Convex Hull Algorithm Research Articles

Railway vehicle bearings risk monitoring based on normal region estimation for no-fault data situations

A risk monitoring method based on normal region estimation (NRE) is systematically proposed for the actual situation of the lack of fault data in the condition identification and monitoring of railway vehicle bearings. First, the basic concept of normal domain theory is expounded, and the formal expression of normal domain is given. Secondly, the academic thoughts and implementation steps of risk monitoring based on NRE are summarized. Then, two algorithms based on convex hull and support vector data description (SVDD) are proposed respectively to solve the core problem of boundary estimation. Finally, the rolling-bearing vibration acceleration data was used for the experiment, and the performance of the two algorithms is compared. The results show that both algorithms are effective. In contrast, the convex hull algorithm is faster, and the SVDD algorithm is smoother and more flexible. In practical applications, the two algorithms can be selected according to different requirements of real time and accuracy.

Automatic Ear Detection and Segmentation over Partially Occluded Profile Face Images

Automated, non invasive ear detection in images and video is becoming increasingly required in several contexts, including nonivasive biometric identification, biomedical analysis, forensics, and many others. In biometric recognition systems, fast and robust ear detection is a crucial step within the recognition pipeline. Existing approaches to ear detection are susceptible to fail in the presence of typical everyday situations that prevent a crisp imaging of the ears, like partial occlusions, ear accessories, or uncontrolled camera and illumination conditions. Even more, most of the proposed solutions work efficiently only within a previously detected rectangular region of interest, which limits their applicability and lowers the accuracy of the overall detection. In this paper we evaluate the use of Convolutional Neural Networks (CNNs) together with Geometric Morphometrics (GM) for automatic ear detection in the presence of partial occlusions, and a Convex Hull algorithm for the ear area segmentation. A CNN was trained with a set of ear images landmarked by experts using GM to achieve high consistency. After training, the CNN is able to detect ears over profile faces, even in the presence of partial occlusions. We analyze the performance of the proposed ear detection and segmentation method over partially occluded ear images using the CVL Dataset

Preprocessing 2D data for fast convex hull computations.

This paper presents a method to reduce a set of n 2D points to a smaller set of s 2D points with the property that the convex hull on the smaller set is the same as the convex hull of the original bigger set. The paper shows, experimentally, that such reduction accelerates computations; the time it takes to reduce from n down to s points plus the time of computing the convex hull on the s points is less than the time to compute the convex hull on the original set of n points. The method accepts 2D points expressed as real numbers and thus extends our previous method that required points as integers. The method achieves a percentage of reduction of points of over 90% in a collections of four datasets. This amount of reduction provides speedup factors of at least two for various common convex hull algorithms. Theoretically, the reduction method executes in time within O(n) and thus is suitable for preprocessing 2D data before computing the convex hull by any known algorithm.

Energy efficient secure data collection with path-constrained mobile sink in duty-cycled unattended wireless sensor network

This paper addresses the problem of secure data transmission and balanced energy consumption in an unattended wireless sensor network (UWSN) comprising of multiple static source nodes and a mobile sink in the presence of adversaries. The proposed system comprises of three phases: the identification of data collection points (convex nodes), path planning by the mobile sink, and secure data transmission. An energy-aware convex hull algorithm is used for the identification of data collection points for data transmission to the mobile sink. Data transmission from sensor nodes to the nearest data collection point is performed using multihop communication and from sensor nodes to the mobile sink in a single hop. Data are securely transmitted through an elliptic curve cryptography based ElGamal scheme for message authentication. A data packet is associated with a digital signature. The variation in a digital signature and threshold energy obtained using support vector machine is used to determine the presence of malicious nodes in the network. The performance of the proposed system is evaluated using Cooja simulator by Contiki for various node counts under a static sink and mobile sink, with different threat scenarios. The results indicate that the proposed system is resilient against threats and provides satisfactory performance

