Convex Hull Algorithm Research Articles

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.

Rapid preconditioning of data for accelerating convex hull computations

Given a dataset of two-dimensional points in the plane with integer coordinates, the method proposed reduces a set of n points down to a set of s points s ≤ n, such that the convex hull on the set of s points is the same as the convex hull of the original set of n points. The method is O(n). It helps any convex hull algorithm run faster. The empirical analysis of a practical case shows a percentage reduction in points of over 98%, that is reflected as a faster computation with a speedup factor of at least 4.

An enhanced version and an incremental learning version of visual-attention-imitation convex hull algorithm

This paper presents an enhanced version and an incremental learning version of the visual-attention-imitation convex hull algorithm reported in our latest paper in Liu et al. (2012) [3]. The enhanced algorithm merges the virtue of point comparison of the Graham scan algorithm into the visual-attention-imitation convex hull algorithm. In comparison with its previous edition, the proposed algorithm achieved a significant time saving. In view of machine learning, there are interesting situations where training data acquisition must take place over time. An incremental learning version is also proposed in this paper in order to compute convex hulls of point sets whose points are acquired over time. The incremental learning version reuses the prior results and computes the new convex hull without processing of previous points. Experimental results show that the incremental learning version is more flexible and more efficient for incremental learning tasks.

Self-Improving Algorithms for Coordinatewise Maxima and Convex Hulls

Finding the coordinate-wise maxima and the convex hull of a planar point set are probably the most classic problems in computational geometry. We consider these problems in the self-improving setting. Here, we have $n$ distributions $\mathcal{D}_1, \ldots, \mathcal{D}_n$ of planar points. An input point set $(p_1, \ldots, p_n)$ is generated by taking an independent sample $p_i$ from each $\mathcal{D}_i$, so the input is distributed according to the product $\mathcal{D} = \prod_i \mathcal{D}_i$. A self-improving algorithm repeatedly gets inputs from the distribution $\mathcal{D}$ (which is a priori unknown), and it tries to optimize its running time for $\mathcal{D}$. The algorithm uses the first few inputs to learn salient features of the distribution $\mathcal{D}$, before it becomes fine-tuned to $\mathcal{D}$. Let $\text{OPTMAX}_\mathcal{D}$ (resp. $\text{OPTCH}_\mathcal{D}$) be the expected depth of an \emph{optimal} linear comparison tree computing the maxima (resp. convex hull) for $\mathcal{D}$. Our maxima algorithm eventually achieves expected running time $O(\text{OPTMAX}_\mathcal{D} + n)$. Furthermore, we give a self-improving algorithm for convex hulls with expected running time $O(\text{OPTCH}_\mathcal{D} + n\log\log n)$. Our results require new tools for understanding linear comparison trees. In particular, we convert a general linear comparison tree to a restricted version that can then be related to the running time of our algorithms. Another interesting feature is an interleaved search procedure to determine the likeliest point to be extremal with minimal computation. This allows our algorithms to be competitive with the optimal algorithm for $\mathcal{D}$.

A new method of minimum convex hull in computer applications

The minimum convex hull is one of the widely studied problems in computational geometry, as well as widely applied in many fields such as in GIS. This paper, through analysis of the disadvantage of the traditional minimum convex hull serial algorithm, puts forward a new method of the minimum convex hull. It introduces three new concepts such as 'absolute vertex', 'absolutely wrong vertex' and 'possible vertex' in minimum convex hull, which can improve the algorithm computing efficiency, and increase the applicability of minimum convex hull in large number of spatial data. In the end, through comparative analysis, compared to the traditional serial algorithm, this paper's algorithm has obvious advantages on seeking minimum convex hull vertex in large number of spatial data, this algorithm execution efficiency is higher than the traditional serial algorithm for minimum convex hull, and it also can improved the applicability of minimum convex hull.

Image Space Rendering of Point Clouds Using the HPR Operator

AbstractThe hidden point removal (HPR) operator introduced by Katz et al. [KTB07] provides an elegant solution for the problem of estimating the visibility of points in point samplings of surfaces. Since the method requires computing the three‐dimensional convex hull of a set with the same cardinality as the original cloud, the method has been largely viewed as impractical for real‐time rendering of medium to large clouds. In this paper we examine how the HPR operator can be used more efficiently by combining several image space techniques, including an approximate convex hull algorithm, cloud sampling, and GPU programming. Experiments show that this combination permits faster renderings without overly compromising the accuracy.

