Delaunay Triangulation Research Articles

A DTSD model based on PS-InSAR surface multi-type deformation monitoring of villages in the mining area

Evaluating building damage in mining areas using Interferometric Synthetic Aperture Radar (InSAR) has inherent challenges. This work presents a Delaunay Triangulation of Surface Deformation (DTSD) model that utilizes Permanent Scatter InSAR to analyze various types of deformations in villages. This model created a network of irregular triangles using Delaunay triangulation and PS points as the input. The calculation involved determining the inclination of triangular edges and the torsion of spatial Bezier curves fitted by these edges. The PS points' maximum inclination and curvature values were identified by solving over-determined equations. Results from a slurry injection mine in Huaibei, China, indicate that the various types of deformations in the neighboring communities were below 8 %, and the buildings experienced minimal damage. The DTSD model offers a theoretical framework for monitoring and assessing various types of surface deformation and designing essential zones for building protection.

Automatic identification and interpretation of discontinuities of rock slope from a 3D point cloud based on UAV nap-of-the-object photogrammetry

Research on rock slopes has attracted considerable attention in the fields of infrastructure construction and disaster prevention. The search for an efficient and reliable method for discontinuity collection is an important task for various studies of jointed rock slope. Capturing high-precision and complete rock exposure images based on unmanned aerial vehicle (UAV) multi-angle and nap-of-the-object photogrammetry technology is proposed to realize the construction of a millimeter-level 3D point cloud for the high and steep slope. This study develops a new automatic methodology for discontinuity identification and interpretation. A Delaunay triangulation network is created for connecting adjacent points in the point cloud to calculate normal vectors and search for neighbor points efficiently. Combined with the modified region-growing algorithm, an automatic procedure which identifies discontinuities and acquires geometrical parameters efficiently and accurately is established. The proposed approach is applied to the high-steep rock slope on the northern bank of the Sequ Grand Bridge in the Changdu area of Tibet. Compared with the results from the manual survey, the proposed method is more reliable and exhibits high accuracy for discontinuity identification and interpretation on rock exposure.

Machine learning aided understanding and manipulating thermal transport in amorphous networks

Thermal transport plays a pivotal role across diverse disciplines, yet the intricate relationship between amorphous network structures and thermal conductance properties remains elusive due to the absence of a reliable and comprehensive network’s dataset to be investigated. In this study, we have created a dataset comprising multiple amorphous network structures of varying sizes, generated through a combination of the node disturbance method and Delaunay triangulation, to fine-tune an initially random network toward both increased and decreased thermal conductance C. The tuning process is guided by the simulated annealing algorithm. Our findings unveil that C is inversely dependent on the normalized average shortest distance Lnorm connecting heat source nodes and sink nodes, which is determined by the network topological structure. Intuitively, the amorphous network with increased C is associated with an increased number of bonds oriented along the thermal transport direction, which shortens the heat transfer distance from the source to sink node. Conversely, thermal transport encounters impedance with an augmented number of bonds oriented perpendicular to the thermal transport direction, which is demonstrated by the increased Lnorm. This relationship can be described by a power law C=Lnormα, applicable to the diverse-sized amorphous networks we have investigated.

Constructing topology‐constrained distance cartograms with application on spatial interaction data

AbstractA distance cartogram is a deformed map where the distance between points conforms to a specific proximity indicator. Its readability is crucial, requiring a similar spatial arrangement of points between the original map and cartogram. Previous studies mainly incorporated angle changes of point pairs into the optimization objective. However, this soft constraint fails to provide high readability for spatial interaction data with numerous points and links. This study emphasizes the significance of maintaining Delaunay triangulation during deformation. To achieve this, topology‐constrained particle swarm optimization (TC‐PSO) is proposed, in which triangle intersections and flipping are prevented during optimization. Additionally, a topology error is introduced to evaluate the difference in triangulation between the original and deformed maps. TC‐PSO outperforms previous approaches by exhibiting the smallest topology error and producing more readable cartograms in simulation experiments and Baidu index data. These show TC‐PSO's advantage as a cartographic tool.

