Convex Hull Method Research Articles

Comparison of Kernel Density and Local Convex Hull Methods for Assessing Distribution Ranges of Large Mammalian Herbivores

AbstractWhen assessing distribution range shifts, precise information is required on distribution limits, densities in occupied regions, unoccupied gaps, and changes in these measures over time. The local convex hull method recently developed for home range delineation to provide these measures was compared with that of the widely applied parametric kernel density estimation and with the commonly used tile method. The assessment used location records from 14 years of aerial surveys on four mammalian herbivores selected because of their distinct distribution patterns. Impala showed an almost continuous distribution with few gaps, wildebeest a wide distribution with regional concentrations, waterbuck a linear distribution along rivers, and sable antelope a widespread but patchy distribution. The kernel method tended to extend ranges beyond observed records, obscuring gaps within distributions. With parametric kernel approaches, bandwidth obtained via Least Squares Cross Validation techniques was not optimal when the local abundance was widely disparate, as was the case for wildebeest. The LoCoH method most effectively revealed meaningful gaps. The LoCoH method is advantageous for precisely mapping the distributions of conspicuous species for which the absence of records indicates true gaps in occurrence.

Hand gesture recognition from multibeam sonar imagery

Abstract: Divers perform demanding tasks in a complex and hazardous underwater environment, which prevents them from carrying special devices that may allow them to communicate with their robotic diving buddies. In this world of natural human-robot interaction in the underwater environment, envisioned by the FP7 Cognitive Robotics project CADDY, hand detection and gesture interpretation is a prerequisite. While hand gesture recognition is most often performed with cameras (mono and stereo), their use in the underwater environment is compromised due to water turbidity and lack of sunlight at greater depths. This paper deals with this lack of performance by introducing the concept of using high resolution multibeam sonars (often referred to as acoustic cameras) for diver hand gesture recognition. In order to ensure reliable communication between the diver and the robot, it is of great importance that the classification precision is as high as possible. This paper presents results of hand gesture recognition which is performed by using two approaches: convex hull method and the support vector machine (SVM). A novel approach that fuses the two methods is introduced as a way of increasing the precision of classification. The results obtained on more than 1000 real sonar samples show that the precision using the convex hull method is around 92%, and using the SVM around 94%, while fusing the two approaches provides around 99% classification precision.

Design for Additive Manufacturing: Automated Build Orientation Selection and Optimization

Additive manufacturing, or 3D printing, is an emerging type of production technology that is seen as the core technology for future high-value engineered products. Due to the additive nature of stacking and unifying individual layers, the part and process design is substantially different from conventional production methods. This paper addresses one of the challenging design aspects for additive manufacturing, namely the determination of the build orientation. The build orientation has a large impact on the final part quality and must therefore be chosen wisely. This paper presents an approach to support the build orientation selection by a feature-based design algorithm. After automated part tessellation and the detection of outer part surfaces, the algorithm determines candidate build orientations through a ray-tracing and convex hull method. Candidate solutions are ranked based on minimizing overhang structures, as this also minimizes the need for additional support structures.

Movement patterns of cheetahs (Acinonyx jubatus) in farmlands in Botswana.

ABSTRACTBotswana has the second highest population of cheetah (Acinonyx jubatus) with most living outside protected areas. As a result, many cheetahs are found in farming areas which occasionally results in human-wildlife conflict. This study aimed to look at movement patterns of cheetahs in farming environments to determine whether cheetahs have adapted their movements in these human-dominated landscapes. We fitted high-time resolution GPS collars to cheetahs in the Ghanzi farmlands of Botswana. GPS locations were used to calculate home range sizes as well as number and duration of visits to landscape features using a time-based local convex hull method. Cheetahs had medium-sized home ranges compared to previously studied cheetah in similar farming environments. Results showed that cheetahs actively visited scent marking trees and avoided visiting homesteads. A slight preference for visiting game farms over cattle farms was found, but there was no difference in duration of visits between farm types. We conclude that cheetahs selected for areas that are important for their dietary and social needs and prefer to avoid human-occupied areas. Improved knowledge of how cheetahs use farmlands can allow farmers to make informed decisions when developing management practices and can be an important tool for reducing human-wildlife conflict.

