Delaunay Triangulation Technique Research Articles

An integrated exploration of heat kernel invariant feature and manifolding technique for 3D object recognition system

Spectral Graph theory has been utilized frequently in the field of Computer Vision and Pattern Recognition to address challenges in the field of Image Segmentation and Image Classification. In the proposed method, for classification techniques, the associated graph's Eigen values and Eigen vectors of the adjacency matrix or Laplacian matrix created from the images are employed. The Laplacian spectrum and a graph's heat kernel are inextricably linked. Exponentiating the Laplacian eigensystem over time yields the heat kernel, which is the solution to the heat equations. In the proposed technique K-Nearest neighborhood and Delaunay triangulation techniques are used to generate a graph from the 3D model. The graph is then represented into Normalized Laplacian (NL) and Laplacian matrix (L). From each Normalized Laplacian and Laplacian matrix, the feature vectors like Heat Content Invariant and Laplacian Eigen values are extracted. Then, using all of the available clustering algorithms on datasets, the optimum feature vector for clustering is determined. For clustering various manifolding techniques are employed. In the suggested method, the graph heat kernel is constructed using industry-standard objects which are taken from the Engineering bench mark Data set.

Estimating Volume of the Tomato Fruit by 3D Reconstruction Technique

Due to its nutritional and economic value, the tomato is considered one of the main vegetables in terms of production and consumption in the world. For this reason, an important study is the volume of the fruit related to the loss of mass. This process develops in the fruit mainly after the harvest. This parameter affects the economic value of the crop, the scientific community has been progressively addressing the problem. However, there is no non-contact method that allows volume estimation. In this work a quantitative method is developed that allows to estimate the volume of the tomato fruit by means of a 3D reconstruction technique. The method is based on a camera that acquires different views of the silhouette of the fruit and by means of image processing a 3D point cloud is generated and later a Delaunay triangulation technique, which allows the estimation of the 3D volume of the tomato fruit. This volume estimation allows the design of precise strategies focused on the prediction of tomato post-harvest by producers, distributors and consumers.

Digital Image Segmentation Using Delaunay Triangulation Algorithm

Image segmentation is the process of partitioning a digital image into multiple segments according to some homogeneity criterion. Different approaches are suited to different types of images and the quality of output of a particular algorithm is difficult to measure quantitatively due to the fact that there may be much “correct” segmentation for a single image. Although the field encounters several challenges, this research work seeks to present a segmentation algorithm for gray intensity images. Image features extraction is first performed to obtain the approximate, if not exact, representation of a given image. Image enhancement was also carried out by exploiting the principle of histogram equalization which is one of the well-known image enhancement techniques. The proposed approach is based on the Delaunay (DT), one of the techniques in computational geometry, which generates clusters of intensity values using information from the vertices of the external boundary of triangulation. This makes it possible to produce segmented image regions. The algorithm was tested on sampled images before and after enhancement and the production compared. Our algorithm successfully extracts cogent features from a given image and made use of the Delaunay Triangulation to carry out segmentation. The method is robust, precise and independent of translation, rotation and scaling and that makes the result quite good for image segmentation. Image segmentation based on Delaunay triangulation technique seem to be a promising future research area with respect to its applicability to underwater mine and submarine detection, better target recognition, medical imaging as well as to automated computer vision.

Research on a mapping method of Chang’E-4 lunar rover’s panoramic camera

As a scientific payload of Chang’E-4 lunar rover, the panoramic camera not only detects lunar geology but can be directly used for mapping and constructing the lunar terrain in the lunar rover’s navigation and planning. We choose one model for calibrating the camera early; however, we often need to choose another model for the convenience of mapping work afterward. This paper proposes a distortion removal method based on the model parameter transformation algorithm, which overcomes the mismatch problem between the mapping model and the calibration model. The support points dense matching, spatial forward intersection, least-square bundle adjustment, discrete point cloud generation, and Delaunay triangulation technique are used together to achieve the topographic mapping work of panoramic camera images. A control field is constructed in the laboratory and used to test the feasibility and accuracy of the proposed distortion model parameter transformation method using the images taken by Chang’E-4 lunar rover’s panoramic camera located in Site LE00210. The result shows that after distortion model transformation, the position accuracy was higher than 1.6 cm, while the relative distance accuracy was higher than 4%. The proposed algorithm has been successfully applied to the mapping work of Chang’E-4 lunar rover’s panoramic camera.