Generating grid maps via the snake model

Generating grid maps via the snake model

Representing Infinite Periodic Hyperbolic Delaunay Triangulations Using Finitely Many Dirichlet Domains

The Delaunay triangulation of a set of points P on a hyperbolic surface is the projection of the Delaunay triangulation of the set P~\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\widetilde{P}$$\\end{document} of lifted points in the hyperbolic plane. Since P~\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\widetilde{P}$$\\end{document} is infinite, the algorithms to compute Delaunay triangulations in the plane do not generalize naturally. Using a Dirichlet domain, we exhibit a finite set of points that captures the full triangulation. We prove that an edge of a Delaunay triangulation has a combinatorial length (a notion we define in the paper) smaller than 12g-6\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$12g-6$$\\end{document} with respect to a Dirichlet domain. To achieve this, we introduce new tools, of intrinsic interest, that capture the properties of length-minimizing curves in the context of closed curves. We then use these to derive structural results on Delaunay triangulations and exhibit certain distance minimizing properties of both the edges of a Delaunay triangulation and of a Dirichlet domain. The bounds produced in this paper depend only on the topology of the surface. They provide mathematical foundations for hyperbolic analogs of the algorithms to compute periodic Delaunay triangulations in Euclidean space.

Collaborative Methods of Resolving Road Graphic Conflicts Based on Cartographic Rules and Generalization Operations

The resolution of road graphic conflicts is a key aspect of map generalization, which involves both scale reduction and the symbolization of map features. This study proposes collaborative methods of road graphic conflict resolution considering different road characteristics. These methods consider both geometric and semantic characteristics, and they incorporate the bend characteristics of roads, the road symbol size, and road semantics. Constrained Delaunay triangulation skeleton lines are used to categorize road graphic conflicts, which are made up of four independent conflict types and four group conflict types. Based on their characteristics, three collaborative methods are designed to deal with the different types of road graphic conflicts: collaboration between deletion and the snake displacement model, collaboration between the snake displacement model and collinearity, and collaboration among simplification, smoothing, and the beam displacement model. Two types of independent conflicts can be processed using only one simple operation. This study summarizes the cartographic rules for resolving road graphic conflicts, and these are used along with geometric features to drive the collaborative methods or one simple operation presented here. The experimental results indicate that the method proposed in this study can effectively resolve road graphic conflicts.

Efficient Crowd Anomaly Detection Using Sparse Feature Tracking and Neural Network

Crowd anomaly detection is crucial in enhancing surveillance and crowd management. This paper proposes an efficient approach that combines spatial and temporal visual descriptors, sparse feature tracking, and neural networks for efficient crowd anomaly detection. The proposed approach utilises diverse local feature extraction methods, including SIFT, FAST, and AKAZE, with a sparse feature tracking technique to ensure accurate and consistent tracking. Delaunay triangulation is employed to represent the spatial distribution of features in an efficient way. Visual descriptors are categorised into individual behaviour descriptors and interactive descriptors to capture the temporal and spatial characteristics of crowd dynamics and behaviour, respectively. Neural networks are then utilised to classify these descriptors and pinpoint anomalies, making use of their strong learning capabilities. A significant component of our study is the assessment of how dimensionality reduction methods, particularly autoencoders and PCA, affect the feature set’s performance. This assessment aims to balance computational efficiency and detection accuracy. Tests conducted on benchmark crowd datasets highlight the effectiveness of our method in identifying anomalies. Our approach offers a nuanced understanding of crowd movement and patterns by emphasising both individual and collective characteristics. The visual and local descriptors facilitate high-level analysis by closely relating to semantic information and crowd behaviour. The analysis observed shows that this approach offers an efficient framework for crowd anomaly detection, contributing to improved crowd management and public safety. The proposed model achieves accuracy of 99.5 %, 96.1%, 99.0% and 88.5% in the UMN scenes 1, 2, and 3 and violence in crowds datasets, respectively.

