Showing papers on "Delaunay triangulation published in 2023"

SIFT Matching by Context Exposed

Abstract: This paper investigates how to step up local image descriptor matching by exploiting matching context information. Two main contexts are identified, originated respectively from the descriptor space and from the keypoint space. The former is generally used to design the actual matching strategy while the latter to filter matches according to the local spatial consistency. On this basis, a new matching strategy and a novel local spatial filter, named respectively blob matching and Delaunay Triangulation Matching (DTM) are devised. Blob matching provides a general matching framework by merging together several strategies, including rank-based pre-filtering as well as many-to-many and symmetric matching, enabling to achieve a global improvement upon each individual strategy. DTM alternates between Delaunay triangulation contractions and expansions to figure out and adjust keypoint neighborhood consistency. Experimental evaluation shows that DTM is comparable or better than the state-of-the-art in terms of matching accuracy and robustness. Evaluation is carried out according to a new benchmark devised for analyzing the matching pipeline in terms of correct correspondences on both planar and non-planar scenes, including several state-of-the-art methods as well as the common SIFT matching approach for reference. This evaluation can be of assistance for future research in this field.

FSGANv2: Improved Subject Agnostic Face Swapping and Reenactment

Abstract: We present Face Swapping GAN (FSGAN) for face swapping and reenactment. Unlike previous work, we offer a subject agnostic swapping scheme that can be applied to pairs of faces without requiring training on those faces. We derive a novel iterative deep learning–based approach for face reenactment which adjusts significant pose and expression variations that can be applied to a single image or a video sequence. For video sequences, we introduce a continuous interpolation of the face views based on reenactment, Delaunay Triangulation, and barycentric coordinates. Occluded face regions are handled by a face completion network. Finally, we use a face blending network for seamless blending of the two faces while preserving the target skin color and lighting conditions. This network uses a novel Poisson blending loss combining Poisson optimization with a perceptual loss. We compare our approach to existing state-of-the-art systems and show our results to be both qualitatively and quantitatively superior. This work describes extensions of the FSGAN method, proposed in an earlier conference version of our work (Nirkin et al. 2019), as well as additional experiments and results.

Everett Map Construction for Modeling Static Hysteresis: Delaunay-Based Interpolant Versus B-Spline Surface

Abstract: The Everett map is a component used by the Preisach model (PM) that stores hysteresis behavior. In magnetics it often contains the characterized magnetic properties of soft-magnetic material. Fundamentally, the Everett map is created from scattered data points, obtained from a set of magnetic measurements, which must be interpolated to obtain a continuous map. The commonly adopted method to perform the interpolation is based on a Delaunay triangulation computation and subsequent polynomial or B-spline surface fit. However, this approach introduces artifacts in the modeled hysteresis results. Therefore, this work presents an alternative method to construct an artifact-free Everett map, by reconstructing a set of measured hysteresis loops with a pre-processing algorithm and representing the data with a scattered B-spline surface. When applied in the PM, a set of test hysteresis loops was reproduced with high accuracy and without artifacts, compared to the commonly used Delaunay-based interpolant.

A Novel Type of Boundary Extraction Method and Its Statistical Improvement for Unorganized Point Clouds Based on Concurrent Delaunay Triangular Meshes

Abstract: Currently, three-dimensional (3D) laser-scanned point clouds have been broadly applied in many important fields, such as non-contact measurements and reverse engineering. However, it is a huge challenge to efficiently and precisely extract the boundary features of unorganized point cloud data with strong randomness and distinct uncertainty. Therefore, a novel type of boundary extraction method will be developed based on concurrent Delaunay triangular meshes (CDTMs), which adds the vertex-angles of all CDTMs around a common data point together as an evaluation index to judge whether this targeted point will appear at boundary regions. Based on the statistical analyses on the CDTM numbers of every data point, another new type of CDTM-based boundary extraction method will be further improved by filtering out most of potential non-edge points in advance. Then these two CDTM-based methods and popular α-shape method will be employed in conducting boundary extractions on several point cloud datasets for comparatively analyzing and discussing their extraction accuracies and time consumptions in detail. Finally, all obtained results can strongly demonstrate that both these two CDTM-based methods present superior accuracies and strong robustness in extracting the boundary features of various unorganized point clouds, but the statistically improved version can greatly reduce time consumption.