θ(1) time algorithm for 2D convex hull on a reconfigurable mesh computer architecture

θ(1) time algorithm for 2D convex hull on a reconfigurable mesh computer architecture

Convex-Hull Algorithms: Implementation, Testing, and Experimentation

From a broad perspective, we study issues related to implementation, testing, and experimentation in the context of geometric algorithms. Our focus is on the effect of quality of implementation on experimental results. More concisely, we study algorithms that compute convex hulls for a multiset of points in the plane. We introduce several improvements to the implementations of the studied algorithms: plane-sweep, torch, quickhull, and throw-away. With a new set of space-efficient implementations, the experimental results—in the integer-arithmetic setting—are different from those of earlier studies. From this, we conclude that utmost care is needed when doing experiments and when trying to draw solid conclusions upon them.

Segmented convex-hull algorithms for near-separable NMF and NTF

Many computational problems in machine learning can be represented with near-separable matrix factorization models. In a geometric approach, linear separability means that the entire set of data points can be modeled as a conical combination of a few data points, referred to as the extreme rays that express meaningful features. In this study, we propose segmented convex-hull algorithms for estimating the extreme rays of the simplicial cone generated by observations in the near-separable and inconsistent non-negative matrix factorization (NMF) and non-negative tensor factorization (NTF) models. The segmentation is based on the concept of hierarchical convex-hull NMF. The proposed algorithms are used to solve near-separable noisy blind source separation problems and classification problems. For the former, the experimental results demonstrate that they significantly outperform the state-of-the-art geometry-based NMF algorithms and the basic hierarchical alternating least squares NTF, if observations are noisy with signal-to-noise ratio lower than 100 dB. For the latter, the classification results also provide strong evidence for the effectiveness of the proposed approach with respect to existing geometry-based NMF algorithms.

Object Pose Estimation in Accommodation Space using an Improved Fruit Fly Optimization Algorithm

The accommodation space changes as flexible products are packed into it. In order to improve the automatic loading of containers, it is necessary to solve the problem of object pose estimation in accommodation space. The goal of this study is to establish a method for pose estimation of a target object in the accommodation space. Firstly, the paper introduces basic algorithms and concepts, including the quick hull (Qhull) algorithm, oriented bounding box (OBB) algorithm, and fruit fly optimization algorithm (FOA). Secondly, the constraint conditions and the objective function of pose estimation are set up according to the pose variables in three-dimensional (3D) space, and a solution method for pose estimation is established using an improved FOA. Then, the algorithms with different population parameters are simulated, and the optimal parameters are obtained. The bounding box algorithm is used for system optimization, whereas a convex hull is used to simplify the target object significantly, reducing the corresponding running time. Finally, the hardware platform of the industrial robot is established, the initial and final poses of the end-effector are obtained using the proposed method, and tests are performed for different cases. The results show that the application of convex hull algorithm can significantly simplify a target object reducing the running time, and half individuals of the population guide the entire population to search for an optimal pose (6 degrees of freedom) in accommodation space.

X-ray 영상에서 객체 기반의 노출 지수 측정 방법

The exposure index (EI) prevents systematic errors such as excessive or under-exposure by indicating the approximate value of the absorbed dose of the detector. We propose an EI measurement method with an object-based ROI except collimator and background region to measure more reliable EI values in X-ray images from digital flat-panel detectors. The boundary between the collimator and the background region has strong edges and linear components. Therefore, the ROI is detected by using simple and fast algorithms such as the canny edge detector, probabilistic Hough transform, and convex hull algorithm. The difference in the average pixel values between the ground truth (GT) values and the proposed method is approximately 5.13 (±1%).

