On Constructing Approximate Convex Hull

Hossain, M. Z.; Amin, M. Ashraful

doi:10.4236/ajcm.2013.31a003

Cited by 10 publications

(5 citation statements)

References 15 publications

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“…While this principle is also shared by other approximated convex hull algorithms such as [14] and [17], we introduce a computation reduction technique for FPGA implementation as follows. A naive calculation of one inner product in Eq.…”

Section: Algorithmmentioning

confidence: 99%

“…Fortunately, convex hulls are often used to roughly grab abstract object shapes in applications such as collision detection and path planning, where computation of the exact convex hulls is not necessarily needed. For such application domains, approximate convex hull computing algorithms [14]- [17] are acceptable. In this paper, we propose an online approximate convex hull algorithm for unsorted point sets and present its FPGA implementation.…”

Section: Introductionmentioning

confidence: 99%

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A Hardware Oriented Approximate Convex Hull Algorithm and its FPGA Implementation

Mori

Manabe

Shibata

2022

IEICE Trans. Fundamentals

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The convex hull is the minimum convex surrounding a given set of points. Since the process of finding convex hulls has various practical application fields including embedded real-time systems, efficient acceleration of convex hull algorithms is an important problem in computer geometry. In this paper, we discuss an FPGA acceleration approach to address this problem. In order to compute the convex hull of an unsorted point set, it is necessary to store all the points during the computation, and thus the capacity of a on-chip memory is likely to be a major constraint for efficient FPGA implementation. On the other hand, approximate convex hulls are often sufficient for practical applications. Therefore, we propose a hardware oriented approximate convex hull algorithm, which can process the input points as a stream without storing all the points in the memory. We also propose some computation reduction techniques for efficient FPGA implementation. Then, we present FPGA implementation of the proposed algorithm, which is parallelized both in temporal and spatial domains, and evaluate its effectiveness in terms of performance and accuracy. As a result, we demonstrated 11 to 30 times faster performance compared to the widely-used convex hull software library Qhull. In addition, accuracy assessment revealed that the maximum approximation error normalized to the diameters of point sets was 0.038%, which was reasonably small for practical use cases.

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Section: Algorithmmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Hardware Oriented Approximate Convex Hull Algorithm and its FPGA Implementation

Mori

Manabe

Shibata

2022

IEICE Trans. Fundamentals

View full text Add to dashboard Cite

show abstract

“…Entangled states form a convex set in the spaces, and as shown in Figure 1, W states also form a convex set inside the set of GHZ states. Therefore, inspired by [24], we introduce the convex hull approximation [25] here. The construction of convex hull is one of the most fundamental problems in computational geometry.…”

Section: Convex Hull Approximationmentioning

confidence: 99%

A Convex Hull-Based Machine Learning Algorithm for Multipartite Entanglement Classification

Wang

2022

Applied Sciences

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Quantum entanglement becomes more complicated and capricious when more than two parties are involved. There have been methods for classifying some inequivalent multipartite entanglements, such as GHZ states and W states. In this paper, based on the fact that the set of all W states is convex, we approximate the convex hull by some critical points from the inside and propose a method of classification via the tangent hyperplane. To accelerate the calculation, we bring ensemble learning of machine learning into the algorithm, thus improving the accuracy of the classification.

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“…The paper [12] suggests numerous methods of convex hull approximate formation, which have linear complexity. Such algorithms are widely used for tasks where speed is a critical parameter.…”

Section: A Review Of Algorithms For Finding the Minimum Convex Hullsmentioning

confidence: 99%

Innovative GPU accelerated algorithm for fast minimum convex hulls computation

Potebnia¹,

Pogorilyy²

2015

Annals of Computer Science and Information Systems

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Abstract-Innovative algorithm for forming graph minimum convex hulls using the GPU is proposed. High speed and linear complexity of this method are achieved by distribution of the graph's vertices into separate units and their filtering. The key factor for improving the performance of innovative algorithm is the massively-parallel implementation of local hulls formation using video accelerators. A computational process is controlled by means of auxiliary matrices. A number of experimental studies of the algorithm have been carried out, and its suitability for application in the hull processing for large-scale problems has been demonstrated. The speed of the new method is 10 -20 times higher compared to using functions of the professional mathematical package Wolfram Mathematica.

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On Constructing Approximate Convex Hull

Abstract:
The algorithms of convex hull have been extensively studied in literature, principally because of their wide range of applications in different areas. This article presents an efficient algorithm to construct approximate convex hull from a set of n points in the plane in O Show more

Cited by 10 publications

References 15 publications

A Hardware Oriented Approximate Convex Hull Algorithm and its FPGA Implementation

A Hardware Oriented Approximate Convex Hull Algorithm and its FPGA Implementation

A Convex Hull-Based Machine Learning Algorithm for Multipartite Entanglement Classification

Innovative GPU accelerated algorithm for fast minimum convex hulls computation

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On Constructing Approximate Convex Hull

Abstract: The algorithms of convex hull have been extensively studied in literature, principally because of their wide range of applications in different areas. This article presents an efficient algorithm to construct approximate convex hull from a set of n points in the plane in O Show more

Cited by 10 publications

References 15 publications

A Hardware Oriented Approximate Convex Hull Algorithm and its FPGA Implementation

A Hardware Oriented Approximate Convex Hull Algorithm and its FPGA Implementation

A Convex Hull-Based Machine Learning Algorithm for Multipartite Entanglement Classification

Innovative GPU accelerated algorithm for fast minimum convex hulls computation

Contact Info

Product

Resources

About

Abstract:
The algorithms of convex hull have been extensively studied in literature, principally because of their wide range of applications in different areas. This article presents an efficient algorithm to construct approximate convex hull from a set of n points in the plane in O Show more