Analysis and Modeling of Polygonality in Retinal Tissue Based on Voronoi Diagram and Delaunay Tessellations

Abstract: Several important properties of biological systems are directly related and even determined by the spatial distribution of their constituent elements. Those elements interact with each other and tend to use space in an optimal way, regarding their specific function and environmental constraints. A detailed methodology, based on Voronoi polygons and Delaunay triangles method employed to extract information on the spatial distribution of cells, is presented. On the other hand, diabetic retinopathy (DR) is defined as microvascular pathology. However, some data have suggested that the retinal photoreceptor (RPs) might be important in the pathogenesis of this ocular disease. In this study, the organization of the PRs in control and diabetic-induced rats was compared, using multiphoton microscopy. The PR mosaic was imaged at different locations in non-stained retinas. Thus, this work investigated the pathological changes in the cellular structures of the retina in the early stages of diabetes in laboratory animals. Of the different proposed tools that are highly reliable to be tested with human retinas, the metrics mean averaged distance and the mean square deviation of the angles are found (P < 0.05).

A Delaunay Edges and Simulated Annealing-Based Integrated Approach for Mesh Router Placement Optimization in Wireless Mesh Networks

Abstract: Wireless Mesh Networks (WMNs) can build a communications infrastructure using only routers (called mesh routers), making it possible to form networks over a wide area at low cost. The mesh routers cover clients (called mesh clients), allowing mesh clients to communicate with different nodes. Since the communication performance of WMNs is affected by the position of mesh routers, the communication performance can be improved by optimizing the mesh router placement. In this paper, we present a Coverage Construction Method (CCM) that optimizes mesh router placement. In addition, we propose an integrated optimization approach that combine Simulated Annealing (SA) and Delaunay Edges (DE) in CCM to improve the performance of mesh router placement optimization. The proposed approach can build and provide a communication infrastructure by WMNs in disaster environments. We consider a real scenario for the placement of mesh clients in an evacuation area of Kurashiki City, Japan. From the simulation results, we found that the proposed approach can optimize the placement of mesh routers in order to cover all mesh clients in the evacuation area. Additionally, the DECCM-based SA approach covers more mesh clients than the CCM-based SA approach on average and can improve network connectivity of WMNs.

A Multi-Strategy Improved Sparrow Search Algorithm for Coverage Optimization in a WSN

Abstract: To address the problems of low monitoring area coverage rate and the long moving distance of nodes in the process of coverage optimization in wireless sensor networks (WSNs), a multi-strategy improved sparrow search algorithm for coverage optimization in a WSN (IM-DTSSA) is proposed. Firstly, Delaunay triangulation is used to locate the uncovered areas in the network and optimize the initial population of the IM-DTSSA algorithm, which can improve the convergence speed and search accuracy of the algorithm. Secondly, the quality and quantity of the explorer population in the sparrow search algorithm are optimized by the non-dominated sorting algorithm, which can improve the global search capability of the algorithm. Finally, a two-sample learning strategy is used to improve the follower position update formula and to improve the ability of the algorithm to jump out of the local optimum. Simulation results show that the coverage rate of the IM-DTSSA algorithm is increased by 6.74%, 5.04% and 3.42% compared to the three other algorithms. The average moving distance of nodes is reduced by 7.93 m, 3.97 m, and 3.09 m, respectively. The results mean that the IM-DTSSA algorithm can effectively balance the coverage rate of the target area and the moving distance of nodes.

ARAP Revisited Discretizing the Elastic Energy using Intrinsic Voronoi Cells

Abstract: As-rigid-as-possible (ARAP) surface modelling is widely used for interactive deformation of triangle meshes. We show that ARAP can be interpreted as minimizing a discretization of an elastic energy based on non-conforming elements defined over dual orthogonal cells of the mesh. Using the intrinsic Voronoi cells rather than an orthogonal dual of the extrinsic mesh guarantees that the energy is non-negative over each cell. We represent the intrinsic Delaunay edges extrinsically as polylines over the mesh, encoded in barycentric coordinates relative to the mesh vertices. This modification of the original ARAP energy, which we term iARAP, remedies problems stemming from non-Delaunay edges in the original approach. Unlike the spokes-and-rims version of the ARAP approach it is less susceptible to the triangulation of the surface. We provide examples of deformations generated with iARAP and contrast them with other versions of ARAP. We also discuss the properties of the Laplace-Beltrami operator implicitly introduced with the new discretization.