Detecting the Competition between Moso Bamboos and Broad-Leaved Trees in Mixed Forests Using a Terrestrial Laser Scanner

The growth of individual trees in a forest is affected by many factors, a crucial one being the intensity of competition among trees, because it affects the spatial structure of the forest and is in turn influenced by silvicultural practices. In a mixed forest in particular, the growth of trees is affected by multiple interactions. To analyse the competition between moso bamboo (Phyllostachys pubescens (Pradelle) Mazel ex J.Houz.) and broad-leaved trees in a mixed forest, data were extracted by sampling six spots within such a forest using terrestrial laser scanning (TLS). The convex hull algorithm was used for calculating the overlap volume between the crowns of the broad-leaved trees and the bamboo canopy. Bamboos growing at least 3 m away from any of the broad-leaved trees were the most numerous and the diameter at breast height (DBH) is larger than those growing closer than that, which suggests that broad-leaved trees suppressed the growth of bamboo if they are closer but promote it beyond 3 m up to a point at which the distance is too great for any such effect. The modified Hegyi’s competition index was constructed based on the canopy factor, which may better describe the competitive interaction among the trees and bamboos. Using TLS can enhance our understanding of the competition among trees in mixed forests and help in planning the spatial structure of such forests in general and provide a benchmark for choosing planting distances in particular.

Assessing the estimation of trawling catches using LiDAR sensor technology

The measurement of total catch on-board a fishing vessel is generally a very complex process, especially to scientific observers. In this context, hauls of large volume, intricate fishing operations and limited access to the capture increase this problem. In this paper, we propose a methodology to address the estimation of catch volume in codends of a crustacean fishery through LiDAR (light and radar) technology. A sensor was used to acquire a three-dimensional representation of an object located at a fixed distance from the device, thereby simulating a fishing codend. Then, a convex-hull algorithm was applied to this representation to obtain an estimation of its volume. Additionally, to obtain further insights, an experimental laboratory setup was used to emulate the volume estimation of catches on a fishing vessel. The dataset acquired by the system was subsequently analyzed to study the percentage errors associated with the estimation process and to test whether the selected variables are significant. The results indicate that there is considerable uncertainty related to the volume estimation, but it can be addressed using a statistical model. This work constitutes the first attempt to provide a methodology to estimate the catch volume of a codend in a Chilean fishery by generating new measurement alternatives for fishery monitoring programs, enforcement and management institutions, as well as the fishing industry.

SymmetricHull: A Convex Hull Algorithm Based on 2D Geometry and Symmetry

Thanks to the advances in hardware (sensors and cameras) the number of points that convex hull algorithms must process is now much greater than when these algorithms were developed. This limitation entails focusing current research in convex hull algorithms on finding approaches capable of processing large sets of points. From the many works proposed in this area, the heuristic by Akl-Toussaint deserves a special mention, with outstanding results in execution times. In this article, we take the basic principles of this heuristic to create a convex hull algorithm, called SymmetricHull, that takes advantage of geometric and symmetric properties of the formed quadrants in 2D spaces. The proposed algorithm achieves better exe-cution times than that heuristic, reducing the basic operations to a series of comparisons between consecutive points in an array lexicographically sorted by its y coordinate. SymmetricHull organizes the set of points by quadrants and, instead of using the orientation function as the main operation, it appends the slope s between the analyzed point and its predecessor as a property of the point structure (without causing numerical errors). Point operations can be summarized as follows: 1) a rapid discard of a point, based on its coordinates and the ones of its neighbors; 2) a simple comparison between the property s of the current point and the one of its predecessor in the sorted array, in order to determine whether the current point is a strong candidate to be a part of the convex hull; 3) the addition of a point to a stack of candidates for the convex hull; and 4) the simple elimination of a point from the stack of candidates by comparing the property s of the current point with its predecessors in the stack. Our experiments show that SymmetricHull optimizations achieve good results, in terms of time and number of operations required (multiplications, sums, pushs and pops), being espe-cially efficient with point sets greater than 10^4.

