NEW RESULTS IN COMPUTATIONAL GEOMETRY RELEVANT TO PATTERN RECOGNITION IN PRACTICE

LetP andQ be two convex polygons withm andn vertices, respectively, which are specified by their cartesian coordinates in order. A simpleO(m+n) algorithm is presented for computing the intersection ofP andQ. Unlike previous algorithms, the new algorithm consists of a two-step combination of two simple algorithms for finding convex hulls and triangulations of polygons.

An Isomorphic Fundamental Theorem of the Convex Hull Construction is given and proved. A representative serial algorithm convex hull with half-dividing and recurrence is commented as compared example. A more efficient new serial algorithm to find a convex hull based on a dynamical maximum base line pitch is given; its general characters are: 1) find out the outside-most points as the initial apexes, 2) divide the original distributed domain of a given 2D point set into four sub-domain at most, 3) construct a current apex with a maximum pitch to its base line in every sub-domain. Another new improved serial convex algorithm based on a minimum lever half line pitch coiling with 4-domains and 4-derections in all sub-domains is advanced; its isomorphic new characteristics are: 1) take a new pattern of 1-clusters, 4-domains and 4-directions, 2) construct a current apex with a minimum pitch from its lever half line in every sub-domain, 3) the computational time for finding a current apex is less. Further, a more efficient new parallel algorithm for finding convex hull based on 2-clusters, 2-domains and 4-directions is created; its isomorphic new characteristics are: 1) take pattern of 2-clusters, 2-domains and 4-directions, 2) have great isomorphic new potentialities to construct a better, newer and more efficient parallel algorithm for finding convex hull with m-Clusters, n-Domains and p-Directions (m > 2, n > 2, p > 2).

We prove that the greedy triangulation heuristic for minimum weight triangulation of convex polygons yields solutions within a constant factor from the optimum. For interesting classes of convex polygons, we derive small upper bounds on the constant approximation factor. Our results contrast with Kirkpatrick's Ω(n) bound on the approximation factor of the Delaunay triangulation heuristic for minimum weight triangulation of convexn-vertex polygons. On the other hand, we present a straightforward implementation of the greedy triangulation heuristic for ann-vertex convex point set or a convex polygon takingO(n 2) time andO(n) space. To derive the latter result, we show that given a convex polygonP, one can find for all verticesv ofP a shortest diagonal ofP incident tov in linear time. Finally, we observe that the greedy triangulation for convex polygons having so-called semicircular property can be constructed in timeO(n logn).

In this paper, a representative algorithm convex hull with half-dividing and recurrence is commented; and according to the isomorphic fundamental theorem of the convex hull construction, a more efficient new algorithm to find a convex hull based on the dynamical base line with a maximum pitch of the dynamical base line is given. The general characters of the new algorithm are: 1) find out the outside-most poles which are the leftmost, rightmost, topmost and bottommost points of the given 2D point set, i.e. the four initial poles which have the maximum or the minimum coordinate value of the X or Y axis among all the points in the given 2D point set; 2) divide the original distributed domain into four sub-domains with the initial poles; 3) in every sub-domain, construct a current pole with a maximum pitch to its base line based on the last pole got just dynamically and sequentially, and draw the rims of this convex polygon with these poles for intelligent approximating for a convex hull of the given 2D point set step by step.

