A GENETIC ALGORITHM-BASED APPROACH FOR DETECTION OF SIGNIFICANT VERTICES FOR POLYGONAL APPROXIMATION OF DIGITAL CURVES

2004 ◽  
Vol 04 (02) ◽  
pp. 223-239 ◽  
Author(s):  
BISWAJIT SARKAR ◽  
LOKENDRA KUMAR SINGH ◽  
DEBRANJAN SARKAR
Keyword(s):  
Genetic Algorithm ◽  
A Priori ◽  
Approximation Error ◽  
Compact Representation ◽  
Polygonal Approximation ◽  
Original Curve ◽  
Planar Curve ◽  
Digital Curve ◽  
Digital Planar Curve ◽  
Curve Form

A polygonal approximation captures the essential features of a digital planar curve and yields a compact representation. Those points of the digital curve that carry vital information about the shape of the curve form the vertices of the approximating polygon and are called significant vertices. In this paper, we present a genetic algorithm-based approach to locate a specified number of significant points, such that the approximation error between the original curve and its polygonal version obtained by joining the adjacent significant points is minimized. By using a priori knowledge about the shape of the curve we confine our search to only those points of the curve that have the potential of qualifying as significant points. We also incorporate chromosome differentiation to improve upon the effectiveness of the search in arriving at a near-optimal polygonal approximation. Finally, we show that the proposed method performs remarkably well when evaluated in terms of the metrics available for assessing the goodness of a polygonal approximation algorithm.

GENETIC ALGORITHMS FOR POLYGONAL APPROXIMATION OF DIGITAL CURVES

1999 ◽  
Vol 13 (07) ◽  
pp. 1061-1082 ◽  
Author(s):  
PENG-YENG YIN
Keyword(s):  
Genetic Algorithm ◽  
Genetic Algorithms ◽  
Learning Strategy ◽  
Approximation Error ◽  
Experimental Results ◽  
Polygonal Approximation ◽  
The Third ◽  
Digital Curve

In this paper, three polygonal approximation approaches using genetic algorithms are proposed. The first approach approximates the digital curve by minimizing the number of sides of the polygon and the approximation error should be less than a prespecified tolerance value. The second approach minimizes the approximation error by searching for a polygon with a given number of sides. The third approach, which is more practical, determines the approximating polygon automatically without any given condition. Moreover, a learning strategy for each of the proposed genetic algorithm is presented to improve the results. The experimental results show that the proposed approaches have better performances than those of existing methods.

POLYGONAL APPROXIMATION OF DIGITAL CURVE BASED ON REVERSE ENGINEERING CONCEPT

2013 ◽  
Vol 13 (04) ◽  
pp. 1350017 ◽  
Author(s):  
KUMAR S. RAY ◽  
BIMAL KUMAR RAY
Keyword(s):  
Reverse Engineering ◽  
Linear Time ◽  
Line Drawing ◽  
Approximation Error ◽  
Zero Approximation ◽  
Polygonal Approximation ◽  
Digital Curve ◽  
Symmetric Approximation ◽  
Engineering Concept ◽  
Automatic Algorithm

This paper applies reverse engineering on the Bresenham's line drawing algorithm [J. E. Bresenham, IBM System Journal, 4, 106–111 (1965)] for polygonal approximation of digital curve. The proposed method has a number of features, namely, it is sequential and runs in linear time, produces symmetric approximation from symmetric digital curve, is an automatic algorithm and the approximating polygon has the least non-zero approximation error as compared to other algorithms.

scholarly journals An Analysis on Polygonal Approximation Techniques for Digital Image Boundary

2021 ◽  
Author(s):  
Kiruba Thangam Raja ◽  
Bimal Kumar Ray
Keyword(s):  
Optimal Algorithm ◽  
Linear Time ◽  
Detection Threshold ◽  
Geographical Information ◽  
Polygonal Approximation ◽  
Main Category ◽  
Approximation Techniques ◽  
Planar Curve ◽  
Break Points ◽  
Digital Planar Curve