Modelling mist flow for investigating liquid loading in gas wells

This paper presents a dynamic simulation approach to investigating liquid loading in gas wells for a fluid flowing in the mist flow regime. Two-component gas-liquid two-phase flow is considered, using coupled thermodynamic and hydrodynamic models as well as constitutive equations that incorporate the Peng-Robinson equation of state and the convex hull algorithm. The behaviour of the flow properties is investigated as phase change occur during flow. The accumulation of liquids is explored by investigating the distribution of the liquid density in the tubing, which is explicitly determined from the flow variables. The calculated phase densities are validated using data obtained from NIST RefProp and the results show good agreement. This procedure can provide substantial benefits in investigating the phenomena of liquid loading in gas wells compared to critical velocity predicting models that determine the stagnation velocity under isothermal conditions.

A fast convex hull algorithm inspired by human visual perception

This paper proposes a convex hull algorithm for high dimensional point set, which is faster than the well-known Quickhull algorithm in many cases. The main idea of the proposed algorithm is to exclude inner points by early detection of global topological properties. The algorithm firstly computes an initial convex hull of $2*d + 2^{d}$ extreme points. Then, it discards all the inner points which are inside the inscribed ball of the initial convex hull. The other inner points are processed recursively according to the relationships of points and facets. Maximum inscribed circle affine transformations are also designed to accelerate the computation of the convex hull. Experimental results show that the proposed algorithm achieves a significant saving of computation time in comparison with the Quickhull algorithm in 3, 4 and 5 dimensional space. The space efficiency of the proposed algorithm is also demonstrated by experimental results.

An Automated Segmentation Method for Lung Parenchyma Image Sequences Based on Fractal Geometry and Convex Hull Algorithm

Statistically solitary pulmonary nodules are about 6% to 17% of juxtapleural nodules. The accurate segmentation of lung parenchyma sequences of juxtapleural nodules is the basis of subsequent pulmonary nodule segmentation and detection. In order to solve the problem of incomplete segmentation of the juxtapleural nodules and segmentation inefficiency, this paper proposes an automated framework to combine the threshold iteration method to segment the lung parenchyma images and the fractal geometry method to detect the depression boundary. The framework includes an improved convex hull repair to complete the accurate segmentation of the lung parenchyma. The evaluation results confirm that the proposed method can segment juxtapleural lung parenchymal images accurately and efficiently.

A factor graph evidence combining approach to image defogging

In this paper we introduce an evidence combining inference approach based on factor graphs. The method presented here is quite general in nature and exploits the capability of factor graphs to combine results from multiple algorithms which correspond to different generative models or graphical structures. We do this by using layers across the factor graph to represent each of the algorithms under consideration. For purposes of inference, we convert each of these layers into a simplicial complex using a convex hull algorithm. This allows us to obtain a simplicial spanning tree for each of these simplicial complexes. Making use of this simplicial spanning tree, which corresponds to the reparameterisation of the junction tree of the factor graph, exact inference can be performed using the sum/max-product algorithm. Furthermore, we employ a Procrustean transformation so as to avoid degenerate cases in the inference process. We illustrate how the method can be used for evidence combining in image defogging and compare it against other alternatives elsewhere in literature.

A framework for recursive algorithms in low-energy broadcast networks

ABSTRACTWith recent research in sensor networks and IoT technologies, algorithms for broadcast networks should not only seek to minimise runtime but also energy utilisation. We consider the scenario where processors conserve energy by going into a sleep state for the vast majority of the time. Algorithms under these conditions face additional challenges. Specifically, hibernating processors will not know when tasks that have a random runtime complete. This problem is compounded in recursive algorithms where each task’s runtime depends upon the runtime of the recursive calls. We provide a framework, breadth-first recursion, that supports recursive algorithms in this setting. As a simple example, we provide a quick-sort algorithm which is optimal for both time and energy utilisation. We then provide an energy-efficient convex hull algorithm with output sensitive runtime that is sublinear for many realistic distributions for processor placement. Further, we provide simulations that show that our algorithms are practical and significantly faster than previous results.The left side of the image represents our algorithmic technique of breadth first recursion. Inside each box is filled with code and represents the recursive calls of a recursive algorithm. They are arranged in a recursion tree and there is an arrow indicating the order that they are executed. On the right side is a representation of the basic components of our model. They represent low-energy broadcast devices in a single-hop network.