본 연구의 목적은 농촌지역의 너구리 행동권과 핵심지역의 면적을 분석하는 것으로서, 이를 위해 22개체를 포획하여 원격 무선추적을 실시하였다. 이 중 3개월 이상 무선 추적이 실시된 9개체의 행동권을 분석한 결과 평균 <TEX>$0.80km^2$</TEX> (100% MCP)를 나타내었다. 성별 행동권은 수컷이 평균 <TEX>$0.98km^2$</TEX> (100% MCP)를 나타내었고, 암컷은 평균 <TEX>$0.58km^2$</TEX> (100% MCP)를 나타내어 수컷의 행동권이 넓었다. 그러나 95% MCP (Minimum Convex Polygon)를 적용했을 경우 수컷이 평균 <TEX>$0.63km^2$</TEX>, 암컷이 <TEX>$0.42km^2$</TEX>로서 차이가 많이 줄었다. 또한 암수 쌍이 함께 무선 추적된 두 쌍의 행동권은 95% MCP를 적용했을 경우 암수가 각각 <TEX>$0.26km^2$</TEX>와 <TEX>$0.28km^2$</TEX>로서 차이가 매우 적거나, <TEX>$0.36km^2$</TEX>와 <TEX>$0.36km^2$</TEX>로 통일했으며, 4 계절 모두 짝을 지어 함께 지냈다. 따라서 짝이 없거나 영역이 정해지지 않은 등의 경우를 제외하고 정상적으로 암수가 한 쌍이 되어 지내는 일상의 경우에는 암수의 행동권이 같다고 판단되어진다. 원격 무선 추적된 너구리 중 4 개체는 암수 쌍을 이루고 있었으며, 이들 두 쌍 모두 일부 일처제를 이루고 함께 이동하며 생활하였다. The objectives of this paper are to estimate home range and core habitat area of raccoon dog living in the rural area of Korea. A radio-telemetry study was carried out on 22 raccoon dog individuals. Among these individuals, 4 raccoon dogs made 2 pairs and they were monogamous and moved together all the year round. Mean home-range size of 9 individuals which were radio-tracked more than 3 months was <TEX>$0.80km^2$</TEX> (100% MCP). The mean home range size of male individuals was <TEX>$0.98km^2$</TEX> (N=5, 100% MCP) and that of female individuals was <TEX>$0.58km^2$</TEX> (N=4, 100% MCP). On the other hand, in case 95% MCP(Mininlum Convex Polygon) was applied, the gap of home-range size between sex distinction was closed to <TEX>$0.63km^2$</TEX> (male) and <TEX>$0.42km^2$</TEX> (female). The home range size of two pairs of which the male and the female were radio-tracked at the same time showed little difference. In case of one pair, the home range size(95% MCP) was <TEX>$0.28km^2$</TEX> (male) and <TEX>$0.26km^2$</TEX> (female) and in case of the other pair, it was <TEX>$0.36km^2$</TEX> each (male and female). Consequently there seems no significant difference in the home-range size between a male and a female racoon dog except the unusual cases such as unpaired individuals or the ones with no fixed territory.

Recently the authors have shown that the versatility of the reconfigurable mesh can be exploited to devise 0(1) time algorithms for a number of important computational tasks relevant to image processing, computer graphics, and computer vision. Specifically, we have shown that if one or two n-vertex (convex) polygons are pretiled, one vertex per processor, onto a reconfigurable mesh of size sqrt n X sqrt n, then a number of geometric problems can be solved in 0(1) time. These include testing an arbitrary polygon for convexity, the point location problem, the supporting lines problem, the stabbing problem, constructing the common tangents of two separable convex polygons, deciding whether two convex polygons intersect, and computing the smallest distance between the boundaries of two convex polygons. The novelty of these algorithms is that the problems are solved in the dense case. The purpose of this paper is to add to the list of problems that can be solved in 0(1) time in the dense case. The problems that we address are: determining the minimum area corner triangle for a convex polygon, determining the k-maximal vertices of a restricted class of convex polygons, updating the convex hull of a convex polygon in the presence of a set of query points, and determining a point that belongs to exactly one of two given convex polygons.

The convex hull has been extensively studied in computational geometry and its applications have spread over an impressive number of fields. How to find the convex hull is an important and challenging problem. Although many algorithms had been proposed for that, most of them can only tackle the problem in two or three dimensions and the biggest issue is that those algorithms rely on the samples' coordinates to find the convex hull. In this paper, we propose an approximation algorithm named FVDM, which only utilizes the information of the samples' distance matrix to find the convex hull. Experiments demonstrate that FVDM can effectively identify the vertices of the convex hull.

Counting thin and bushy triangulations of convex polygons

Computational geometry is the mathematical science of computation by using the algorithm analysis to solve the problems of geometry. The problems of computational include polygon triangulations, convex hulls, Voronoi diagrams, and motion planning. Convex hull is the set of points that form a convex polygon that covers the entire set of points. The algorithms for determining the convex hull, among others, Graham Scan, Jarvis March, and Divide and Conquer. In the two-dimensional case, Graham Scan algorithm is highly efficient in the use of time complexity. This article discusses the quest convex hull of the data bank debtors, some of the data used to look at the classification accuracy of the convex hull formed. The coordinates of all the data found by using principal component analysis.After the data are analyzed, we get the accuracy of classification by 74%.