Development of an Automated System for Three-Dimensional J-Integral Analysis

By integrating the 3D solid modeler with the universal FEM code, an automatic nonlinear analysis system for 3D crack problems has been developed. A geometry model, that is, a solid containing one or several 3D cracks is defined. Multiple distributions of local node density are selected and automatically overlapped with each other over the geometry model using fuzzy knowledge processing. Nodes are created by the bucketing method, and tetrahedral square tetrahedral solid elements are generated by the Delaunay triangulation technique. A complete finite element (FE) model is created and stress analysis is performed. In this system, analysts can significantly reduce the burden of introducing 3D cracks into FE models and estimating fracture mechanics parameters. This paper describes a methodology for realizing such a function and demonstrates the validity of this system.

Evaluating the thermal stratification of Köyceğiz Lake (SW Turkey) using in-situ and remote sensing observations

The goal of this study is to evaluate the thermal properties of Köyceğiz Lake using in-situ measurements and satellite based thermal infrared imagery. In-situ measurements of surface water temperature and water depth, as well as meteorological data, were used in the analysis. Images of the Landsat 8 TIRS (Thermal Infrared (IR) Sensors) at IR channels were taken from the data archives of United State Geological Survey (USGS), and were validated with surface in-situ measurements. Specific Electrical conductivity (SEC) measurements done at the bottom of the lake were also used for a better understanding of the water thermal stratification and types (cold/hot) that impact on the underwater physical properties of the lake. In-situ measurements at the water surface were interpolated using a new method known as ‘Empirical Bayesian Kriging (EBK)’. The 2D and 3D (dimensional) temperature maps were generated using the Delaunay triangulation technique which utilizes nearest neighbor interpolation method. The results show that the correlation coefficient (R2) between water surface temperatures (WST) from in-situ measurements and IR channels is found to be greater than 0.86. The analysis of 2D and 3D temperature mapping of the lake water revealed evidences for subaqueous cold spring occurrence in the northern part and subaqueous hot springs in the south-western part of Koycegiz Lake. It is concluded that correlating in-situ water temperature measurements to Landsat 8 TIRS images is an efficient method for temporal and spatial evaluation of lake water characteristics.

Characterizing Fabric Anisotropy of Air-Pluviated Sands

Sand particles depositing through air generally align their largest dimensions in horizontal plane, forming a cross anisotropic fabric. Therefore, sands display varying strength, permeability, compressibility with directions. This study characterizes fabric anisotropy in loose and dense air-pluviated sand specimens scanned by X-ray Computed Tomography (X-ray CT) using a series of image processing techniques. The principal component analysis, three-dimensional watershed analysis, and Delaunay triangulation technique are used to compute directional parameters, including particle long axes, contact normals, and branch vectors, and scalar parameters, including index void ratios, coordination number, and average branch vector length. The particle long axes and branch vectors displayed preferred horizontal directions while the contact normals displayed preferred vertical directions. The dense specimen has smaller index void ratios, larger coordination number, and smaller average branch vector length than the loose specimen.

Particulate material fabric characterization from volumetric images by computational geometry

This study develops computational geometry techniques to characterize fabric anisotropy from volumetric images. Although numerous laboratory test results have demonstrated the importance of fabric anisotropy on the macro-mechanical behavior of granular soils, the fabric characterization methods are underexplored. The advances of X-ray Computed Tomography (X-ray CT) techniques enable researchers to scan three-dimensional (3D) volumetric images of granular soils to observe fabric. Taking the advantage of X-ray CT, this study integrates principal component analysis, 3D watershed analysis, and Delaunay triangulation technique to compute key parameters for fabric characterization, including particle long axes, contacts and contact normals, branch vectors, void ratios, coordination number, and average branch vector length. The developed methodologies are validated through the loose and dense natural river sand specimens (containing particles from sub-angular to well-rounded). The developed computational geometry techniques may facilitate soil experimentalists to explain the observed soil behavior in laboratory tests induced by fabric anisotropy, enable constitutive modelers to integrate fabric in constitutive models, and enable discrete element modelers to calibrate their simulation models.

Exact and heuristic algorithms for Space Information Flow.