QR Code Image Correction based on Corner Detection and Convex Hull Algorithm

Since the angular deviation produced when shooting a QR code image by a camera would cause geometric distortion of the QR code image, the traditional algorithm of QR code image correction would produce distortion. Therefore this paper puts forward the algorithm which combines corner detection with convex hull algorithm. Firstly, binaryzation of the collected QR code image with uneven light is obtained by the methods of local threshold and mathematical morphology. Next, the outline of the QR code and the dots on it are found and the distorted image is recovered by perspective collineation, according to the algorithm raised by this paper. Finally, experimental verification is made that the algorithm raised by this paper can correctly find the four apexes of QR code and achieves good effects of geometric correction. It will also significantly increase the recognition rate of seriously distorted QR code images

Biologically Inspired Perimeter Detection for Whole-Arm Grasping

Grasping is a useful ability that allows manipulators to constrain objects to a desired location or trajectory. Whole-arm grasping is a specific method of grasping an object that uses the entire surface of the manipulator to apply contact forces. Elephant trunks and snakes and octopus arms are illustrative of these methods. One of the greatest challenges of whole-arm grasping in poorly defined environments is accurately identifying the perimeter of an object. Existing algorithms for this task use restrictive assumptions or place unrealistic demands on the required hardware. Here, a new algorithm (termed Octograsp) has been developed as a method of gaining information on the shape of the grasped object through tactile information alone. The contact information is processed using an inverse convex hull algorithm to build a model of the object’s shape and position. The performance of the algorithm is examined using both simulated and experimental hardware. Methods of increasing the level of contact information through repeated contact attempts are presented. It is demonstrated that experimentally obtained, coarsely spaced, contact information can result in an accurate model of an object’s shape and position.

A Fast Convex Hull Algorithm of Planar Point Set

In this paper ,a new algorithm is proposed for improving speed of calculating convex hull of planar point set .The algorithm creates a square mesh to manage points ,when eliminating points which are obviously in convex hull ,selecting or eliminating of points can be converted to that of grid , work of calculation depends on points near edges of convex hull and density of grid but not the number of points ;at the meantime ,remainder points are sorted roughly .When calculating convex hull of remainder points ,a method is presented which can take advantage of order of remainder points ,it calculates boundaries of convex hull segment by segment ,then ,combines the boundaries to form convex hull.

Hyperspectral Data Geometry-Based Estimation of Number of Endmembers Using p-Norm-Based Pure Pixel Identification Algorithm

Hyperspectral endmember extraction is a process to estimate endmember signatures from the hyperspectral observations, in an attempt to study the underlying mineral composition of a landscape. However, estimating the number of endmembers, which is usually assumed to be known a priori in most endmember estimation algorithms (EEAs), still remains a challenging task. In this paper, assuming hyperspectral linear mixing model, we propose a hyperspectral data geometry-based approach for estimating the number of endmembers by utilizing successive endmember estimation strategy of an EEA. The approach is fulfilled by two novel algorithms, namely geometry-based estimation of number of endmembers—convex hull (GENE-CH) algorithm and affine hull (GENE-AH) algorithm. The GENE-CH and GENE-AH algorithms are based on the fact that all the observed pixel vectors lie in the convex hull and affine hull of the endmember signatures, respectively. The proposed GENE algorithms estimate the number of endmembers by using the Neyman–Pearson hypothesis testing over the endmember estimates provided by a successive EEA until the estimate of the number of endmembers is obtained. Since the estimation accuracies of the proposed GENE algorithms depend on the performance of the EEA used, a reliable, reproducible, and successive EEA, called <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$p$</tex></formula> -norm-based pure pixel identification (TRI-P) algorithm is then proposed. The performance of the proposed TRI-P algorithm, and the estimation accuracies of the GENE algorithms are demonstrated through Monte Carlo simulations. Finally, the proposed GENE and TRI-P algorithms are applied to real AVIRIS hyperspectral data obtained over the Cuprite mining site, Nevada, and some conclusions and future directions are provided.

