Greedy Triangulation Research Articles

A MORPHOLOGICAL MONITORING TOOL BASED ON STRUCTURE LIGHT IMAGES OF ISOLATED LIVER REPERFUSION

Isolated organ reperfusion system is always used in the preservation and transplantation of liver, and keeping the vitality monitor is a key point during the perfusion processing. Morphological changes are one of the important observation indicators, especially in liver preservation. In this pursuit, the present study envisaged the development of a liver morphological monitor tool based on the structure light images. An isolated healthy rat liver was employed in the perfusion system to obtain the 3D structure lights images using the Intel Real sense camera. Data for the point cloud images were analyzed using computer programs that provided a continuous procedure consisting of (i) liver segmentation, (ii) feature point identification, (iii) measurement of basic parameters like the length, width, and height, and (iv) measurement of the volume and upper surface area of the donor liver. Image segmentation was performed using the plane model segmentation in the Point Cloud Library (PCL). The basic parameters were measured by using the transformation of coordinate, and the volume and upper surface area were measured using the greedy triangulation in PCL. The proposed method showed a high quality in liver segmentation, the basic parameters of the liver were reasonable (length: 5.63[Formula: see text]cm, width: 4.57[Formula: see text]cm, height: 1.30[Formula: see text]cm), and exhibited a good feature point identification. The volume and upper surface area were close to that of the observed values (Volume: 11.719[Formula: see text]cm3, upper surface area: 26.5741[Formula: see text]cm2). However, a little error occurred in the greedy triangulation during the calculation of the upper surface area. The proposed method in this study was effective in measuring the parameters of liver, although the accuracy of surface area measurement needs further improvement.

Research on Tunnel Construction Monitoring Method Based on 3D Laser Scanning Technology

A tunnel is a symmetric structure working under uncertain load. In the traditional method of monitoring and measurement of tunnel deformation, only a small number of symmetric measuring point displacements are engaged to represent the overall deformation of the tunnel, and it is difficult to fully reflect the displacement changes of the tunnel during the construction process. In this paper, a deformation monitoring method is proposed for the tunnel construction process based on 3D laser scanning technology. Initially, 3D laser scanning was used to obtain scattered clouds of irregular structures considering the New Austrian Tunneling Method (NATM). Afterward, the modified B-spline interpolation and greedy triangulation were used to fit the surfaces. Moreover, the normal vector matrix was innovatively applied to express the deformation of the tunnel fitting surface, which solved the problem of scattered point clouds in 3D laser scanning. A normal vector was obtained by the intersection of the normal of one fitted surface with the other. Subsequently, the maximum entropy method was introduced to form the probability density function of the normal vector, and the 1% and 5% probability eigenvalues were used to analyze the overall deformation trend of the tunnel. Finally, the eigenvalue of 5% probability, which was less affected by construction uncertainties, was selected for analysis. This way, the analysis and prediction method for overall tunnel deformation was established.

Three-Dimensional Reconstruction of Rolling Contact Fatigue Characteristics

Focusing on the 3D topographic characteristics of rolling contact fatigue, a reconstruction method of the fatigue surface of roller based on point cloud data was proposed in this research. A 3D laser scanner was used to capture the data of point cloud on the surface of the fatigue roller. The gradient segmentation method was used to achieve segmentation of the fatigue contact surface, and the Kd-Tree algorithm in Statistical Outlier Removal filter was adopted to remove different types of noise. The greedy triangulation and hole repair and reconstruction of the curled point cloud were conducted. The experimental results showed that the segmentation accuracy of the fatigue contact surface was above 97.7%, the curling error rate of point cloud was 0.09%, and the maximum deviation of the reconstructed fatigue roller surface was 0.0199 mm. These methods can be applied to analyze the working conditions of roller specimen and contact fatigue.