Space Information Flow (SIF) is a new promising research area that studies network coding in geometric space, such as Euclidean space. The design of algorithms that compute the optimal SIF solutions remains one of the key open problems in SIF. This work proposes the first exact SIF algorithm and a heuristic SIF algorithm that compute min-cost multicast network coding for N (N ≥ 3) given terminal nodes in 2-D Euclidean space. Furthermore, we find that the Butterfly network in Euclidean space is the second example besides the Pentagram network where SIF is strictly better than Euclidean Steiner minimal tree. The exact algorithm design is based on two key techniques: Delaunay triangulation and linear programming. Delaunay triangulation technique helps to find practically good candidate relay nodes, after which a min-cost multicast linear programming model is solved over the terminal nodes and the candidate relay nodes, to compute the optimal multicast network topology, including the optimal relay nodes selected by linear programming from all the candidate relay nodes and the flow rates on the connection links. The heuristic algorithm design is also based on Delaunay triangulation and linear programming techniques. The exact algorithm can achieve the optimal SIF solution with an exponential computational complexity, while the heuristic algorithm can achieve the sub-optimal SIF solution with a polynomial computational complexity. We prove the correctness of the exact SIF algorithm. The simulation results show the effectiveness of the heuristic SIF algorithm.

Connectivity Restoration in Wireless Sensor Networks via Space Network Coding

The problem of finding the number and optimal positions of relay nodes for restoring the network connectivity in partitioned Wireless Sensor Networks (WSNs) is Non-deterministic Polynomial-time hard (NP-hard) and thus heuristic methods are preferred to solve it. This paper proposes a novel polynomial time heuristic algorithm, namely, Relay Placement using Space Network Coding (RPSNC), to solve this problem, where Space Network Coding, also called Space Information Flow (SIF), is a new research paradigm that studies network coding in Euclidean space, in which extra relay nodes can be introduced to reduce the cost of communication. Unlike contemporary schemes that are often based on Minimum Spanning Tree (MST), Euclidean Steiner Minimal Tree (ESMT) or a combination of MST with ESMT, RPSNC is a new min-cost multicast space network coding approach that combines Delaunay triangulation and non-uniform partitioning techniques for generating a number of candidate relay nodes, and then linear programming is applied for choosing the optimal relay nodes and computing their connection links with terminals. Subsequently, an equilibrium method is used to refine the locations of the optimal relay nodes, by moving them to balanced positions. RPSNC can adapt to any density distribution of relay nodes and terminals, as well as any density distribution of terminals. The performance and complexity of RPSNC are analyzed and its performance is validated through simulation experiments.

An effective computation strategy for assessing operational flexibility of high-dimensional systems with complicated feasible regions

The volumetric flexibility index(FIv) of a chemical system can be viewed geometrically as the ratio between the hypervolume of feasible region and that of a hypercube bounded by the expected upper and lower limits of uncertain process parameters. Although several methods have already been developed to compute FIv, none of them are effective for solving the high-dimensional problems defined in nonconvex, non-simply connected or disconnected regions. While the available shortcut approaches are not accurate enough, successful tuning of the algorithmic parameters is mandatory for producing credible estimates with the more elaborate existing strategies.The above practical issues in volume estimation are thoroughly addressed in the present research. The most critical step in the proposed procedure is to characterize the feasible region accurately. To this end, the domain boundaries in parameter space are first identified with the feasible proximity points obtained by following a random line search algorithm. The Delaunay triangulation technique is then implemented to generate simplexes on the basis of such near-boundary points. By checking the centroids of these simplexes, the infeasible ones may be identified and eliminated. Finally, the hypervolumes of all feasible simplexes are summed to determine the volumetric flexibility index.Extensive case studies with 2–7 uncertain parameters have been carried out to show the superior capabilities of the proposed computation strategies.

Adaptive mixed-hybrid and penalty discontinuous Galerkin method for two-phase flow in heterogeneous media