Alternative method to determine parting direction automatically for generating core and cavity of two-plate mold using B-rep of visibility map

The existing method to determine the parting direction for core and cavity of two-plate mold is usually limited to decided types of direction. This limitation reduces the capability of the existing method to select the best parting direction for a 3D CAD model of an object. This paper introduces a new algorithm for another alternative that overcomes the limitation and takes less computational time by using the boundary representation (B-rep) of a visibility map to determine the parting direction. By extracting the geometric and topological information of a visibility (V) map, a B-rep entity is created to represent the V-map, which replaces the existing method that uses convex hull algorithms. To illustrate the capability of the algorithm, the 3D CAD model of objects with regular and freeform faces, holes, protrusion, and depression is presented.

Imbalanced Learning for RR Lyrae Stars Based on SDSS and GALEX Databases

Abstract We apply machine learning and Convex-Hull algorithms to separate RR Lyrae stars from other stars like main-sequence stars, white dwarf stars, carbon stars, CVs, and carbon-lines stars, based on the Sloan Digital Sky Survey and Galaxy Evolution Explorer (GALEX). In low-dimensional spaces, the Convex-Hull algorithm is applied to select RR Lyrae stars. Given different input patterns of (u − g, g − r), (g − r, r − i), (r − i, i − z), (u − g, g − r, r − i), (g − r, r − i, i − z), (u − g, g − r, i − z), and (u − g, r − i, i − z), different convex hulls can be built for RR Lyrae stars. Comparing the performance of different input patterns, u − g, g − r, i − z is the best input pattern. For this input pattern, the efficiency (the fraction of true RR Lyrae stars in the predicted RR Lyrae sample) is 4.2% with a completeness (the fraction of recovered RR Lyrae stars in the whole RR Lyrae sample) of 100%, increases to 9.9% with 97% completeness and to 16.1% with 53% completeness by removing some outliers. In high-dimensional spaces, machine learning algorithms are used with input patterns (u − g, g − r, r − i, i − z), (u − g, g − r, r − i, i − z, r), (NUV − u, u − g, g − r, r − i, i − z), and (NUV − u, u − g, g − r, r − i, i − z, r). RR Lyrae stars, which belong to the class of interest in our paper, are rare compared to other stars. For the highly imbalanced data, cost-sensitive Support Vector Machine, cost-sensitive Random Forest, and Fast Boxes is used. The results show that information from GALEX is helpful for identifying RR Lyrae stars, and Fast Boxes is the best performer on the skewed data in our case.

Monitoring Damage Using Acoustic Emission Source Location and Computational Geometry in Reinforced Concrete Beams

Non-destructive testing in reinforced concrete (RC) for damage detection is still limited to date. In monitoring the damage in RC, 18 beam specimens with varying water cement ratios and reinforcements were casted and tested using a four-point bending test. Repeated step loads were designed and at each step load acoustic emission (AE) signals were recorded and processed to obtain the acoustic emission source location (AESL). Computational geometry using a convex hull algorithm was used to determine the maximum volume formed by the AESL inside the concrete beam in relation to the load applied. The convex hull volume (CHV) showed good relation to the damage encountered until 60% of the ultimate load at the midspan was reached, where compression in the concrete occurred. The changes in CHV from 20 to 40% and 20 to 60% load were five and 13 times from CHV of 20% load for all beams, respectively. This indicated that the analysis in three dimensions using CHV was sensitive to damage. In addition, a high water-cement ratio exhibited higher CHV formation compared to a lower water-cement ratio due to its ductility where the movement of AESL becomes wider.