Geometric Modeling of Rosa roxburghii Fruit Based on Three-Dimensional Point Cloud Reconstruction

Fruit three-dimensional (3D) model is crucial to estimating its geometrical and mechanical properties and improving the level of fruit mechanical processing. Considering the complex geometrical features and the required model accuracy, this paper proposed a 3D point cloud reconstruction method for the Rosa roxburghii fruit based on a three-dimensional laser scanner, including 3D point cloud generation, point cloud registration, fruit thorns segmentation, and 3D reconstruction. The 3D laser scanner was used to obtain the original 3D point cloud data of the Rosa roxburghii fruit, and then the fruit thorns data were removed by the segmentation algorithm combining the statistical outlier removal and radius outlier removal. By analyzing the effects of five-point cloud simplification methods, the optimal simplification method was determined. The Poisson reconstruction algorithm, the screened Poisson reconstruction algorithm, the greedy projection triangulation algorithm, and the Delaunay triangulation algorithm were utilized to reconstruct the fruit model. The number of model vertices, the number of facets, and the relative volume error were used to determine the best reconstruction algorithm. The results indicated that this model can better reconstruct the actual surface of Rosa roxburghii fruit. The method provides a reference for the related application.

A Novel Indoor Structure Extraction Based on Dense Point Cloud

Herein, we propose a novel indoor structure extraction (ISE) method that can reconstruct an indoor planar structure with a feature structure map (FSM) and enable indoor robot navigation using a navigation structure map (NSM). To construct the FSM, we first propose a two-staged region growing algorithm to segment the planar feature and to obtain the original planar point cloud. Subsequently, we simplify the planar feature using quadtree segmentation based on cluster fusion. Finally, we perform simple triangulation in the interior and vertex-assignment triangulation in the boundary to accomplish feature reconstruction for the planar structure. The FSM is organized in the form of a mesh model. To construct the NSM, we first propose a novel ground extraction method based on indoor structure analysis under the Manhattan world assumption. It can accurately capture the ground plane in an indoor scene. Subsequently, we establish a passable area map (PAM) within different heights. Finally, a novel-form NSM is established using the original planar point cloud and the PAM. Experiments are performed using three public datasets and one self-collected dataset. The proposed plane segmentation approach is evaluated on two simulation datasets and achieves a recall of approximately 99%, which is 5% higher than that of the traditional plane segmentation method. Furthermore, the triangulation performance of our method compared with the traditional greedy projection triangulation show that our method performs better in terms of feature representation. The experimental results reveal that our ISE method is robust and effective for extracting indoor structures.

Quantitative evaluation for shape characteristics of aggregate particles based on 3D point cloud data

The aggregate with good shape characteristics are conducive to the formation of the internal structure of asphalt pavement and have an important impact on the pavement performance. In order to quantify the aggregate shape characteristics more comprehensively, the quantitative evaluation method for the shape of aggregate particles based on 3D point cloud data was proposed. Basalt, granite and limestone aggregates with size of 9.5 mm, 13.2 mm and 16 mm were obtained by screening. Each type of aggregates was divided into five different shapes of the tetrahedron, pentahedron, hexahedron, elongate and flake. The image acquisition system based on Gocator 3D intelligent sensor was used to collect 3D point cloud data of the aggregates. The noise in the 3D point cloud data collected was removed by the cascade filtering method and then the greedy triangulation algorithm was used to reconstruct the 3D aggregate digitized surface. Finally, the characteristic parameters such as length, width, height, volume and the maximum diameter of the 3D convex hull were extracted from the reconstructed aggregate particles, and the shape indexes of the aggregate, such as the isometric ratio, flakiness ratio, sphericity and roundness indexes, were calculated based on the extracted characteristics. The experimental results show that the 3D shape index of road aggregates proposed in this paper can be used for the comprehensive quantitative evaluation of the morphological characteristics of aggregates with different lithology, particle sizes and shapes. It is instructive to improve the performance of the asphalt mixture and study the aggregate gradation.