평면 점집합에서 정렬을 고려한 개선된 컨벡스 헐 알고리즘

본 연구에서는 임의의 정렬되지 않은 점집합에서 정렬을 고려한 개선된 Convex Hull 알고리즘을 제안한다. 이 알고리즘은 Convex Hull의 극점 특성을 이용하여 처리 데이터를 한정하기 때문에 계산복잡도가 낮다. 각 단계마다 볼록 정점을 판별하는 조건을 이용하여 한 번의 스캔으로 완전한 Convex Set을 구한다. 알고리즘 초기에 점집합의 정렬이 필요한데, 이때 걸리는 시간이 알고리즘 전체 동작시간의 대부분을 차지하기 때문에 값과 인덱스를 대치하여 빠르게 정렬하였다. 일반적인 상황을 가정하여 랜덤한 점집합으로 알고리즘의 동작시간을 측정하였으며 기존의 알고리즘에 비해 약 두 배의 속도 향상이 있음을 확인하였다. In this paper, we suggest an improved Convex Hull algorithm considering sort in plane point set. This algorithm has low computational complexity since processing data are reduced by characteristic of extreme points. Also it obtains a complete convex set with just one processing using an convex vertex discrimination criterion. Initially it requires sorting of point set. However we can't quickly sort because of its heavy operations. This problem was solved by replacing value and index. We measure the execution time of algorithms by generating a random set of points. The results of the experiment show that it is about 2 times faster than the existing algorithm.

Iterative Algorithm for 3D Convex Hulls and its Optimization for Multiprocessor Architecture

Iterative Algorithm for 3D Convex Hulls and its Optimization for Multiprocessor Architecture

Parallel computing applied to the stochastic dynamic programming for long term operation planning of hydrothermal power systems

In this paper, parallel processing techniques are employed to improve the performance of the stochastic dynamic programming applied to the long term operation planning of electrical power system. The hydroelectric plants are grouped into energy equivalent reservoirs and the expected cost functions are modeled by a piecewise linear approximation, by means of the Convex Hull algorithm. In order to validate the proposed methodology, data from the Brazilian electrical power system is utilized.

Boundary query solution using convex hull algorithm

An important issue in database (DB) systems is responding to different users’ queries in an acceptable time. To do this, we should define different queries based on users’ real needs and we should consider suitable solutions. In this article, we express a new query called ‘boundary query’ which is used for achieving an overall view of a subject in the DB. This query does not return all query answers but it returns boundary values that cover all answers for the related query. In this article, we map a DB environment to a vector space based on necessary attributes. Then we implement the proposed method, and based on the results, we observe that the proposed method's run time is acceptable for huge DBs.

Fast Algorithm for Convex Hull of Planer Point Set

The convex hull is one of main research problems in computational geometry, it has been wildly used in computer graphics, pattern recognition, image processing, GIS and military, etc. In this paper, a simple and fast algorithm for the convex hull of planer point set is proposed by deleting those “useless” points. In case of points distributed randomly in the planer area, our algorithm is more efficient than the classical Graham Scan Algorithm in terms of processing.

Application of Convex Hull Algorithm for Defect Detection in Selected Biological Materials

Conventional convex hull algorithm determines the smallest convex polygon that contains the analyzed shape. The article presents a modification of this algorithm, which allows us to select the concavity to detect. In contrast to the typical convex hull algorithm, the data are analyzed in portions. This paper proposes the use of this modified algorithm for the defects detection on medical images. Two types of images were used: micro-computer tomography images of dental root canals filled with sealer and magnetic resonance images of a patient hand with rheumatoid arthritis. Those images contained some defects that needed to be measured. Prepared algorithm greatly facilitated this process by supporting the user in the segmentation process. The achieved results were positively evaluated by experts - doctors: rheumatologists and endodontists.

Automatic Sort Order of Checkerboard Corners Based on Convex Hull Algorithm

As a familiar mark in applications of computer vision, checkerboard can be used in camera calibration and pose measurement of dimensional object. When the checkerboard corners have been detected, for further calibration and measurement, the next necessary step is to rank these corners. This paper presents an automatic sort order of checkerboard corners based on convex hull Algorithm. As a result, the image dots of corners can be automatically matched with its corresponding physical dots without any artificial manipulation. Experimental results show the method is maneuverable and efficient with high stability.