Polygonal approximation (PA) techniques have been widely applied in the field of pattern recognition, classification, shape analysis, identification, 3D reconstruction, medical imaging, digital cartography, and geographical information system. In this paper, we focus on some of the key techniques used in implementing the PA algorithms. The PA can be broadly divided into three main category, dominant point detection, threshold error method with minimum number of break points and break points approximation by error minimization. Of the above three methods, there has been always a tradeoff between the three classes and optimality, specifically the optimal algorithm works in a computation intensive way with a complexity ranges from O (N2) to O (N3).The heuristic methods approximate the curve in a speedy way, however they lack in the optimality but have linear time complexity. Here a comprehensive review on major PA techniques for digital planar curve approximation is presented.

A Technique to Approximate Digital Planar Curve with Polygon

2017 ◽  
pp. 150-169
Author(s):  
Mangayarkarasi Ramaiah ◽  
Bimal Kumar Ray
Keyword(s):  
State Of The Art ◽  
Experimental Results ◽  
Planar Curve ◽  
Digital Curve ◽  
Comparative Results ◽  
Digital Planar Curve

This chapter presents a technique which uses the sum of height square as a measure to define the deflection associated with a pseudo high curvature points on the digital planar curve. The proposed technique iteratively removes the pseudo high curvature points whose deflection is minimal, and recalculates the deflection associated with its neighbouring pseudo high curvature points. The experimental results of the proposed technique are compared with recent state of the art iterative point elimination methods. The comparative results show that the proposed technique produces the output polygon in a better way than others for most of the input digital curve.

Wave Energy Converter Array Optimization: A Review of Current Work and Preliminary Results of a Genetic Algorithm Approach Introducing Cost Factors

2015 ◽  
Author(s):  
Chris Sharp ◽  
Bryony DuPont
Keyword(s):  
Genetic Algorithm ◽  
Objective Function ◽  
Wave Energy ◽  
Reference Model ◽  
A Priori ◽  
System Optimization ◽  
Primary Energy ◽  
Close Relative ◽  
Cost Information ◽  
Multiple Test

Currently, ocean wave energy is a novel means of electricity generation that is projected to potentially serve as a primary energy source in coastal areas. However, for wave energy converters (WECs) to be applicable on a scale that allows for grid implementation, these devices will need to be placed in close relative proximity to each other. From what’s been learned in the wind industry of the U.S., the placement of these devices will require optimization considering both cost and power. However, current research regarding optimized WEC layouts only considers the power produced. This work explores the development of a genetic algorithm (GA) that will create optimized WEC layouts where the objective function considers both the economics involved in the array’s development as well as the power generated. The WEC optimization algorithm enables the user to either constrain the number of WECs to be included in the array, or allow the algorithm to define this number. To calculate the objective function, potential arrays are evaluated using cost information from Sandia National Labs Reference Model Project, and power development is calculated such that WEC interaction affects are considered. Results are presented for multiple test scenarios and are compared to previous literature, and the implications of a priori system optimization for offshore renewables are discussed.

scholarly journals An integral equation formulation of the N-body dielectric spheres problem. Part 1: Numerical analysis

2020 ◽  
Author(s):  
Muhammad Hassan ◽  
Benjamin Stamm
Keyword(s):  
Integral Equation ◽  
Numerical Analysis ◽  
Error Analysis ◽  
Convergence Rates ◽  
A Priori ◽  
Approximation Error ◽  
Spherical Particles ◽  
Integral Equation Formulation ◽  
Dielectric Spheres ◽  
The Stability

In this article, we analyse an integral equation of the second kind that represents the solution of N interacting dielectric spherical particles undergoing mutual polarisation. A traditional analysis can not quantify the scaling of the stability constants- and thus the approximation error- with respect to the number N of involved dielectric spheres. We develop a new a priori error analysis that demonstrates N-independent stability of the continuous and discrete formulations of the integral equation. Consequently, we obtain convergence rates that are independent of N.

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