In this paper, we present a hybrid method, which consists of a mixed-hybrid finite element method and a penalty discontinuous Galerkin method, for the approximation of a fractional flow formulation of a two-phase flow problem in heterogeneous media with discontinuous capillary pressure. The fractional flow formulation is comprised of a wetting phase pressure equation and a wetting phase saturation equation which are coupled through a total velocity and the saturation affected coefficients. For the wetting phase pressure equation, the continuous mixed-hybrid finite element method space can be utilized due to a fundamental property that the wetting phase pressure is continuous. While it can reduce the computational cost by using less degrees of freedom and avoiding the post-processing of velocity reconstruction, this method can also keep several good properties of the discontinuous Galerkin method, which are important to the fractional flow formulation, such as the local mass balance, continuous normal flux and capability of handling the discontinuous capillary pressure. For the wetting phase saturation equation, the penalty discontinuous Galerkin method is utilized due to its capability of handling the discontinuous jump of the wetting phase saturation. Furthermore, an adaptive algorithm for the hybrid method together with the centroidal Voronoi–Delaunay triangulation technique is proposed. Five numerical examples are presented to illustrate the features of proposed numerical method, such as the optimal convergence order, the accurate and efficient velocity approximation, and the applicability to the simulation of water flooding in oil field and the oil-trapping or barrier effect phenomena.

Three-dimensional Reconstruction of Objects Obtained by Two Orthogonal Cameras

This paper presents a technique for 3D reconstruction of objects from a sequence of images acquired with two cameras. The cameras are mounted so that their axes remain orthogonal, both toward the subject. A mechanical device, controlled in angular position, allows movement of the cameras as they acquire an image sequence. From the images acquired different views of the silhouette of the object are extracted. The silhouettes processing to generate a 3D point cloud and generate a mesh using Delaunay triangulation techniques. Controlling the angular position of the cameras, the algorithm for the image processing and the three-dimensional reconstruction is performed using a GUI developed in Visual C++. The results of the reconstruction process are modeled in a virtual environment to get a real view of the object.

Tagging-the-triangle algorithm for partitioning features with inconsistent boundaries

In spatial data sets, gaps or overlaps among features are frequently found in spatial tessellations due to the non-abutting edges with adjacent features. These non-abutting edges in loose tessellations are also called inconsistent boundaries or slivers; polygons containing at least one inconsistent boundary are called inconsistent polygons or sliver polygons. The existing algorithms to solve topological inconsistencies in sliver polygons suffer from one or more of three major issues, namely determination of tolerances, excessive CPU processing time for large data sets and loss of vertex history. In this article, we introduce a new algorithm that mitigates these three issues. Our algorithm efficiently searches the features with inconsistent polygons in a given spatial data set and logically partitions them among adjacent features. The proposed algorithm employs the constrained Delaunay triangulation technique to generate labelled triangles from which inconsistent polygons with gaps and overlaps are identified using label counts. These inconsistent polygons are then partitioned using the straight skeleton method. Moreover, each of these partitioned gaps or overlaps is distributed among the adjacent features to improve the topological consistency of the spatial data sets. We experimentally verified our algorithm using the real land cadastre data set. The comparison results show that the proposed algorithm is four times faster than the existing algorithm for data sets with 200,000 edges.

3차원 균열을 갖는 구조물에 대한 건전성 평가(II)

3차원 균열은 항공기나 압력용기 계통에서 흔히 발견되는 결함중의 하나이다. 균열을 갖는 구조물에 대한 정확한 응력확대계수 해석과 균열성장속도는 파괴강도와 피로수명을 평가하는데 필요로 한다. 3차원 유한요소법은 구조물에 존재하는 표면균열의 응력확대계수를 구하는데 이용되어 진다. 기하모델, 즉 균열을 포함하는 솔리드모델을 정의한 후, 절점이 버켓법에 의해 생성되어 진다. 요소생성은 사변형 솔리드요소를 데라우니 삼각화 기술에 의해 생성하도록 하였다. 시스템의 정확도와 효용성을 체크하기 위해 내압을 받는 원통형용기에 균열이 존재하는 경우의 응력확대계수 해석을 수행하였다. 개발된 시스템을 이용한 해석결과는 ASME 식과 Raju-Newnam식과 비교하여 5%이내의 차이를 보였다. 【Three Surface cracks are among the more common flaws in aircraft and pressure vessel components. Accurate stress intensity analyses and crack growth rate data of surface-cracked components are needed for reliable prediction of their fatigue life and fracture strengths. Three Dimensional finite element method (FEM) was used to obtain the stress intensity factor for surface cracks existing in structures. A geometry model, i.e. a solid containing one or several 3D cracks is defined. Nodes are generated by bucket method, and quadratic tetrahedral solid elements are generated by the Delaunay triangulation techniques. To examine accuracy and efficiency of the present system, the stress intensity factor for a semi-elliptical surface crack in cylindrical structures subjected to pressure is calculated. Analysis results by present system showed good agreement with those by ASME equation and Raju-Newman's equation.】