Alternating size field optimizing and parameterization domain CAD model remeshing

Tessellating CAD models into triangular meshes is a long-lasting problem. Size field is widely used to accommodate varieties of requirements in remeshing, and it is usually discretized and optimized on a prescribed background mesh and kept constant in the subsequent remeshing procedure. Instead, we propose optimizing the size field on the current mesh, then using it as guidance to generate the next mesh. This simple strategy eliminates the need of building a proper background mesh and greatly simplifies the size field query. For better quality and convergence, we also propose a geodesic distance based initialization and adaptive re-weighting strategy in size field optimization. Similar to existing methods, we also view the remeshing of a CAD model as the remeshing of its parameterization domain, which guarantees that all the vertices lie exactly on the CAD surfaces and eliminates the need for costly and error-prone projection operations. However, for vertex smoothing which is important for mesh quality, we carefully optimize the vertex's location in the parameterization domain for the optimal Delaunay triangulation condition, along with a high-order cubature scheme for better accuracy. Experiments show that our method is fast, accurate and controllable. Compared with state-of-the-art methods, our approach is fast and usually generates meshes with smaller Hausdorff error, larger minimal angle with a comparable number of triangles.

Effects of microscopic pore-throat structure on gas–liquid relative permeability: Porous media construction and pore-scale simulation

The porous media structure of the oil/gas reservoir changes greatly after long-term development, which subsequently influences the macroscopic relative permeability. To clarify the effects of microscopic pore-throat structure on macroscopic relative permeability, we first proposed a method to generate two-dimensional porous media images with adjustable structure parameters. The method is based on Delaunay triangulation and is similar to the pore-network generation process, which can provide binary images for direct numerical simulation of flow through porous media. Then, we established the single component multiphase Shan–Chen lattice Boltzmann method coupling the real gas equation of state. Finally, we discussed the effect of pore radius, coordination number, pore-throat ratio, pore shape, and wettability on the gas–liquid relative permeability curve using the lattice Boltzmann simulation. This study provides an effective method to generate porous media and explain the mechanism of relative permeability change at the pore scale.

Graph deep learning recognition of port ship behavior patterns from a network approach

The detection and recognition of ship mobile behavior patterns based on automatic identification system (AIS) data are crucial for ship navigation and maritime supervision. However, present methods, such as rule-based constraints and density clustering extraction, still suffer from restrictions imposed by artificial settings of parameters and thresholds. The lack of neighborhood context information in unstructured and serialized ship trajectory vector data makes it challenging to incorporate advanced methods such as deep learning for pattern learning. This study builds multiple semi-supervised deep learning graph neural network (GNN) models based on the message passing paradigm for recognizing ship mobile behavior patterns by constructing an AIS trajectory network and computing multi-order node features through Delaunay triangulation. It can get rid of the dependence on parameters of traditional rule-based and unsupervised learning methods. It also reduces the dependence on auxiliary information in trajectory qualitative by introducing multi-order node features. We conducted the experiments on cargo ship data from New York and Singapore to test our method. The model's classification accuracy is more than 99% for the New York dataset and more than 95% for the Singapore dataset. This method can be extended to other types of ships and traffic trajectory vector data with the excellent application potential of GNN in pattern recognition of vector mobile data. The code and experimental data are available at: https://github.com/destiny1103/DT-GNN.