Skin Cancer Classification using Delaunay Triangulation and Graph Convolutional Network

Abstract: Oftentimes, many people or even medical workers misdiagnose skin cancer, which may lead to malpractice and thus, resulting in delayed recovery or life-threatening complications. In this research, a Graph Convolutional Network (GCN) method is proposed as a classification model and Delaunay triangulation as its feature extraction method to classify various types of skin cancers. Delaunay triangulation serves the purpose of boundary extraction, and this implementation allows the model to focus only on the cancerous lesion and ignore the skin around it. This way, the types of skin cancer can be predicted more accurately. Furthermore, GCN offers many advantages in medical image analysis over traditional CNN models. GCN can model interactions between different regions and structures in an image and perform messaging between nodes, whereas CNN is not explicitly designed to do such thing. Other than that, GCN can also leverage transfer learning and few-shot learning techniques to address the challenges of limited annotated medical image datasets. However, the result shows that the proposed model tends to overfit and is unable to generate correct predictions for new skin cancer images. There are several reasons that could lead the model to overfit, such as imbalance data, incorrect feature extraction, insufficient features for data prediction, or the data containing noise. Keywords—Skin cancer; Delaunay triangulation; graph convolutional network; GCN; multilabel image classification; convolutional neural network; CNN

Characterization of aperiodic surfaces with mesh-based parameters

Abstract: Abstract For technical surfaces, it is important to know their functional purpose and to characterize them accordingly. Therefore, ISO 21920–2 in 2D and ISO 25178–2 in 3D offer parameters that can assess surface functional properties. The topographic portions of a surface, for example hills and dales, can be classified as features and evaluated using feature parameters. However, no parameter exists to describe the spatial distribution of features with regard to the degree of homogeneity for aperiodic surfaces. Here we show the application of the Delaunay triangulation to quantify the spatial distribution respectively the geometric relationship of features. Therefore, the feature points are determined by watershed analysis and the resulting point cloud is meshed in 2D. Based on that mean and standard deviation of the triangle side lengths and the area disorder (AD) are calculated as new parameters. The method is demonstrated for sandblasted and chrome-plated specimens. In addition simulation is used to generate more data for analysis. With the proposed approach the distinction and extent of uniform, homogeneous or inhomogeneous spatial distributions of features with parameter AD can be determined.

A Hybrid Hierarchical Navigation Architecture for Highly Dynamic Environments Using Time-Space Optimization

Abstract: Navigation of mobile robots within crowded environments is an essential task in various use cases, such as delivery, health care, or logistics. Common navigation approaches have weaknesses when deployed as a standalone system. For instance, global planners excel in planning collision-free paths in static environments when the map is perfectly known but can not consider dynamic or unknown obstacles. Learning-based local planners have shown superior performance in dynamic obstacle avoidance but can not handle long planning horizons due to their myopic nature. To address these issues, we adopt a hierarchical motion planning framework to handle complex long-range navigation problems. Three modules are designed for different planning horizons leveraging different observations. First, an extended hybrid A-Star approach is proposed to efficiently search for an optimal solution in the time-state space and produce reasonable landmarks for the subsequent modules. Second, an intermediate planner is proposed, which utilizes Delaunay Triangulation to encode obstacles and provides safer and more robust subgoals for the third module, the learning-based local planner trained using Deep Reinforcement Learning. The proposed approach is compared to two baseline navigation systems and outperforms them in terms of safety, efficiency, and robustness.

The projector algorithm: a simple parallel algorithm for computing Voronoi diagrams and Delaunay graphs

Abstract: The Voronoi diagram is a certain geometric data structure which has found numerous applications in various scientific and technological fields. The theory of algorithms for computing 2D Euclidean Voronoi diagrams of point sites is rich and useful, with several different and important algorithms. However, this theory has been quite steady during the last few decades in the sense that no essentially new algorithms have entered the game. In addition, most of the known algorithms are serial in nature and hence cast inherent difficulties on the possibility to compute the diagram in parallel. In this paper we present the projector algorithm: a new and simple algorithm which enables the (combinatorial) computation of 2D Voronoi diagrams. The algorithm is significantly different from previous ones and some of the involved concepts in it are in the spirit of linear programming and optics. Parallel implementation is naturally supported since each Voronoi cell (actually, even just portions of one cell) can be computed independently of the other cells. A new combinatorial structure for representing the cells (and any convex polytope) is described along the way and the computation of the induced Delaunay graph is obtained almost automatically.

Nfinder: automatic inference of cell neighborhood in 2D and 3D using nuclear markers