Home-Range and Foraging Areas of the Dawn BatEonycteris spelaeain Agricultural Areas of Thailand

We studied the foraging behaviour of the dawn bat Eonycteris spelaea, a cave roosting nectarivore widespread in SE Asia, and principal pollinator of economically important crops. We radio-tracked 17 individuals for five to 19 nights over a three month period. The bats were from three cave colonies in agricultural habitats in southern Thailand. They traveled between one and 17.9 km ( ± SD: 4.4 km ± 5.07, median = 2.34) from their roosting cave to food sources. The mean home-range size of the individuals varied with the method used in its calculation from 518.4 ha (100% Minimum Convex Polygon, MCP) to 564.5 ha (100% Local Convex Hull method, LoCoH) and 460.8 ha (95% Kernel density estimation, KDE). The mean size of foraging areas used by the bats also varied according to the method of calculation from 14.26 ha (100% MCP), 13.25 ha (100% LoCoH) and 38.52 ha (95% KDE) and accounted for 21.9%, 20.08% and 40.5% of the respective home-range size. The bats foraged in one to three foraging areas each night. The gr...

Stochastic optimization models for energy management in carbonization process of carbon fiber production

Industrial producers face the task of optimizing production process in an attempt to achieve the desired quality such as mechanical properties with the lowest energy consumption. In industrial carbon fiber production, the fibers are processed in bundles containing (batches) several thousand filaments and consequently the energy optimization will be a stochastic process as it involves uncertainty, imprecision or randomness. This paper presents a stochastic optimization model to reduce energy consumption a given range of desired mechanical properties. Several processing condition sets are developed and for each set of conditions, 50 samples of fiber are analyzed for their tensile strength and modulus. The energy consumption during production of the samples is carefully monitored on the processing equipment. Then, five standard distribution functions are examined to determine those which can best describe the distribution of mechanical properties of filaments. To verify the distribution goodness of fit and correlation statistics, the Kolmogorov–Smirnov test is used. In order to estimate the selected distribution (Weibull) parameters, the maximum likelihood, least square and genetic algorithm methods are compared. An array of factors including the sample size, the confidence level, and relative error of estimated parameters are used for evaluating the tensile strength and modulus properties.The energy consumption and N2 gas cost are modeled by Convex Hull method. Finally, in order to optimize the carbon fiber production quality and its energy consumption and total cost, mixed integer linear programming is utilized. The results show that using the stochastic optimization models, we are able to predict the production quality in a given range and minimize the energy consumption of its industrial process.

Efficient Algorithms for Automated Inspection of Freeform Surfaces

This paper reports the development of efficient algorithms for automated inspection of freeform surfaces using point cloud data collected using an inspection system. The registration process to align the point cloud with the input CAD surface model is carried out in two phases, viz, rough registration followed by an accurate (fine) registration. For rough registration, algorithms based on the bounding box method and the convex hull method have been proposed. Fine registration is carried out using a computational geometry approach using a tessellated representation of the surface model. A random sampling technique has been integrated with the final registration algorithm to speed up the registration process. The algorithms have been compared with those reported in literature. Results show that the proposed algorithms substantially reduce the computational time, without sacrificing the accuracy of registration.

TernAPI program for the calculation of ternary phase diagrams with isolated miscibility gaps by the convex hull method

The first public version of TernAPI (ternary diagrams assessment programming interface) software package for ternary phase diagrams calculation by the convex hull method has been developed. Its reliability and efficiency have been proved on a large set of systems of different kind: organic liquids and fluids mixtures, water solutions, salts, oxides, metallic alloys. A remarkable advantage of TernAPI is a stable work in the case of isolated miscibility gaps (“islands”) described by a uniform Gibbs energy surface equation. It also contains several improvements of phase diagram calculation algorithm, a new module for x–T diagrams polythermal sections calculation and possibility of optimization of thermodynamic models parameters. NRTL model parameters for the acetic acid–N,N-dimethylformamide–cyclohexene ternary system have been optimized in this work. The specialized language based on Ruby and YAML is used for the description of thermodynamic models of phases.

