. [ABSTRACT FROM AUTHOR]

Outlier detection is a major topic in robust statistics due to the high practical significance of anomalous observations. Many existing methods, however, either are parametric or cease to perform well when the data are far from linearly structured. In this paper, we propose a quantity, Delaunay outlyingness, that is a nonparametric outlyingness score applicable to data with complicated structure. The approach is based on a well‐known triangulation of the sample, which seems to reflect the sparsity of the pointset to different directions in a useful way. We derive results on the asymptotic behavior of Delaunay outlyingness in case of a sufficiently simple set of observations. Simulations and an application to empirical data are also discussed. [ABSTRACT FROM AUTHOR]