POINT CLOUD SMOOTH SAMPLING AND SURFACE RECONSTRUCTION BASED ON MOVING LEAST SQUARES

Abstract. In point cloud data processing, smooth sampling and surface reconstruction are important aspects of point cloud data processing. In view of the current point cloud sampling method, the point cloud distribution is not uniform, the point cloud feature information is incomplete, and the reconstructed model surface is not smooth. This paper proposes a method of smoothing sampling processing and surface reconstruction using point cloud using moving least squares method. This paper first introduces the traditional moving least squares method in detail, and then proposes an improved moving least squares method for point cloud smooth sampling and surface reconstruction. In this paper, the algorithm is designed for the proposed theory, combined with C++ and point cloud library PCL programming, using voxel grid sampling and uniform sampling and moving least squares smooth sampling comparison, after sampling, using greedy triangulation algorithm surface reconstruction. The experimental results show that the improved moving least squares method performs point cloud smooth sampling more uniformly than the voxel grid sampling and the feature information is more prominent. The surface reconstructed by the moving least squares method is smooth, the surface reconstructed by the voxel grid sampling and the uniformly sampled data surface is rough, and the surface has a rough triangular surface. Point cloud smooth sampling and surface reconstruction based on moving least squares method can better maintain point cloud feature information and smooth model smoothness. The superiority and effectiveness of the method are demonstrated, which provides a reference for the subsequent study of point cloud sampling and surface reconstruction.

基于距离反比插值的激光雷达点云贪婪三角网构建及应用

基于距离反比插值的激光雷达点云贪婪三角网构建及应用

Calculation method of surface shape feature of rice seed based on point cloud

Surface shape feature is a very important index of seed classification. A method to calculate the three dimensional characteristics of the rice seed based on its surface point cloud was investigated. First of all, a laser scanner was used to acquire the three dimensional point cloud (TDPC) of a rice seed, then based on the principal component analysis (PCA) the TDPC were translated and rotated to normalize coordinate system. The length, width and thickness of rice seed, and furthermore its elongation, flakiness, shape factor and sphericity could be calculated by the oriented bounding box (OBB). We can generate mesh surface of the rice seed surface point cloud by the greedy triangulation algorithm, then calculate the surface area of the rice seed. On the basis of the slice method, an improved method based on rice seed TDPC was proposed to calculate the volume of rice seed. Compare the calculated length, width thickness and volume of different rice seeds with manual measurement. It is found that the average error is less than 1.5%. A ball whose radius is known instead of a rice seed to be used to verify the validity of the surface area by comparing the calculated value with their theoretical value, the mean error is 0.55%. The results showed the calculation method could acquire the surface shape feature of rice seed based on the TDPC and it is valid enough for application, this method is applicable for measurement of other irregular object as well.

Lower Bounds on the Dilation of Plane Spanners

(I) We exhibit a set of 23 points in the plane that has dilation at least [Formula: see text], improving the previous best lower bound of [Formula: see text] for the worst-case dilation of plane spanners. (II) For every [Formula: see text], there exists an [Formula: see text]-element point set [Formula: see text] such that the degree [Formula: see text] dilation of [Formula: see text] equals [Formula: see text] in the domain of plane geometric spanners. In the same domain, we show that for every [Formula: see text], there exists a an [Formula: see text]-element point set [Formula: see text] such that the degree [Formula: see text] dilation of [Formula: see text] equals [Formula: see text] The previous best lower bound of [Formula: see text] holds for any degree. (III) For every [Formula: see text], there exists an [Formula: see text]-element point set [Formula: see text] such that the stretch factor of the greedy triangulation of [Formula: see text] is at least [Formula: see text].