Abstract: In tissues and organisms, the coordination of neighboring cells is essential to maintain their properties and functions. Therefore, knowing which cells are adjacent is crucial to understand biological processes that involve physical interactions among them, e.g. cell migration and proliferation. In addition, some signaling pathways, such as Notch or extrinsic apoptosis, are highly dependent on cell-cell communication. While this is straightforward to obtain from membrane images, nuclei labelling is much more ubiquitous for technical reasons. However, there are no automatic and robust methods to find neighboring cells based only on nuclear markers.In this work, we describe Nfinder, a method to assess the cell's local neighborhood from images with nuclei labeling. To achieve this goal, we approximate the cell-cell interaction graph by the Delaunay triangulation of nuclei centroids. Then, links are filtered by automatic thresholding in cell-cell distance (pairwise interaction) and the maximum angle that a pair of cells subtends with shared neighbors (non-pairwise interaction). We systematically characterized the detection performance by applying Nfinder to publicly available datasets from Drosophila melanogaster, Tribolium castaneum, Arabidopsis thaliana and C. elegans. In each case, the result of the algorithm was compared to a cell neighbor graph generated by manually annotating the original dataset. On average, our method detected 95% of true neighbors, with only 6% of false discoveries. Remarkably, our findings indicate that taking into account non-pairwise interactions might increase the Positive Predictive Value up to + 11.5%.Nfinder is the first robust and automatic method for estimating neighboring cells in 2D and 3D based only on nuclear markers and without any free parameters. Using this tool, we found that taking non-pairwise interactions into account improves the detection performance significantly. We believe that using our method might improve the effectiveness of other workflows to study cell-cell interactions from microscopy images. Finally, we also provide a reference implementation in Python and an easy-to-use napari plugin.

Delaunay Tetrahedron-Based Connectivity Approach for 3D Wireless Sensor Networks

Abstract: Connectivity is an important aspect of wireless sensor networks. Providing connectivity in 3D wireless sensor networks is very crucial when the network size is larger. There are several studies that discuss connectivity in the 2D sensor network. However, these are not always suitable when the network area is non-planar. In this paper, we focus on the connectivity of sensor networks in 3D space. We propose a Delaunay tetrahedron-based relay node placement strategy for connectivity and evaluate sensor density for the requirement. Sensor networks on the mountain are a form of a 3D surface topography. The target region is triangulated using the Delaunay triangle. Reduction in hops for data forwarding consumes less energy. Using such techniques, we developed an energy-efficient algorithm. Through simulation, we demonstrate that the proposed method guarantees connectivity with an optimal number of sensor nodes.

A meta-graph approach for analyzing whole slide histopathological images of human brain tissue with Alzheimer's disease biomarkers

Abstract: Recently, high-performance deep learning models have enabled automatic and precise analysis of medical images with high content. In digital histopathology, a challenge lies in analyzing Whole Slide Images (WSI) due to their large size, often requiring splitting them into smaller patches for deep learning models. This leads to the loss of global tissue information and limits the classification or clustering of patients based on tissue characteristics. In this study, we develop a meta-graph approach for semantic spatial analysis of WSI of human brain tissue containing tau protein aggregates, a hallmark of Alzheimer’s disease (AD) in gray matter. Our pipeline extracts morphological features of tau aggregates, such as forming neuritic plaques, and builds a graph based on Delaunay triangulation at the WSI level to extract topological features. This generates morphological and topological data from WSI for patient classification and clustering. We tested this pipeline on a dataset of 15 WSIs from different AD patients. We aim to identify new insights into AD evolution and provide a generic framework for WSI characterization and analysis.

A close-range photogrammetric model for tracking and performance-based forecasting earthmoving operations

Abstract: Purpose This paper aims to present a highly accessible and affordable tracking model for earthmoving operations in an attempt to overcome some of the limitations of current tracking models. Design/methodology/approach The proposed methodology involves four main processes: acquiring onsite terrestrial images, processing the images into 3D scaled cloud data, extracting volumetric measurements and crew productivity estimations from multiple point clouds using Delaunay triangulation and conducting earned value/schedule analysis and forecasting the remaining scope of work based on the estimated performance. For validation, the tracking model was compared with an observation-based tracking approach for a backfilling site. It was also used for tracking a coarse base aggregate inventory for a road construction project. Findings The presented model has proved to be a practical and accurate tracking approach that algorithmically estimates and forecasts all performance parameters from the captured data. Originality/value The proposed model is unique in extracting accurate volumetric measurements directly from multiple point clouds in a developed code using Delaunay triangulation instead of extracting them from textured models in modelling software which is neither automated nor time-effective. Furthermore, the presented model uses a self-calibration approach aiming to eliminate the pre-calibration procedure required before image capturing for each camera intended to be used. Thus, any worker onsite can directly capture the required images with an easily accessible camera (e.g. handheld camera or a smartphone) and can be sent to any processing device via e-mail, cloud-based storage or any communication application (e.g. WhatsApp).