RGB-D Indoor Plane-based 3D-Modeling using Autonomous Robot

Abstract. 3D model of indoor environments provide rich information that can facilitate the disambiguation of different places and increases the familiarization process to any indoor environment for the remote users. In this research work, we describe a system for visual odometry and 3D modeling using information from RGB-D sensor (Camera). The visual odometry method estimates the relative pose of the consecutive RGB-D frames through feature extraction and matching techniques. The pose estimated by visual odometry algorithm is then refined with iterative closest point (ICP) method. The switching technique between ICP and visual odometry in case of no visible features suppresses inconsistency in the final developed map. Finally, we add the loop closure to remove the deviation between first and last frames. In order to have a semantic meaning out of 3D models, the planar patches are segmented from RGB-D point clouds data using region growing technique followed by convex hull method to assign boundaries to the extracted patches. In order to build a final semantic 3D model, the segmented patches are merged using relative pose information obtained from the first step.

Home range and diving behaviour of Heaviside's dolphins monitored by satellite off the west coast of South Africa

Three Heaviside's dolphins Cephalorhynchus heavisidii were fitted with satellite depth recorders off the west coast of South Africa during February–April 1997 and monitored for 51, 73 and 130 days, respectively. In total, 345 locations were received from the three animals, but only 27 from one male. Using α-local convex hull and minimum convex polygon methods, respectively, the home range for the remaining male was estimated at 1 520 and 2 347 km2, with corresponding core-area estimates (50% of locations) of 134 and 123 km2. For the female, the home range estimates were 672 and 1 027 km2, and those for the core area were 71 and 230 km2. The female's home range was the smallest yet described for this species, and the animal was resighted nearly three years later within 13 km of the tagging site. Binned dive data were received at 6-hourly intervals. From comparison of maximum dive depth and time-at-depth data, we concluded that dives <4 m deep were associated with surfacing bouts. Dives to below 4 m occurred throughout 24 h but were shallower during the day and deepest either at dusk or at night. This pattern was consistent with earlier descriptions of offshore movement during the day and may be related to the diel vertical migration of its principal prey, shallow-water hake Merluccius capensis.

DRCH: A Method for 3D Convex Hull

A novel three-dimensional (3D) convex hull method is proposed, which is called dimensionality reduction convex hull method (DRCH).Through having 3d point set map to 2d plane, most initial 3D points in the convex hull are removed. Then, the remaining points are to generate 3D convex hull using any convex hull algorithm. The experiment demonstrates 3D DRCH is faster than general 3D convex hull algorithms. Its time complexity is O(r log r), where r is the number of points not in the hull. And DRCH can be generalized to higher-dimensional problems.

Methods for estimating cortical motor representation size and location in navigated transcranial magnetic stimulation.

Navigated transcranial magnetic stimulation (nTMS) is used for locating and outlining cortical representation areas, e.g., of motor function and speech. At present there are no standard methods of measuring the size of the cortical representation areas mapped with nTMS. The aim was to compare four computation methods for estimating muscle representation size and location for nTMS studies. The motor cortex of six subjects was mapped to outline the motor cortical representation of hand muscles. Four methods were compared to assess cortical representation size in nTMS. These methods included: (1) spline interpolation method, (2) convex hull method, which outlines all positive motor responses, (3) Voronoi tessellation method, which assigns a specific cortical area for each stimulus location, and (4) average point-area method, which computes an average representation area for each stimulus with the assumption of evenly spaced stimulus locations, i.e., the use of a grid. All applied methods demonstrated good repeatability in measuring muscle representation size and location, while the spline interpolation and the convex hull method demonstrated systematically larger representation areas (p<0.05) as compared to the average point-area method. Spline interpolation method demonstrated the best repeatability in location. Unlike the previous methods, the presented methods can be applied for the estimation of the representation area of nTMS-induced activation without the use of an evenly spaced stimulus grid. The spline interpolation method and the Voronoi tessellation method could be used for evaluating motor cortical muscle representation size and location with nTMS, e.g., to study cortical plasticity.

Approximate convex skyline: A partitioned layer-based index for efficient processing top-k queries

