An Analysis on Polygonal Approximation Techniques for Digital Image Boundary

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

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.

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

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.