Delaunay Triangulation Voxelization for Print Orientation-Based Topology Optimization in Additive Manufacturing

Abstract: For topology optimization in additive manufacturing, the support structures have a significant impact on production cost and can be minimized by choosing the optimal print orientation, where model voxelization plays an important role on the computing accuracy and efficiency. To overcome the inherent insufficiency of the cube voxelization, we propose a new voxelization modeling method based on the Delaunay Triangulation to match arbitrary shapes with fewer voxels at arbitrary angle, and speed up the computing efficiency by the gradient descent method for the optimal voxelization. Our method can be widely used in the future for accurate modeling and result optimization in the case of solving the optimal orientation.

GEOMODELATOR – from static geologic models to structured grids for numerical simulations

Abstract: Conversion of static geologic models into numerical simulation grids is a pre-requisite to undertake site-specific assessments of geologic subsurface utilisation in terms of risk assessments, design and operational optimisations as well as long-term predictions.GEOMODELATOR is a Python-based Open Source software package which enables modellers to translate static geologic models into regular structured simulation grids with element partitions following a complex model geometry.For that purpose, geologic models generated by means of Geographic Information Systems (GIS), Computer-Aided Design (CAD) or other specific geologic modelling software packages are integrated in form of point cloud data together with the desired structured simulation grid geometry.GEOMODELATOR maps geometric features such as lithologic horizons, faults and any kind of other geometric data by 3D Delaunay triangulation onto the pre-defined grid element centres, and provides the modeller with Visualization Toolkit (VTK) data and Python numpy arrays for visual model inspection and their direct application in numerical simulations, respectively.The present contribution shows the application of GEOMODELATOR to different numerical simulation studies addressing fluid flow as well as transport of heat and chemical species in geological subsurface utilisation.

Ruppert's delaunay triangulation refinement scheme for optimal RSUs placement in vehicle to infrastructure communication network

Abstract: Road Side Units (RSUs) are the essential component of vehicular communication for the objective of improving safety and mobility in the road transportation. RSUs are generally deployed at the roadside and more specifically at the intersections in order to collect traffic information from the vehicles and disseminate alarms and messages in emergency situations to the neighborhood vehicles cooperating with the network. However, the development of a predominant RSUs placement algorithm for ensuring competent communication in VANETs is a challenging issue due to the hindrance of obstacles like water bodies, trees and buildings. In this paper, Ruppert's Delaunay Triangulation Refinement Scheme (RDTRS) for optimal RSUs placement is proposed for accurately estimating the optimal number of RSUs that has the possibility of enhancing the area of coverage during data communication. This RDTRS is proposed by considering the maximum number of factors such as global coverage, intersection popularity, vehicle density and obstacles present in the map for optimal RSUs placement, which is considered as the core improvement over the existing RSUs optimal placement strategies. It is contributed for deploying requisite RSUs with essential transmission range for maximal coverage in the convex map such that each position of the map could be effectively covered by at least one RSU in the presence of obstacles. The simulation experiments of the proposed RDTRS are conducted with complex road traffic environments. The results of this proposed RDTRS confirmed its predominance in reducing the end-to-end delay by 21.32%, packet loss by 9.38% with improved packet delivery rate of 10.68%, compared to the benchmarked schemes.

A Three-Dimensional Level-Set Front Tracking Technique for Automatic Multi-Step Simulations of In-Flight Ice Accretion

Abstract: This paper presents a novel fully-automatic remeshing procedure, based on the level-set method and Delaunay triangulation, to model three-dimensional boundary problems and generate a new conformal body-fitted mesh. The proposed methodology is applied to long-term in-flight ice accretion, which is characterized by the formation of extremely irregular ice shapes. Since ice accretion is coupled with the aerodynamic flow field, a multi-step procedure is implemented. The total icing exposure time is subdivided into smaller time steps, and at each time step a three-dimensional body-fitted mesh, suitable for the computation of the aerodynamic flow field around the updated geometry, is generated automatically. The methodology proposed can effectively deal with front intersections, as shown with a manufactured example. Numerical simulations over a NACA0012 swept wing both in rime and glaze conditions are compared with the experimentally measured ice shapes from the 1st AIAA Ice Prediction Workshop.

Formation Control Over Delaunay Triangulation Networks With Guaranteed Collision Avoidance

Abstract: This article addresses the collision avoidance of networked swarms of mobile agents. A gradient-based control scheme with artificial potential fields guides all the agents into a distance-based formation. While, in the relevant literature, unbounded forces are used to achieve collision avoidance, this article shows a way to guarantee collision avoidance that respects control input limitations. To this end, it is proposed to use Morse potential functions, and it is shown how to parameterize them appropriately. The results are extended to the case that a switching proximity communication network in form of a Delaunay triangulation is applied to the networked system. It is shown that under which conditions the collision avoidance is preserved among the overall network. The proposed method is evaluated experimentally with mobile robots.