A top-k query returns k tuples with the highest (or the lowest) scores from a relation. Layer-based methods are the representative ones for processing top-k queries efficiently. These methods construct a list of layers, where the ith layer contains the tuples that can potentially be the top-i answer. Thus, the layer-based methods can answer top-k queries by reading at most k layers. To construct layers, the existing layer-based methods use convex skyline, convex hull or skyline methods. Among them, the convex skyline is constructed by computing the convex hull over the skyline. Accordingly, the layer size of the convex skyline is relatively smaller than those of the convex hull, and the index building time is relatively shorter than those of the skyline. However, for large and high-dimensional databases, the convex skyline suffers from long index building time and large memory usage, because most objects can become the skyline points. This paper focuses on how to build an index, which contains a smaller number of objects comparing to the skyline and uses less time to construct an index comparing to the convex skyline. Specifically, we propose a method, called the Approximate Convex Skyline Enhanced (simply, AppCSE), which reduces the index building time and memory usage of the convex skyline. In the proposed method, we first construct the skyline, and then, partition the region of the skyline into multiple subregions, and compute the convex hull in each subregion with virtual objects. After that, AppCSE combines the objects obtained by computing the convex hull. Through various experiments with synthetic and real datasets, we demonstrate that the proposed method significantly reduces the index building time and memory usage comparing to the existing methods. In addition, we show that the degradation of query performance is negligible when using AppCSE as the layering scheme.

Home range and activity patterns of Conepatus semistriatus (Carnivora, Mephitidae) in Emas National Park, Brazil

Skunks (Mephitidae) have not been well studied throughout the Neotropics. In Brazil there is a general lack of data on the ecology, behavior, distribution, systematics, morphology and biogeographic patterns of the two species occurring in the country (Conepatus semistriatus and C. chinga). The focus of this study was on understanding the home range and activity patterns of C. semistriatus. Field research was conducted in the Emas National Park, where three skunks with radio-collars were located on 157 separate occasions. The observed patterns of activity indicate that the species is predominantly nocturnal, with a great expenditure of time on foraging. Temperature had a direct influence on the animal’s behavior, but there was no apparent influence of light on activity patterns. Average home range areas were 1.39 ± 0.87 km2 (Minimum Convex Polygon method) and 0.69 ± 0.25 km2 (Local Convex Hull method). There was high home range overlap between individuals, 0.27 km2 based on the Minimum Convex Polygon method, at sites with easy access to resources.

Site fidelity in space use by spider monkeys (Ateles geoffroyi) in the Yucatan peninsula, Mexico.

Animal home ranges may vary little in their size and location in the short term but nevertheless show more variability in the long term. We evaluated the degree of site fidelity of two groups of spider monkeys (Ateles geoffroyi) over a 10- and 13-year period, respectively, in the northeastern Yucatan peninsula, Mexico. We used the Local Convex Hull method to estimate yearly home ranges and core areas (defined as the 60% probability contour) for the two groups. Home ranges varied from 7.7 to 49.6 ha and core areas varied from 3.1 to 9.2 ha. We evaluated the degree of site fidelity by quantifying the number of years in which different areas were used as either home ranges or core areas. Large tracts were used only as home ranges and only for a few years, whereas small areas were used as either core area or home range for the duration of the study. The sum of the yearly core areas coincided partially with the yearly home ranges, indicating that home ranges contain areas used intermittently. Home ranges, and especially core areas, contained a higher proportion of mature forest than the larger study site as a whole. Across years and only in one group, the size of core areas was positively correlated with the proportion of adult males in the group, while the size of home ranges was positively correlated with both the proportion of males and the number of tree species included in the diet. Our findings suggest that spider monkey home ranges are the result of a combination of long-term site fidelity and year-to-year use variation to enable exploration of new resources.

Calculation of phase equilibria and construction of phase diagrams by convex hull method

Recent findings for a new method developed to calculate phase equilibria are reviewed and analyzed. This method is based on the construction of the convex hulls for characteristic functions in heterogeneous systems. The theoretical basis of this method, as well as the possibilities and features of its practical application in scientific research and teaching chemical thermodynamics, is considered. Software packages developed at the Department of Chemistry of Moscow State University are briefly described.

참외 수확로봇을 위한 타원 정합기반의 인식 기법 개발

In this paper, vision-based positioning algorithm for melon harvesting robot is presented. RGB value of the input image was converted into HSI value then, melon area was extracted after performing the binarization using HUE value. After morphological filtering was applied to remove noise, outermost boundary points were obtained using border following and convex hull method. Elliptical fitting for melons was perform by the RANSAC algorithm, the center point of ellipse, the length of the short and long axis, and rotation angle were obtained. We verified the effectiveness of the proposed method by various simulation experiments and confirmed actual feasibility of the proposed method by applying to the real melon.