Urban road network evolution mechanism based on the ‘direction preferred connection’ and ‘degree constraint’

The urban road network is a complex system that exhibits the properties of self-organization and emergence. Recent theoretical and empirical studies have mainly focused on the structural properties of the urban road networks. This research concentrates on some important parameters such as degree, average degree, meshedness coefficient, betweeness, etc. These parameters of the real road network exhibit specific statistical properties. Some studies show that perhaps these specific statistical properties are caused by a compromise mechanism of the formation of a minimum spanning tree and the greedy triangulation. Inspired by these results, we propose a principle to construct the network (we call it a MG network in this paper) whose structure is located between the minimum spanning tree and the greedy triangulation at first. The structural properties of the MG network are analyzed. We find the formation mechanism of the MG network cannot explain the urban road network evolution well. Then, based on the formation mechanism of the MG network, we add the ‘direction preferred connection’ and ‘degree constraint’ principles to the urban road network evolution simulation process. The result of the simulation network turns out to be a planar network that is in accordance with reality. Compared with the real road network’s structural properties, we find the simulation results are so consistent with it. It indicates the validation of the model and also demonstrates perhaps the ‘direction preferred connection’ and ‘degree constraint’ principle can explain the urban road network evolution better.

Stopping Rules for Randomized Greedy Triangulation Schemes

Many algorithms for performing inference in graphical models have complexity that is exponential in the treewidth — a parameter of the underlying graph structure. Computing the (minimal) treewidth is NPcomplete, so stochastic algorithms are sometimes used to find low width tree decompositions. A common approach for finding good decompositions is iteratively executing a greedy triangulation algorithm (e.g. minfill) with randomized tie-breaking. However, utilizing a stochastic algorithm as part of the inference task introduces a new problem — namely, deciding how long the stochastic algorithm should be allowed to execute before performing inference on the best tree decomposition found so far. We refer to this dilemma as the Stopping Problem and formalize it in terms of the total time needed to answer a probabilistic query. We propose a rule for discontinuing the search for improved decompositions and demonstrate the benefit (in terms of time saved) of applying this rule to Bayes and Markov network instances.

A new asymmetric inclusion region for minimum weight triangulation

As a global optimization problem, planar minimum weight triangulation problem has attracted extensive research attention. In this paper, a new asymmetric graph called one-sided β-skeleton is introduced. We show that the one-sided circle-disconnected $${(\sqrt{2}\beta)}$$ -skeleton is a subgraph of a minimum weight triangulation. An algorithm for identifying subgraph of minimum weight triangulation using the one-sided $${(\sqrt{2}\beta)}$$ -skeleton is proposed and it runs in $${O(n^{4/3+\epsilon}+\min\{\kappa \log n, n^2\log n\})}$$ time, where ? is the number of intersected segmented between the complete graph and the greedy triangulation of the point set.

An almost four-approximation algorithm for maximum weight triangulation

We consider the following planar maximum weight triangulation (MAT) problem: given a set of n points in the plane, find a triangulation such that the total length of edges in triangulation is maximized. We prove an \(\Omega(\sqrt{n})\) lower bound on the approximation factor for several heuristics: maximum greedy triangulation, maximum greedy spanning tree triangulation and maximum spanning tree triangulation. We then propose the Spoke Triangulation algorithm, which approximates the maximum weight triangulation for points in general position within a factor of almost four in O(nlog n) time. The proof is simpler than the previous work. We also prove that Spoke Triangulation approximates the maximum weight triangulation of a convex polygon within a factor of two.

Triangulations without minimum-weight drawing

It is known that some triangulation graphs admit straight-line drawings realizing certain characteristics, e.g., greedy triangulation, minimum-weight triangulation, Delaunay triangulation, etc. Lenhart and Liotta (1997) in their pioneering paper on “drawable” minimum-weight triangulations raised an open problem: `Does every triangulation graph whose skeleton is a forest admit a minimum-weight drawing?' In this paper, we answer this problem by disproving it in the general case and even when the skeleton is restricted to a tree or, in particular, a star.