Image Morpher

The "Image Morphing with the Beier-Neely Method" research paper extensively explores image transformation techniques, with a special focus on the Beier- Neely approach. Image morphing, the art of seamlessly transforming one image into another, has garnered significant attention for its applications in animation, filmmaking, and scientific visualization. The research paper delves into the historical context and importance of image morphing, particularly emphasizing the role of the Beier-Neely method in addressing the limitations of earlier techniques. Classical image morphing methods, characterized by pixel-level interpolation, suffer from visual artifacts, manual correspondence definition, and sluggishness. These shortcomings set the stage for the introduction of the feature-based Beier-Neely method, which revolutionized image morphing by allowing control points on features, facilitating smooth transitions and natural transformations. This research papers objectives are clearly articulated, with the primary aim of implementing the Beier- Neely method to produce high-quality image morphs. The research paper proposes a system architecture that underscores the use of feature-based control points, Delaunay triangulation, affine transformations, and the significance of visual feedback. Additionally, it provides a detailed analysis of the mathematical foundations and algorithmic intricacies of the Beier-Neely method, elucidating the theoretical framework driving its effectiveness. Overall, the research paper provides a comprehensive exploration of image morphing techniques, highlighting the pivotal role played by the Beier-Neely method in advancing the field.. Key Words: Image Morphing, Beier-Neely Method, Seamless Transitions, Feature-based Control Points, System Architecture, Mathematical Foundations

An overall adjustment method for relative corrections of master reference stations in the BDS/GNSS network RTK system

We here address problems of nonunique paths and poor fault tolerance in the traditional shortest path transfer method and propose an overall adjustment method of relative corrections of master reference stations in BDS/GNSS Network RTK systems. Our method comprehensively considers the vector relationship of baseline error corrections, the baseline closure error of Delaunay triangulation and the interpolation relationship between stations to realize the one-time generation, obtaining all relative error corrections of the master reference station in a network RTK system. The test results showed that our method can achieve a success rate of more than 95% and an incorrect rate of less than 0.01%. The error corrections, generated by the two methods, are verified and analysed by the positioning accuracy of the rover. The results show that the positioning accuracy of the method in this paper is improved by about 17% over the shortest path transfer method.

Quantitative research on the degree of disorder of traditional settlements: a case study of Liangjia Village, Jingxing, Hebei Province

Traditional settlements are vital carriers of Chinese history and culture, reflecting the direct and original needs of generations. However, the modernization of settlements will inevitably disrupt the spontaneous growth patterns inherent in traditional settlements. The degree of disorder of the settlement is not only the embodiment of its form, but also the concrete manifestation of its construction intention. We use the degree of disorder in settlements to assess the construction intentions of the settlements, the results allow us to assess whether new planning aligns with the original construction logic, thereby assessing the extent of interference by modernization in traditional villages. This can provide guidance and assistance for settlement conservation and future planning. By using the Delaunay triangulation network, street polar histogram and direction entropy, and comprehensibility of settlements, this paper quantitatively analyzes the degree of disorder in the three levels of architecture, street and local environment of the settlement. Liangjia Village, the example in this research, is divided into three areas—two new and one old. degree of disorders in architecture, streets, and local environment are calculated and compared with the overall settlement. The study finds that the construction logic for buildings and streets remains stable throughout development. However, notable differences exist in environmental construction principles between new and old sections. The analysis suggests that traditional settlements, guided by inherent principles, maintain stability under external influences, serving as a benchmark for future planning and modernization decisions.

Distributed multi-UAV shield formation based on virtual surface constraints

This paper proposes a method for the deployment of a multi-agent system of unmanned aerial vehicles (UAVs) as a shield with potential applications in the protection of infrastructures. The shield shape is modeled as a quadric surface in the 3D space. To design the desired formation (target distances between agents and interconnections), an algorithm is proposed where the input parameters are just the parametrization of the quadric and the number of agents of the system. This algorithm guarantees that the agents are almost uniformly distributed over the virtual surface and that the topology is a Delaunay triangulation. Moreover, a new method is proposed to check if the resulting triangulation meets that condition and is executed locally. Because this topology ensures that the formation is rigid, a distributed control law based on the gradient of a potential function is proposed to acquire the desired shield shape and proofs of stability are provided. Finally, simulation and experimental results illustrate the effectiveness of the proposed approach.