Pavement Crack Classification via Spatial Distribution Features

Pavement crack types provide important information for making pavement maintenance strategies. This paper proposes an automatic pavement crack classification approach, exploiting the spatial distribution features (i.e., direction feature and density feature) of the cracks under a neural network model. In this approach, a direction coding (D-Coding) algorithm is presented to encode the crack subsections and extract the direction features, and a Delaunay Triangulation technique is employed to analyze the crack region structure and extract the density features. As regarding skeletonized crack sections rather than crack pixels, the spatial distribution features hold considerable feature significance for each type of cracks. Empirical study indicates a classification precision of over 98% of the proposed approach.

Mesoscale finite element prediction of concrete failure

The present paper studies the failure of concrete from the mesoscopic point of view. Biphasic cubic concrete samples containing spherical aggregates embedded in a homogenized mortar have been simulated using standard finite element method. Linear elasticity and damage-plasticity hypotheses are considered for the aggregates and mortar, respectively. Various triaxial loading conditions are assumed for each sample to generate adequate discrete failure points within the stress space. In the next step, the approximated failure surfaces of specimens are constructed using the Delaunay triangulation technique. The effects of mesostructural features such as aggregate grading curve, aggregate volumetric share, and more importantly the controlling parameters of mortar’s damage-plasticity constitutive model have been investigated. Finally, the failure modes of some selected samples have been reported and discussed.

Neutral models for polygonal landscapes with linear networks

Dynamical mosaic models are very useful in ecology to study the influence of patterns on some ecological processes. Examples of such mosaics are patches of agricultural or forested landscapes. They are often built on the basis of either explicit processes or on neutral approaches using random or almost random element generation. Yet, most of the latter, called neutral landscape models, use a grid-based scheme and simulate pixel mosaics that are autonomous and/or independent. This scheme is not perfectly adapted to anthropogenic patchy landscapes made of contiguous and uniform polygons. Landscape ecology for example explains how a landscape may be seen as a complex mosaic of patches and corridors, with dynamical compositions (the patch attributes) and configurations (their shapes and neighbourhoods). This work presents three neutral landscape models dedicated to manipulations of polygonal patchy mosaic configurations as compared to an observed one. These models have respective advantages that can be summarised in an increasing ability to simulate realistic anthropogenic landscape mosaics. The tessellation approach is simple and rapid, but very much constrained by the patch shapes and positions. The Gibbs algorithm method adapted to landscapes is powerful to manipulate patch positions, with still a weak control on patch shapes. The last method based on a Delaunay triangulation technique offers the opportunity to modulate patch shapes and can still be combined with the Gibbs method to optimise the patch positions. With such neutral landscape models, it is possible to explore ecological hypotheses using a wide range of controlled patchy mosaics.

퍼지메쉬를 이용한 3차원 균열에 대한 응력확대계수 해석 시스템

Integrating a 3D solid modeler with a general purpose FEM code, an automatic stress intensity factor analysis system of the 3D crack problems has been developed. A geometry model, i.e. a solid containing one or several 3D cracks is defined. Several distributions of local node density are chosen, and then automatically superposed on one another over the geometry model by using the fuzzy knowledge processing. Nodes are generated and quadratic tetrahedral solid elements are generated by the Delaunay triangulation techniques. Finally, the complete finite element(FE) model generated, and a stress analysis is performed. This paper describes the methodologies to realize such functions, and demonstrates the validity of the present system.

Parametric Design on Bellows of Piping System Using Fuzzy Knowledge Processing

This paper describes a novel automated analysis system for bellows of piping system. An automatic finite element (FE) mesh generation technique, which is based on the fuzzy theory and computational geometry technique, is incorporated into the system, together with one of commercial FE analysis codes and one of commercial solid modelers. In this system, a geometric model, i.e. an analysis model, is first defined using a commercial solid modelers for 3-D shell structures. Node is generated if its distance from existing node points is similar to the node spacing function at the point. The node spacing function is well controlled by the fuzzy knowledge processing. The Delaunay triangulation technique is introduced as a basic tool for element generation. The triangular elements are converted to quadrilateral elements. Practical performances of the present system are demonstrated through several analysis for bellows of piping system.