A scaled line-based kernel density estimator for the retrieval of utilization distributions and home ranges from GPS movement tracks

Utilization distributions (UDs) can be used to describe the intensity with which an animal or human has used a certain geographical location. Within the domain of wildlife ecology, a density distribution model represents one way to describe an animals' home range. Several methods have been developed to derive UDs, and subsequently home ranges. Most of these methods, e.g. kernel density estimation (KDE), and local convex hull methods, have been developed with point-based datasets in mind, and do not utilize additional information that comes with GPS-based tracking data (e.g., temporal information). To employ such additional information we extend the point-based KDE approach to work with sequential GPS-point tracks, the outcome of which is a line-based KDE. We first describe the design criteria for the line-KDE algorithm. Then we introduce the basic modeling approach and its refinement through the introduction of a scaling function. This scaling function modifies the utilization distribution so that a bone-like probability distribution for a single GPS track segment is obtained. Finally we compare the estimated utilization distributions and home ranges for two datasets derived using our line-KDE approach with those obtained using the point-KDE and Brownian Bridge (BB) approaches. Advantages of the line-based KDE by design are (i) a better representation of utilization density near GPS points when compared against the BB approach, and (ii) the ability to model and retain movement corridors when compared against point-KDE.

Factors affecting intraspecific variation in home range size of a large African herbivore

Factors affecting intraspecific variation in home range size have rarely been examined using modern statistical and remote sensing methods. This is especially true for animals in seasonal savanna environments in Africa, despite this biome’s importance for both conservation and development goals. We studied the impacts of spatial and temporal variability in environmental conditions, along with individual and social factors, on home range sizes in African buffalo (Syncerus caffer) in northeastern Namibia. Our data set spans 4 years, is derived from 32 satellite tracking collars, and contains over 35,000 GPS locations. We used the local convex hull method to estimate home range size from 31 buffalo captured at 6 sites. We used a variety of remotely sensed data to characterize potential anthropogenic and natural boundaries, as well as seasonal and temporal heterogeneity in environmental conditions. Using an information-theoretic, mixed effects approach, our analyses showed that home ranges varied over two orders of magnitude and are among the largest recorded for this species. Variables relating to vegetation and habitat boundaries were more important than abiotic environmental conditions and individual or social factors in explaining variation in home range size. The relative contributions of environmental, individual, social, and linear boundary variables to intraspecific home range size have rarely been examined and prior to this had not been assessed for any species in seasonal savannas of Africa. Understanding the factors that condition space-use patterns of wildlife in this area will lead to better-informed conservation and sustainable development decisions.

Online appendix 1:Changing distributions of larger ungulates in the Kruger National Park from ecological aerial survey data

Documenting current species distribution patterns and their association with habitat types is important as a basis for assessing future range shifts in response to climate change or other influences. We used the adaptive local convex hull (a-LoCoH) method to map distribution ranges of 12 ungulate species within the Kruger National Park (KNP) based on locations recorded during aerial surveys (1980–1993). We used log-linear models to identify changes in regional distribution patterns and chi-square tests to determine shifts in habitat occupation over this period. We compared observed patterns with earlier, more subjectively derived distribution maps for these species. Zebra, wildebeest and giraffe distributions shifted towards the far northern section of the KNP, whilst buffalo and kudu showed proportional declines in the north. Sable antelope distribution contracted most in the north, whilst tsessebe, eland and roan antelope distributions showed no shifts. Warthog and waterbuck contracted in the central and northern regions, respectively. The distribution of impala did not change. Compared with earlier distributions, impala, zebra, buffalo, warthog and waterbuck had become less strongly concentrated along rivers. Wildebeest, zebra, sable antelope and tsessebe had become less prevalent in localities west of the central region. Concerning habitat occupation, the majority of grazers showed a concentration on basaltic substrates, whilst sable antelope favoured mopane-dominated woodland and sour bushveld on granite. Buffalo showed no strong preference for any habitats and waterbuck were concentrated along rivers. Although widespread, impala were absent from sections of mopane shrubveld and sandveld. Kudu and giraffe were widespread through most habitats, but with a lesser prevalence in northern mopane-dominated habitats. Documented distribution shifts appeared to be related to the completion of the western boundary fence and widened provision of surface water within the park. Conservation implications: The objectively recorded distribution patterns provide a foundation for assessing future changes in distribution that may take place in response to climatic shifts or other influences.