A comprehensive methodology for residual capacity evaluation of damaged steel tubular columns

Steel tubular sections are extensively used in modern-day construction due to their superior structural efficiency and aesthetic appearance. The thin-walled tubular sections are often subjected to accidental loading due to heavy object impact, collision, or improper handling during transportation. Due to induced geometric defects by unanticipated loads, the load-carrying capacity of the section decreases. This study proposes a methodology to estimate the residual capacity of damaged circular and square tubular specimens in axial compression. Initially, the specimen's surface coordinates were obtained in the form of a dense point cloud using a 3D digital image correlation (DIC) setup. Using a linear interpolation function based on Delaunay triangulation, the dense point cloud was regularized into a set of sparsely spaced nodes that would yield computationally efficient finite element (FE) analysis. The interpolation introduced errors at the locations of sharp curvature on the surface. A systematic smoothing (filtering) approach was proposed to minimize the effect of the interpolation error. The proposed methodology was validated against compression tests on five damaged and three as-built specimens, which consisted of circular and square tubular sections. The average residual strength estimated was found to be 93% of the experimental observations.

Abstract 5222: AI-driven, mIF-based cell-omics reveals spatially resolved cell signature for outcome prediction in NSCLC patients

Abstract Background: Despite the rapidly increasing number of new targeted and immunotherapeutic options over the past two decades, the prognosis of patients with NSCLC, even with early-stage tumors, is still poor and novel biomarkers are needed to better stratify patients in terms of survival and treatment response. A novel approach is to gain a holistic understanding of the cellular composition and formation of the tumor microenvironment (TME). Therefore, we developed a miF-based, AI-driven approach for spatially resolved TME characterization at the cellular level and used this to successfully predict clinical outcome. Methods: We assembled a large bicentric real-world sample group of 1168 patients with resected NSCLC from the Charite and the University Hospital Cologne. For tissue microarray construction, four 1.5 mm tissue cores were punched from each formalin-fixed and paraffin-embedded tumor block. Sections were stained with a 12-plex IF panel followed by H&E staining. All stains were scanned and co-registered with single cell accuracy. Next, we trained a H&E-based tissue segmentation model to detect the different tumor regions: carcinoma, stroma, and necrosis. In addition, we developed a nucleus-based cell detection model, and 12 cell classification models to categorize each detected cell by single-miF channels. Different cell phenotypes were derived from the marker-specific cell classifications. Finally, we trained a model on the Charité cohort using the spatially resolved cell readouts, spot-wise phenotype log-density, co-clustering of marker expression, and frequency of co-occurrence of marker expression through Delaunay triangulation, to predict patient survival on the Cologne cohort. Results: The tissue segmentation model achieved a macro averaged F1 score of 92%. The cell detection model identified a total of 53 million cells that were classified marker-wise with an F1 score of at least 95% on hold-out data. Our final prediction model identified a stable spatially resolved cell signature, consisting of 10 different characteristic cell neighborhood niches, which could be used to predict overall patient survival. The model trained on the Charite cohort was validated with the Cologne cohort and achieved a high performance (C-score of 71). In comparison, the UICC8 stage and the immunoscore (CD20+CD3+/carcinoma cell ratio), which were used as a baseline, achieved C-scores of 63 and 54, respectively. Conclusions: The combination of our large real-world clinical cohort, multiplex panel, and automated AI approach enabled a broad spatially resolved exploration of the TME in NSCLC at single cell resolution. Our model identified a specific cell neighborhood signature predictive of patient survival outperforming the commonly used prognostic scores, UICC8 stage and immunoscore. This allows for an improved patient stratification with potential implication for therapy selection. Citation Format: Simon Schallenberg, Gabriel Dernbach, Sharon Ruane, Cornelius Böhm, Lukas Ruff, Kai Standvoss, Sandip Ghosh, Marco Frentsch, Mihnea Dragomir, Rebecca Fritz, Ines Koch, Corinna Friedrich, Il-Kang Na, Sabine Merkelbach-Bruse, Alexander Quaas, Nikolaj Frost, Kyrill Boschung, Winfried Randerath, Georg Schlachtenberger, Matthias Heldwein, Ulrich Keilholz, Khosro Hekmat, Jens Rückert, Reinhard Büttner, Angela Vasaturo, David Horst, Maximilian Alber, Frederick Klauschen. AI-driven, mIF-based cell-omics reveals spatially resolved cell signature for outcome prediction in NSCLC patients [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2024; Part 1 (Regular Abstracts); 2024 Apr 5-10; San Diego, CA. Philadelphia (PA): AACR; Cancer Res 2024;84(6_Suppl):Abstract nr 5222.