SummaryAn effective strategy for accelerating the calculation of convex hulls is to filter the input points by discarding interior points. In this paper, we present such a straightforward preprocessing approach by discarding the points locating in a convex polygon formed by 16 extreme points. Extreme points of a planar point set do not alter when all points are rotated with the same angle in the plane. Four groups of four extreme points with min or max x or y coordinates can be found for the original point set and three rotated point sets. These 16 extreme points are used to form a planar convex polygon. We discard those points locating in the convex polygon and calculate the desired convex hull of the remaining points. The proposed preprocessing algorithm is evaluated on two computational platforms. Experiments show that, when employing the proposed preprocessing algorithm on the computational platform 1, it achieves speedups of approximately 4 ×∼5× on average and 5 ×∼6× in the best cases over the cases where the proposed approach is not used, while on the computational platform 2, the speedups are approximately 6 ×∼9× on average and 9 ×∼14× in the best cases. Moreover, more than 99% input points can be discarded in most cases.

This paper surveys recent results in the design and analysis of algorithms for solving geometric problems in pattern recognition. Among the problems considered are: the convex hull, the diameter, Voronoi diagrams, the relative neighborhood graph, polygon decomposition, and distance between sets. Some new results are presented; among them a new 0(n) algorithm for merging two convex polygons and a proof that a convex hull algorithm of Kim and Rosenfeld (35) works. Several open problems are also mentioned.

BackgroundCystic echinococcosis (CE), caused by the larval stage of Echinococcus granulosus sensu lato, is a zoonotic parasitic disease of economic and public health importance worldwide, especially in the Mediterranean area. Canids are the main definitive hosts of the adult cestode contaminating the environment with parasite eggs released with feces. In rural and peri-urban areas, the risk of transmission to livestock as well as humans is high because of the free-roaming behavior of owned/not owned dogs. Collecting data on animal movements and behavior using GPS dataloggers could be a milestone to contain the spread of this parasitosis. Thus, this study aims to develop a comprehensive control strategy, focused on deworming a dog population in a pilot area of southern Italy (Campania region) highly endemic for CE.MethodsAccordingly, five sheep farms, tested to be positive for CE, were selected. In each sheep farm, all shepherd dogs present were treated every 2 months with praziquantel. Furthermore, 15 GPS dataloggers were applied to sheep and dogs, and their movements were tracked for 1 month; the distances that they traveled and their respective home ranges were determined using minimum convex polygon (MCP) analysis with a convex hull geometry as output.ResultsThe results showed that the mean daily walking distances traveled by sheep and dogs did not significantly differ. Over 90% of the point locations collected by GPS fell within 1500 mt of the farm, and the longest distances were traveled between 10:00 and 17:00. In all the sheep farms monitored, the area traversed by the animals during their daily activities showed an extension of < 250 hectares. Based on the home range of the animals, the area with the highest risk of access from canids (minimum safe convex polygon) was estimated around the centroid of each farm, and a potential scheme for the delivery of praziquantel-laced baits for the treatment of not owned dogs gravitating around the grazing area was designed.ConclusionsThis study documents the usefulness of geospatial technology in supporting parasite control strategies to reduce disease transmission.Graphical

When trying to find the convex hull (CH) of a point set, humans can neglect most non-vertex points by an initial estimation of the boundary of the point set easily. The proposed CH algorithm imitates this characteristic of visual attention, starts by constructing an initial convex polygon (ICP), and measures the width and length of ICP through a shape estimation step. It then maps the point set into the new one by an affine transformation and makes most of the new points exist in a new initial convex polygon (NICP) which approximated to a regular convex polygon. Next, it discards the interior points in NICP by an inscribed circle and processes the remaining points outside NICP by Quickhull. Finally, the algorithm outputs the vertex set of CH. Two theorems are also proposed to solve an unconstrained optimization problem instead of the iteration method. Compared with four popular CH algorithms, the proposed algorithm can generate CH much faster than them and achieve a better performance.

Convex hull properties and algorithms

Recent developments in the field of computational geometry are discussed with emphasis on those problems most relevant to computer graphics. In particular we consider convex hulls, triangulations of polygons and point sets, finding the CSG representation of a simple polygon, polygonal approximations of a curve, computing geodesic and visibility properties of polygons and sets of points inside polygons, movable separability of polygons and local spatial planning, visibility questions concerning polyhedral terrains, finding minimal spanning covers of sets and various problems that arize in computational morphology including polygon decomposition and detecting symmetry.