scholarly journals Polygonal Approximation of Digital Planar Curve Using Novel Significant Measure

2020 ◽  
Author(s):  
Mangayarkarasi Ramaiah ◽  
Dilip Kumar Prasad
Keyword(s):  
Polygonal Approximation ◽  
Planar Curve ◽  
Significant Measure ◽  
Digital Planar Curve

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.

Polygonal approximation of digital planar curve using local integral deviation

2015 ◽  
Vol 5 (3) ◽  
pp. 302 ◽  
Author(s):  
Mangayarkarasi Ramaiah ◽  
Bimal Kumar Ray
Keyword(s):  
Polygonal Approximation ◽  
Local Integral ◽  
Planar Curve ◽  
Digital Planar Curve

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.

Modelling stochastic changes in curve shape, with an application to cancer diagnostics

2000 ◽  
Vol 32 (02) ◽  
pp. 344-362 ◽  
Author(s):  
Asger Hobolth ◽  
Eva B. Vedel Jensen
Keyword(s):  
Markov Property ◽  
Malignant Tumour ◽  
Cancer Diagnostics ◽  
Second Order ◽  
Polygonal Approximation ◽  
Cell Nuclei ◽  
Planar Curve ◽  
Continuous Approach ◽  
Two Samples ◽  
Limiting Behaviour

Often, the statistical analysis of the shape of a random planar curve is based on a model for a polygonal approximation to the curve. In the present paper, we instead describe the curve as a continuous stochastic deformation of a template curve. The advantage of this continuous approach is that the parameters in the model do not relate to a particular polygonal approximation. A somewhat similar approach has been used in Kent et. al. (1996), who describe the limiting behaviour of a model with a first-order Markov property as the landmarks on the curve become closely spaced; see also Grenander (1993). The model studied in the present paper is an extension of this model. Our model possesses a second-order Markov property. Its geometrical characteristics are studied in some detail and an explicit expression for the covariance function is derived. The model is applied to the boundaries of profiles of cell nuclei from a benign tumour and a malignant tumour. It turns out that the model with the second-order Markov property is the most appropriate, and that it is indeed possible to distinguish between the two samples.

Modelling stochastic changes in curve shape, with an application to cancer diagnostics

2000 ◽  
Vol 32 (2) ◽  
pp. 344-362 ◽  
Author(s):  
Asger Hobolth ◽  
Eva B. Vedel Jensen
Keyword(s):  
Markov Property ◽  
Malignant Tumour ◽  
Cancer Diagnostics ◽  
Second Order ◽  
Polygonal Approximation ◽  
Cell Nuclei ◽  
Planar Curve ◽  
Continuous Approach ◽  
Two Samples ◽  
Limiting Behaviour

Often, the statistical analysis of the shape of a random planar curve is based on a model for a polygonal approximation to the curve. In the present paper, we instead describe the curve as a continuous stochastic deformation of a template curve. The advantage of this continuous approach is that the parameters in the model do not relate to a particular polygonal approximation. A somewhat similar approach has been used in Kent et. al. (1996), who describe the limiting behaviour of a model with a first-order Markov property as the landmarks on the curve become closely spaced; see also Grenander (1993). The model studied in the present paper is an extension of this model. Our model possesses a second-order Markov property. Its geometrical characteristics are studied in some detail and an explicit expression for the covariance function is derived. The model is applied to the boundaries of profiles of cell nuclei from a benign tumour and a malignant tumour. It turns out that the model with the second-order Markov property is the most appropriate, and that it is indeed possible to distinguish between the two samples.

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.

scholarly journals ON THE PRECISION OF CURVE LENGTH ESTIMATION IN THE PLANE

2016 ◽  
Vol 35 (1) ◽  
pp. 1 ◽  
Author(s):  
Ana Isabel Gomez ◽  
Marcos Cruz ◽  
Luis Manuel Cruz-Orive
Keyword(s):  
Error Variance ◽  
Polygonal Approximation ◽  
Prediction Formula ◽  
Line Segments ◽  
Square Grid ◽  
Dna Molecule ◽  
Length Estimation ◽  
Curve Length ◽  
Planar Curve ◽  
Straight Line

The estimator of planar curve length based on intersection counting with a square grid, called the Buffon-Steinhaus estimator, is simple, design unbiased and efficient. However, the prediction of its error variance from a single grid superimposition is a non trivial problem. A previously published predictor is checked here by means of repeated Monte Carlo superimpositions of a curve onto a square grid, with isotropic uniform randomness relative to each other. Nine curvilinear features (namely flattened DNA molecule projections) were considered, and complete data are shown for two of them. Automatization required image processing to transform the original tiff image of each curve into a polygonal approximation consisting of between 180 and 416 straight line segments or ‘links’ for the different curves. The performance of the variance prediction formula proved to be satisfactory for practical use (at least for the curves studied).

An Improved Sequential Polygonal Approximation Algorithm on Skeleton Curves

2009 ◽  
Vol 34 (12) ◽  
pp. 1467-1474
Author(s):  
Zhe LV ◽  
Fu-Li WANG ◽  
Yu-Qing CHANG ◽  
Yang LIU
Keyword(s):  
Approximation Algorithm ◽  
Polygonal Approximation
Sign in / Sign up

Export Citation Format

Share Document