A Delaunay triangulation based dynamic pricing approach to profit‐driven crowdsourced package delivery

AbstractCrowdsourced package delivery (CPD) has gained great interest from the logistics industry and academe due to its signficant economic and environmental impact. A number of progresses have been reported; however, dynamic pricing, as a special and significant part of the uncertain CPD markets, is far less explored. To address the problem, a novel Delaunay Triangulation (DT) based pricing strategy is proposed for dealing with the imbalanced demand and supply in local markets with the aim to maximizing the profit of the CPD platform. To cater to drivers’ wishes further, the hyperbolic temporal discounting function is applied to estimate their psychological rewards in order to increase the possibility of package acceptance. A three‐stage framework consisting of the DT‐based pricing, the matching pruning and the package assigning algorithm is proposed, to figure out the best‐possible package‐driver matching. With the dataset generated by Brinkhoff road network generator in the city of Jinan and Luoyang, China, a series of experiments is conducted to evaluate the proposed approach against several representative baseline approaches. Experimental results show that the approach significantly outperforms the other approaches in terms of effectiveness and efficiency.

Reducing the wrapping effect of set computation via Delaunay triangulation for guaranteed state estimation of nonlinear discrete-time systems

Set computation methods have been widely used to compute reachable sets, design invariant sets and estimate system state for dynamic systems. The wrapping effect of such set computation methods plays an essential role in the accuracy of their solutions. This paper studies the wrapping effect of existing interval, zonotopic and polytopic set computation methods and proposes novel approaches to reduce the wrapping effect for these set computation methods based on the task of computing the dynamic evolution of a nonlinear uncertain discrete-time system with a set as the initial state. The proposed novel approaches include the partition of a polytopic set via Delaunay triangulation and also the representation of a polytopic set by the union of small zonotopes for the following set propagation. The proposed novel approaches with the reduced wrapping effect has been further applied to state estimation of a nonlinear uncertain discrete-time system with improved accuracy. Similar to bisection for interval and zonotopic sets, Delaunay triangulation has been introduced as a set partition tool for polytopic sets, which has opened new research directions in terms of novel set partition, set representation and set propagation for reducing the wrapping effect of set computation.

Aerial Surveillance Leveraging Delaunay Triangulation and Multiple-UAV Imaging Systems

In aerial surveillance systems, achieving optimal object detection precision is of paramount importance for effective monitoring and reconnaissance. This article presents a novel approach to enhance object detection accuracy through the integration of Delaunay triangulation with multi-unmanned aerial vehicle (UAV) systems. The methodology involves positioning multiple UAVs at pre-specified locations using the Delaunay triangulation algorithm with performance of O (n log n). This is compared with the conventional single UAV approach at a near distance. Our findings reveal that the collaborative efforts of multiple UAVs, guided by Delaunay triangulation, significantly improves object detection accuracy, especially when compared to a single UAV operating in close proximity. This research employs advanced image processing techniques to identify objects in the area under surveillance. Results indicate a substantial enhancement in the collective surveillance capabilities of the multi-UAV system, demonstrating its efficacy in unconstrained scenarios. This research not only contributes to the optimization of aerial surveillance operations but also underscores the potential of spatially informed UAV networks for applications demanding heightened object detection accuracy. The integration of Delaunay triangulation with multi-UAV systems emerges as a promising strategy for advancing the capabilities of aerial surveillance in scenarios ranging from security and emergency response to environmental monitoring.