Imaging, image processing and pattern analysis of skin capillary ensembles

BACKGROUND/AIMS: The capillary bed is recognized as the site where metabolic and nutrient processes occur for living tissues at all levels. The evaluation of this vital process is a major concern in microcirculation. Unlike traditional approaches that concentrated on the extreme local properties of this process, a more global analysis toward capillary ensembles is employed here, since capillaries work as a cooperative entirety. As a first step toward ensemble analysis, the static and planar geometric parameters are investigated. Parameters such as the capillary adjacency and size information are very important in predicting and analysing certain malfunctions in the microvascular bed. METHODS/RESULTS: In order to achieve an objective and accurate analysis of these vital parameters, a computerized imaging system is proposed. Not only the number of capillaries and the capillary cross-sectional areas are important in describing the microvascular bed but the planar distribution pattern of the capillaries also carries valid information. This information, unique to the ensemble analysis, can be used to reveal, visualise and quantify the clustering of capillaries; and this information, according to the Krogh model, is fundamental in estimating the tissue oxygen supply. Two spatial models, the closest neighbor and triangulation methods, have been applied to the captured images of capillary ensembles. The closest neighbor technique generates a minimal distance map or displays a distribution, which depicts the local clustering of capillaries. The triangulation technique, on the other hand, generates a mutual distance map, which is a global description of the capillary positions. Triangulation methods have been evaluated but all except the Greedy triangulation method have been rejected due to lack of robustness and model weakness. Therefore, the capillaries are triangulated by the Greedy triangulation method, and the capillary distribution uniformity is defined as one minus the coefficient of variance of the edge lengths of the mutual distance map. CONCLUSIONS: A series of advanced image processing methods have been developed that efficiently extract the capillary position, size and distribution information from the images. These results facilitate the automatic counting of capillaries and the capillary size-related pathological analysis.

The greedy triangulation can be computed from the Delaunay triangulation in linear time

The greedy triangulation of a finite planar point set is obtained by repeatedly inserting a shortest diagonal that does not cross those already in the plane. The Delaunay triangulation, which is the straight-line dual of the Voronoi diagram, can be produced in O( nlog n) worst-case time, and often even faster, by several practical algorithms. In this paper we show that for any planar point set S, if the Delaunay triangulation of S is given, then the greedy triangulation of S can be computed in linear worst-case time (and linear space).

Quasi-Greedy Triangulations Approximating the Minimum Weight Triangulation

This article settles the following two longstanding open problems:•What is the worst case approximation ratio between the greedy triangulation and the minimum weight triangulation?•Is there a polynomial time algorithm that always produces a triangulation whose length is within a constant factor from the minimum?The answer to the first question is that the known lower bound is tight. The second question is answered in the affirmative by using a slight modification of anO(nlogn) algorithm for the greedy triangulation. We also derive some other interesting results. For example, we show that a constant-factor approximation of the minimum weight convex partition can be obtained within the same time bounds.

Constant-Level Greedy Triangulations Approximate the MWT Well

The well-known greedy triangulation GT(S) of a finite point set S is obtained by inserting compatible edges in increasing length order, where an edge is compatible if it does not cross previously inserted ones. Exploiting the concept of so-called light edges, we introduce a definition of GT(S) that does not rely on the length ordering of the edges. Rather, it provides a decomposition of GT(S) into levels, and the number of levels allows us to bound the total edge length of GT(S). In particular, we show |GT(S)| ≤ 3 · 2k + 1|MWT(S)|, where k is the number of levels and MWT(S) is the minimum-weight triangulation of S.

Fast greedy triangulation algorithms

We present a new method for testing compatibility of candidate edges in the greedy triangulation, and new results on the rank of edges in various triangulations. Our edge test requires O(1) time for test and update, O( n) space, and O( n) time to initialize. Based on these results, we present fast greedy triangulation algorithms with expected case running time of O( n log n) for uniform distributions over convex regions. While algorithms with O( n) expected case running times exist, the algorithms presented here are simpler to implement and work well in practice.