항공라이다 데이터의 건물 곡선경계 추출 및 모델링

항공라이다 데이터를 이용한 건물 추출 연구가 많이 진행되어 오고 있으나 대부분의 연구는 건물경계를 직선으로 가정하기 때문에 곡선경계가 포함된 건물의 경계를 올바르게 모델링하지 못하는 한계가 있다. 본 논문은 곡선경계를 포함하는 건물을 항공라이다 데이터로부터 직선과 곡선이 혼합된 경계로 모델링하는 것을 목적으로 한다. 건물점들에 대하여 적응적 컨벡스헐 알고리즘과 큰 반경의 국지적 컨벡스헐 알고리즘을 적용하여 두 세트의 경계점을 추출한다. 경계점들의 평균 점 간격 및 수직이등분선의 교차 비율에 의하여 곡선 세그먼트를 판별한 후, 직선과 곡선 세그먼트에 대하여 각각 다른 정규화 방법을 적용하여 건물경계를 모델링한다. 실험결과, 곡선 세그먼트의 추출 완전성과 정확성이 각각 69%, 100%로서 본 연구의 방법을 통해 대부분의 곡선경계를 올바르게 추출 및 모델링 할 수 있었다. 본 연구의 결과는 수치지도 제작기준을 만족하는 건물경계를 자동으로 생성하는데 효과적으로 활용될 수 있을 것이다. Although many studies have been conducted to extract buildings from airborne lidar data, most of them assume that all the boundaries of a building are straight line segments. This makes it difficult to model building boundaries containing curved segments correctly. This paper aims to model buildings containing curved segments as combination of straight lines and arcs. First, two sets of boundary points are extracted by adaptive convex hull algorithm and local convex hull algorithm with a larger radius. Then, arc segments are determined by average spacing of boundary points and intersection ratio of perpendicular lines. Finally, building boundary is modeled through regularization of least squares line or circle fitting. The experimental results showed that the proposed method can model the curved building boundaries as arc segments correctly by completeness of 69% and correctness of 100%. The approach will be utilized effectively to create automatically digital map that meets the conditions of the Korean digital mapping.

Application Research on Image Color Gamut Visualization Using Volume Rendering Method

Image-dependent color gamut mapping can avoid over compression of the image gamut, so it is able to protect the accuracy in color transfer. The premise of realizing image-dependent color gamut mapping is to determine the image color gamut boundary quickly. Now several techniques for the computation of gamut boundary have been presented in the past, e.g. the convex hull algorithm and the segment maxima algorithm. However, the printing image tend to have a higher resolution, it can be very slow and less efficient while using these methods to determine the image gamut boundary. In this article we will introduce a new pre-processing method based on volume rendering to process the image data to improve the speed of gamut visualization.

GOAL: A parsimonious geographic routing protocol for large scale sensor networks

Geographic routing is well suited for large scale sensor networks, because its per node state is independent of the network size. However, the local minimum caused by holes/obstacles results in the worst-case path stretch of Ω(c2), where c is the path length of the optimal route. Recently, a geographic routing protocol based on the visibility graph (VIGOR) showed that a path stretch of Θ(c) can be achieved. This path stretch, however, is achieved at the cost of communication and storage overhead, which makes the practical deployment of VIGOR in large scale sensor networks challenging. To this end, we propose GOAL (Geometric Routing using Abstracted Holes), a routing protocol that provably achieves a path stretch of Θ(c), with lower communication and storage overhead. To compactly describe holes, we develop a novel distributed convex hull algorithm, which improves the message complexity O(n log2n) of state of art distributed convex hull algorithm to O(n log n). The concise representation of a hole is used by nodes to make locally optimal routing decisions. Our theoretical analysis proves the correctness of the proposed algorithms and the path stretch of Θ(c). Through extensive simulations and experiments on a testbed with 42 EPIC motes, we demonstrate the effectiveness of GOAL and its feasibility for resource constrained wireless sensor networks; specifically, we show that GOAL eliminates part of communication overhead of VIGOR and reduces the memory overhead of VIGOR by up to 51%.